A Study of Non-Newtonian Viscosity and Yield Stress of Blood. in a Scanning Capillary-Tube Rheometer. A Thesis. Submitted to the Faculty

Transcription

1 A Sud of No-Newoia Visosi ad Yield Sess of Blood i a Saig Capilla-Tube Rheomee A Thesis Submied o he Faul of Dexel Uivesi b Sagho Kim i paial fulfillme of he equiemes fo he degee of Doo of Philosoph Deembe 00

2 ii Akowledgmes I wish o expess m siee gaiude o D. Youg I. Cho, fo his guidae ad ispiaio duig m eie eue i gaduae shool. His expeiee ad idea have pove o be ivaluable. I also wish o hak D. David M. Wooo fo sevig as m o-adviso, ad fo his valuable suggesios ad guidae o Biofluid Damis. I wish o expess m appeiaio o he membes of m disseaio ommiee, iludig: D. Ke Choi ad D. Ala Lau fom he MEM Depame, ad D. Pee Lelkes fom he Shool of Biomedial Egieeig. I am deepl idebed o D. Keeh Kese, M. William Hogeaue, ad D. La Goldsei fom Rheologis, I. fo povidig valuable ommes o he es mehods ad daa eduio poedue. A siee appeiaio is exeded o seveal olleagues whose fiedship I have heished duig m gaduae sudies, iludig: D.Woae Kim, D. Sughuk Lee, Chagbeom Kim, Gioug Tak, Dohug Lim, ad Jiog Wee. Las bu o leas, I wish o hak m paes fo hei ubouded suppo houghou m life. Thei eliable povisio of emoioal, spiiual, ad fiaial suppo has allowed me o aomplish asks ha would have ohewise bee impossible.

3 iii Table of Coes LIST OF TABLES...viii LIST OF FIGURES... x ABSTRACT...xiv CHAPTER INTRODUCTION.... Cliial Sigifiae of Blood Visosi.... Moivaio of he Pese Sud Objeives of he Pese Sud Oulie of he Disseaio... 4 CHAPTER CONSTITUTIVE MODELS Newoia Fluid No-Newoia Fluid Geeal No-Newoia Fluid Powe-law Model Coss Model..... Visoplasi Fluid Bigham Plasi Model Casso Model Heshel-Bulkle Model Rheolog of Blood Deemiaio of Blood Visosi... 9

4 iv.3.. Plasma Visosi Hemaoi RBC Defomabili RBC Aggegaio - Majo Fao of Shea-Thiig Chaaeisis Tempeaue Yield Sess ad Thixopop Yield Sess Thixoop - Time Depedee... 4 CHAPTER 3 CONVENTIONAL RHEOMETRY: STATE-OF-THE-ART Ioduio Roaioal Visomee Roaioal Coaxial-Clide Couee Tpe Coe-ad-Plae Capilla-Tube Visomee Yield Sess Measueme Idie Mehod Die Daa Exapolaio Exapolaio Usig Cosiuive Models Die Mehod Poblems wih Coveioal Visomees fo Cliial Appliaios Poblems wih Roaioal Visomees Poblems wih Capilla-Tube Visomees... 48

5 v CHAPTER 4 THEORY OF SCANNING CAPILLARY-TUBE RHEOMETER Saig Capilla-Tube Rheomee SCTR U-Shaped Tube Se Eeg Balae Mahemaial Poedue fo Daa Reduio Powe-law Model Casso Model Heshel-Bulkle H-B Model... 7 CHAPTER 5 CONSIDERATIONS FOR EXPERIMENTAL STUDY Usead Effe Ed Effe Wall Effe Fahaeus-Lidqvis Effe Ohe Effes Pessue Dop a Rise Tube Effe of Desi Vaiaio Aggegaio Rae of RBCs - Thixoop Tempeaue Cosideaios fo Visosi Measueme of Huma Blood Effe of De Coeaio o Visosi of Wae Ioduio Expeimeal Mehod Resuls ad Disussio...07 CHAPTER 6 EXPERIMENTAL STUDY WITH SCTR Expeimes wih SCTR wih Peisio Glass Rise Tubes...

6 vi 6.. Desipio of Isume Tesig Poedue Daa Reduio wih Powe-law Model Resuls ad Disussio Expeimes wih SCTR wih Plasi Rise Tubes Desipio of Isume Tesig Poedue Daa Reduio wih Casso Moel Cuve Fiig Resuls ad Disussio Daa Reduio wih Heshel-Bulkle H-B Model Compaiso of No-Newoia Cosiuive Models Compaiso of Visosi Resuls Compaiso of Yield Sess Resuls Effes of Yield Sess o Flow Paes...64 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS...80 LIST OF REFERENCES...84 APPENDIX A: NOMENCLATURE...94 APPENDIX B: FALLING OBJECT VISCOMETER - LITERATURE REVIEW...97 APPENDIX C: SPECIFICATION OF CCD AND LED ARRAY...00 APPENDIX D: BIOCOATING OF CAPILLARY TUBE...0 APPENDIX E: MICROSOFT EXCEL SOLVER...04 APPENDIX F: NEWTON S METHOD OF ITERATION...06

7 vii APPENDIX G: REPEATABILITY STUDY WITH DISTILLED WATER...08 APPENDIX H: EXPERIMENTAL DATA...0 VITA...

8 viii Lis of Tables -. Visosi of some familia maeials a oom empeaue Rage of shea aes of some familia maeials ad poesses Compaiso of Pusead ad P fo disilled wae Compaiso of Pusead ad P fo bovie blood Desi esimaio Compaiso of iiial guess ad esulig value usig powe-law model Compaiso of iiial guess ad esulig value usig Casso model Compaiso of iiial guess ad esulig value usig Heshel-Bulkle model Compaiso of fou ukows deemied wih Heshel-Bulkle model fo hee oseuive ess Vaious phsiologial sudies wih o-newoia osiuive models Measuemes of wae visosi Measuemes of bovie blood visosi Measuemes of huma blood visosi Compaiso of model osas, h ad τ Compaiso of h = ad hs + h...76 H-. A pial expeimeal daa se of huma blood obaied b a saig apilla-ube heomee wih peisio glass ise ubes...0 H-. A pial expeimeal daa se of disilled wae obaied b a saig apilla-ube heomee wih plasi ise ubes...3 H-3. A pial expeimeal daa se of bovie blood obaied b a saig apilla-ube heomee wih plasi ise ubes...5

9 H-4. A pial expeimeal daa se of huma blood obaied b a saig apilla-ube heomee wih plasi ise ubes...8 ix

10 x Lis of Figues -. Flow uve of a Newoia fluid Flow uve of powe-law fluids Flow uve of a Casso model Flow uve of visoplasi fluids Compaiso of Newoia plasma visosi ad shea-hiig whole blood visosi Vaiaio of he elaive visosi of blood ad suspesio wih igid sphees a a shea ae > 00 s Rouleaux fomaio of huma ed blood ells phoogaphed o a miosope slide showig sigle liea ad bahed aggegaes ad a ewok Elevaed blood visosi a low shea aes idiaes RBC aggegaio Rheomees Shemai diagam of a oei lide visomee Shemai diagam of a o-ad-plae visomee Shemai diagam of a apilla-ube visomee Deemiaio of ield sess b exapolaio Shemai diagam of a U-shaped ube se Fluid-level vaiaio i a U-shaped ube se duig a es Tpial fluid-level vaiaio measued b a SCTR Liquid-solid iefae odiio fo eah fluid olum of a U-shaped ube se Fluid eleme i a apilla ube a ime Veloi pofile of plug flow of blood i a apilla ube... 80

11 xi 5-. Pessue dop esimaio fo disilled wae Pessue dop esimaio fo bovie blood Flow-pae hages due o ed effes Migaio of ells owad o he ee of lume wall effe Fahaeus-Lidquis effe due o he eduio i hemaoi i a ube wih a small diamee ad he ede of ehoes o migae owad he ee of he ube Visosi measuemes fo bovie blood wih hee diffee apilla ubes wih ID of mm wih legh = 00 mm,.0 mm wih legh = 30 mm, ad. mm wih legh = 56 mm Visosi esuls fo huma blood wih wo diffee apilla ubes wih legh of 00 mm wih ID = mm ad 5 mm ID = mm Shemai diagam of a U-shaped ube se fo empeaue measueme Tempeaue measueme a a apilla ube duig a visosi es Shemai diagam of a saig apilla-ube heomee SCTR ssem Vaiaios of boh powe-law idex ad osise idex of de-wae soluio due o effes of de oeaios Visosi daa fo de-wae soluio wih 6 diffee de oeaios a Shemai diagam of a saig apilla-ube heomee wih peisio glass ise ubes Cuve-fiig poedue wih powe-law model fo mieal oil Cuve-fiig poedue wih powe-law model fo huma blood Heigh vaiaio i eah ise ube vs. ime fo mieal oil Visosi measueme fo mieal oil a 5 wih a saig apilla-ube heomee SCTR Heigh vaiaio i eah ise ube vs. ime fo huma blood a

12 xii 6-7. Visosi measueme log-log sale fo huma blood a 37 wih oaig visomee RV ad saig apilla-ube heomee SCTR Visosi measueme log-log sale of uaduleaed huma blood a 37, measued wih saig apilla-ube heomee SCTR ad oe-ad-plae oaig visomee RV, fo wo diffee doos Piue of a SCTR wih plasi ise ubes Heaig pad fo a es wih uaduleaed huma blood Cuve-fiig poedue wih Casso model fo disilled wae Cuve-fiig poedue wih Casso model fo doo Cuve-fiig poedue wih Casso model fo doo Heigh vaiaio i eah ise ube vs. ime fo disilled wae a Visosi measueme fo disilled wae a Heigh vaiaio i eah ise ube vs. ime fo bovie blood wih 7.5% EDTA a Visosi measueme fo bovie blood wih 7.5% EDTA a 5 usig boh oaig visomee RV ad saig apilla-ube Rheomee SCTR Heigh vaiaio i eah ise ube vs. ime fo huma blood a Visosi measueme fo huma blood diffee doos a Shea-sess vaiaio vs. shea ae fo huma blood fom diffee doos a Cuve-fiig poedue wih Heshel-Bulkle model fo bovie blood Visosi measuemes of bovie blood wih 7.5% EDTA a 5, aalzed wih Heshel-Bulkle model Tes wih disilled wae a Tes wih bovie blood a

13 xiii 6-5. Tes wih uaduleaed huma blood a Wall shea sess a a apilla ube vs. shea ae Vaiaios of a plug-flow egio a a apilla ube as a fuio of ime fo bovie blood wih 7.5% EDTA a Veloi pofiles a a apilla ube fo bovie blood wih 7.5% EDTA a a Visosi, b wall shea ae, ad wall shea sess Ploed as a fuio of mea veloi a a apilla ube usig hee o-newoia models fo bovie blood wih 7.5% EDTA...79 B-. Fallig lide visomees...99 C-. Coss seioal view of SV35A8-0 module...0 G-. Repeaabili sud #...08 G-. Repeaabili sud #...09

14 xiv Absa A Sud of No-Newoia Visosi ad Yield Sess of Blood i a Saig Capilla-Tube Rheomee Sagho Kim Pofessos Youg I. Cho ad David M. Wooo The sud of hemoheolog has bee of gea iees i he fields of biomedial egieeig ad medial eseahes fo ma eas. Alhough a umbe of eseahes have ivesigaed oelaios bewee whole blood visosi ad aeial diseases, soke, hpeesio, diabees, smokig, agig, ad gede, he medial ommui has bee slow i ealizig he sigifiae of he whole blood visosi, whih a be pal aibued o he lak of a uompliaed ad liiall paial heomee. The objeives of he pese sud wee o ivesigae he heoeial piiples of a saig apilla-ube heomee used fo measuig boh he visosi ad ield sess of blood wihou a aioagula, o expeimeall validae he saig apilla-ube heomee usig disposable ube ses desiged fo dail liial use i measuig whole blood visosi, ad o ivesigae he effe of o-newoia osiuive models o he blood heolog ad flow paes i he saig apilla-ube heomee. The pese sud iodued deailed mahemaial poedues fo daa eduio i he saig apilla-ube heomee fo boh visosi ad ield-sess measuemes of whole blood. Powe-law, Casso, ad Heshel-Bulkle models wee examied as he osiuive models fo blood i he sud. Boh Casso ad Heshel-Bulkle models gave blood visosi esuls whih wee i good ageeme

15 xv wih eah ohe as well as wih he esuls obaied b a oveioal oaig visomee, wheeas he powe-law model seemed o podue iauae visosiies a low shea aes. The ield sess values obaied fom he Casso ad Heshel-Bulkle models fo uaduleaed huma blood wee measued o be 3.8 ad 7.5 mpa, espeivel. The wo models showed some disepaies i he ield-sess values. I he sud, he wall shea sess was foud o be almos idepede of he osiuive model, wheeas he size of he plug flow egio i he apilla ube vaies subsaiall wih he seleed model, aleig he values of he wall shea ae a a give mea veloi. The model osas ad he mehod of he shea sess alulaio give i he sud a be useful i he diagosis ad eame of adiovasula diseases.

16 CHAPTER. INTRODUCTION.. Cliial Sigifiae of Blood Visosi The sud of hemoheolog has bee of gea iees i he fields of biomedial egieeig ad medial eseah fo ma eas. Hemoheolog plas a impoa ole i aheosleosis [Cavei e al., 987; Resh e al., 99; Lee e al., 998; Kese ad Cho, 00]. Hemoheologial popeies of blood ilude whole blood visosi, plasma visosi, hemaoi, RBC defomabili ad aggegaio, ad fibioge oeaio i plasma. Alhough a umbe of paamees suh as pessue, lume diamee, whole blood visosi, ompliae of vessels, peipheal vasula esisae ae well-kow phsiologial paamees ha affe he blood flow, he whole blood visosi is also a impoa ke phsiologial paamee. Howeve, is sigifiae has o bee full appeiaed e. A umbe of eseahes measued blood visosiies i paies wih ooa aeial disease suh as ishemi hea disease ad moadial ifaio [Ja e al., 975; Lowe e al., 980; Mos e al., 986; Es e al., 988; Roseso, 993]. The foud ha he visosi of whole blood migh be assoiaed wih ooa aeial diseases. I addiio, a goup of eseahes epoed ha whole blood visosi was sigifial highe i paies wih peipheal aeial disease ha ha i healh ools [Ciuffei e al., 989; Lowe e al., 993; Fowkes e al., 994].

17 Ohe eseahes ivesigaed oelaio bewee he hemoheologial paamees ad soke [Goa e al., 985; Coull e al., 99; Fishe ad Meiselma, 99; Bile e al., 994]. The epoed ha soke paies showed wo o moe elevaed heologial paamees, whih iluded whole blood visosi, plasma visosi, ed blood ell RBC ad plae aggegaio, RBC igidi, ad hemaoi. I was also epoed ha boh whole blood visosi ad plasma visosi wee sigifial highe i paies wih esseial hpeesio ha i healh people [Lehe e al., 98, 983; Pesso e al., 99; Shap e al., 996; Tsuda e al., 997; Toh e al., 999]. I diabeis, whole blood visosi, plasma visosi, ad hemaoi wee elevaed, wheeas RBC defomabili was deeased [Hoae e al., 976; Diefass, 977; Hill e al., 98; Poo e al., 98; Leipe e al., 98]. Ohes odued hemoheologial sudies o deemie he elaioships bewee whole blood visosi ad smokig, age, ad gede [Leveso e al., 987; Bowdle ad Fose, 987; Fowkes e al., 994; Es, 995; Ajmai ad Rifkid, 998; Kameeva e al., 998; Yaell e al., 000]. The foud ha smokig ad agig migh ause he elevaed blood visosi. I addiio, i was epoed ha male blood possessed highe blood visosi, RBC aggegabili, ad RBC igidi ha pemeopausal female blood, whih ma be aibued o mohl blood-loss [Kameeva e al., 998].

18 3.. Moivaio of he Pese Sud The medial ommui has bee slow i ealizig he sigifiae of whole blood visosi, whih a be aibued pal o he lak of a uompliaed ad liiall paial mehod of measuig whole blood visosi. I mos liial sudies, mail wo pes of visomee have bee available fo geeal use: oaioal visomees ad apilla ube visomee, as will be disussed i Chape 3. These visomees ae used a laboao ol, ad ae o used i a liial eviome. Uil eel, he mos immediae diffiul has bee he lak of a isume ha is speiall desiged fo dail liial use i measuig whole blood visosi..3. Objeives of he Pese Sud The objeives of he pese sud wee o ivesigae he heoeial piiples of a saig apilla-ube heomee SCTR, whih is apable of measuig he visosi ad ield sess of blood wihou addig a aioagula, o validae he SCTR usig disposable ube ses fo liial appliaios, ad 3 o ivesigae he effe of o-newoia osiuive models o he blood heolog ad flow paes i he SCTR. The pese sud iodued deailed mahemaial poedues fo daa eduio i he SCTR fo boh visosi ad ield-sess measuemes of blood. I

19 4 expeimeal sudies, disilled wae Newoia fluid, bovie blood o-newoia fluid wih 7.5% EDTA, ad uaduleaed huma blood o-newoia fluid wee used fo he measuemes of boh visosi ad ield sess. Powe-law, Casso, ad Heshel-Bulkle models wee examied as osiuive models fo blood i he sud..4. Oulie of he Disseaio Chape eviews he osiuive models appliable fo o-newoia haaeisis iludig shea-hiig ad ield sess. Chape 3 eviews he oveioal heomees ha measue eihe he visosi o ield sess of a fluid. I his hape, ol heomees ha a be appliable o liial appliaios ae disussed. Chape 4 iodues he heo of a saig apilla-ube heomee. Chape 5 disusses he osideaios fo he expeimeal sud, whih ilude usead effe, ed effe, wall effe, empeaue aalsis, de oeaio effe, ad ohe possible faos. Chape 6 peses he esuls of expeimeal sudies pefomed wih a saig apilla-ube heomee. Chape 6 also epos he effe of o-newoia osiuive models o he heologial measuemes ad flow paes of blood i a apilla ube. Chape 7 gives olusios of he sud ad eommedaios fo fuue sud.

20 5 CHAPTER. CONSTITUTIVE MODELS This hape eviews lieaue o o-newoia osiuive models, whih ae appliable o he sud of blood heolog. Visous liquids iludig whole blood a be divided i ems of heologial popeies io Newoia, geeal o- Newoia, ad visoplasi fluids. The haaeisis of blood, whih ilude shea-hiig, ield sess, ad hixoop, ae disussed i his hape... Newoia Fluid Fluid suh as wae, ai, ehaol, ad bezee ae Newoia. This meas ha whe shea sess is ploed agais shea ae a a give empeaue, he plo shows a saigh lie wih a osa slope ha is idepede of shea ae see Fig. -. This slope is alled he visosi of he fluid. All gases ae Newoia, ad ommo liquids suh as wae ad glei ae also Newoia. Also, low moleula weigh liquids ad soluios of low moleula weigh subsaes i liquids ae usuall Newoia. Some examples ae aqueous soluios of suga o sal. The simples osiuive equaio is Newo s law of visosi [Middlema, 968; Bid e al., 987; Muso e al., 998]: τ = µγ& - whee µ is he Newoia visosi ad γ& is he shea ae o he ae of sai.

21 6 The Newoia fluid is he basis fo lassial fluid mehais. Gases ad liquids like wae ad mieal oils exhibi haaeisis of Newoia visosi. Howeve, ma impoa fluids, suh as blood, polmes, pai, ad foods, show o-newoia visosi. Table - shows he wide visosi age fo ommo maeials. Diffee isumes ae equied o measue he visosi ove his wide age. Oe eipoise, P = 0-3 Pa s o mpa s, is appoximael he visosi of wae a oom empeaue. Shea aes oespodig o ma idusial poesses a also va ove a wide age, as idiaed i Table -.

22 7 a 00 Shea sess Shea ae b 0 Visosi Shea ae Fig. -. Flow uves of a Newoia fluid. a Shea sess vs. Shea ae. b Visosi vs. Shea ae.

23 8 Table -. Visosi of some familia maeials a oom empeaue [Baes e al., 989]. Liquid Appoximae Visosi Pa s Glass 0 40 Asphal 0 8 Mole polmes 0 3 Heav sup 0 Hoe 0 Glei 0 0 Olive oil 0 - Ligh oil 0 - Wae 0-3 Ai 0-5

24 9 Table -. Rage of shea aes of some familia maeials ad poesses [Baes e al., 989]. Poess Rage of Shea Raes s - Appliaio Sedimeaio of fie powdes i a suspedig liquid Mediies, pais Levelig due o sufae esio Pais, piig iks Daiig ude gavi 0-0 Paiig, oaig Sew exudes Polme mels, dough Chewig ad swallowig 0 0 Foods Dip oaig 0 0 Pais, ofeioe Mixig ad siig Maufauig liquids Pipe flow Pumpig, blood flow Spaig ad bushig Fuel aomizaio, paiig Rubbig Appliaio of eams ad loios o he ski Ijeio mold gae Polme mels Millig pigmes i fluid bases Pais, piig iks Blade oaig Pape Lubiaio Gasolie egies

25 0.. No-Newoia Fluid A fluids ha do o obe he Newoia elaioship bewee shea sess ad shea ae ae o-newoia. The subje of heolog is devoed o he sud of he behavio of suh fluids. Aqueous soluios of high moleula weigh polmes o polme mels, ad suspesios of fie pailes ae usuall o-newoia.... Geeal No-Newoia Fluid I he ase of geeal o-newoia fluids, he slope of shea sess vesus shea ae uve is o osa. Whe he visosi of a fluid deeases wih ieasig shea ae, he fluid is alled shea-hiig. I he opposie ase whee he visosi ieases as he fluid is subjeed o a high shea ae, he fluid is alled shea-hikeig. The shea-hiig behavio is moe ommo ha he sheahikeig. I geeal, he Newoia osiuive equaio auael desibes he heologial behavio of low moleula weigh polme soluios ad eve high moleula weigh polme soluios a ve slow aes of defomaio. Howeve, visosi a be a sog fuio of he shea ae fo polmei liquids, emulsios, ad oeaed suspesios.

26 ... Powe-law Model Oe of he mos widel used foms of he geeal o-newoia osiuive elaio is a powe-law model, whih a be desibed as [Middlema, 968; Bid e al., 987; Muso e al., 998]: τ mγ& = - whee m ad ae powe-law model osas. The osa, m, is a measue of he osise of he fluid: he highe he m is, he moe visous he fluid is. is a measue of he degee of o-newoia behavio: he geae he depaue fom he ui, he moe pooued he o-newoia popeies of he fluid ae. The visosi fo he powe-law fluid a be expessed as [Middlema, 968; Bid e al., 987; Muso e al., 998]: η = mγ& -3 whee η is o-newoia appae visosi. I is well kow ha he powe-law model does o have he apabili o hadle he ield sess. If <, a sheahiig fluid is obaied, whih is haaeized b a pogessivel deeasig appae visosi wih ieasig shea ae. If >, we have a shea-hikeig fluid i whih he appae visosi ieases pogessivel wih ieasig shea ae. Whe =, a Newoia fluid is obaied. These hee pes of powe-law models ae illusaed i Fig. -. Oe of he obvious disadvaages of he powe-law model is ha i fails o desibe he visosi of ma o-newoia fluids i ve low ad ve high shea ae egios. Sie is usuall less ha oe, η goes o ifii a a ve low shea

27 ae see Fig. - ahe ha o a osa, η 0, as is ofe obseved expeimeall. Visosi fo ma suspesios ad dilue polme soluios beomes osa a a ve high shea ae, a pheomeo ha ao be desibed b he powe-law model.... Coss Model As disussed i he pevious seio, he powe-law model does o have he apabili of hadlig Newoia egios of shea-hiig fluids a ve low ad high shea aes. I ode o oveome his dawbak of he powe-law model, Coss 965 poposed a model ha a be desibed as [Feguso ad Kemblowski, 99; Cho ad Kese, 99; Maosko, 994]: τ = & γ η whee η0 η + + mγ& -4 η 0 ad η = visosiies a ve low ad high shea aes, espeivel m ad = model osas. A a iemediae shea ae, he Coss model behaves like a powe-law model as show i Fig. -3. Howeve, ulike he powe-law model, he Coss model podues Newoia visosiies η 0 ad η a boh ve low ad high shea aes.

28 3... Visoplasi Fluid The ohe impoa lass of o-newoia fluids is a visoplasi fluid. This is a fluid whih will o flow whe a ve small shea sess is applied. The shea sess mus exeed a iial value kow as he ield sess fo he fluid o flow. Fo example, whe opeig a ube of oohpase, we eed o appl a adequae foe i ode o make he oohpase sa o flow. Theefoe, visoplasi fluids behave like solids whe he applied shea sess is less ha he ield sess. Oe he applied shea sess exeeds he ield sess, he visoplasi fluid flows jus like a omal fluid. Examples of visoplasi fluids ae blood, dillig mud, maoaise, oohpase, gease, some lubias, ad ulea fuel sluies.... Bigham Plasi Model Ma pes of food suffs exhibi a ield sess ad ae said o show a plasi o visoplasi behavio. Oe of he simples visoplasi models is he Bigham plasi model, ad i a be expessed as follows [Bid e al., 987; Feguso ad Kemblowski, 99; Maosko, 994]: = m & B γ τ whe τ τ + τ, -5 γ& = 0 whe τ τ, -6 whee τ = a osa ha is iepeed as ield sess

29 4 m B = a model osa ha is iepeed as plasi visosi. Basiall, he Bigham plasi model a desibe he visosi haaeisis of a fluid wih ield sess whose visosi is idepede of shea ae as show i Fig Theefoe, he Bigham plasi model does o have he abili o hadle he shea-hiig haaeisis of o-newoia fluids.... Casso Model This model was oigiall iodued b Casso 959 fo he pediio of he flow behavio of pigme-oil suspesios. The Casso model is based o a suue model of he ieaive behavio of solid ad liquid phases of a wo-phase suspesio [Casso, 959]. The model desibes he flow of visoplasi fluids ha a be mahemaiall desibed as follows [Bid e al., 987; Feguso ad Kemblowski, 99; Cho ad Kese, 99; Maosko, 994]: τ = τ + k & γ whe τ τ, -7 γ& = 0 whe τ τ, -8 whee k is a Casso model osa. The Casso model shows boh ield sess ad shea-hiig o-newoia visosi. Fo maeials suh as blood ad food podus, i povides bee fi ha he Bigham plasi model [Fug 990; Cho ad Kese, 99; Ngue ad Boge, 99; Fug, 993].

30 Heshel-Bulkle Model The Heshel-Bulkle model exeds he simple powe-law model o ilude a ield sess as follows [Heshel ad Bulkle, 96; Tae, 985; Feguso ad Kemblowski, 99; Holdswoh, 993]: τ + = m & γ τ whe τ τ, -9 γ& = 0 whe τ τ, -0 whee m ad ae model osas. Like he Casso model, i shows boh ield sess ad shea-hiig o- Newoia visosi, ad is used o desibe he heologial behavio of food podus ad biologial liquids [Feguso ad Kemblowski, 99; Holdswoh, 993]. I addiio, he Heshel-Bulkle model also gives bee fi fo ma biologial fluids ad food podus ha boh powe-law ad Bigham plasi models.

31 6 00 a b Shea sess Visosi 5 b Shea ae a Fig. -. Flow uves of powe-law fluids. a shea-hiig fluid <. b Newoia fluid =. shea-hikeig fluid >.

32 7 Newoia egios η 0 Visosi log Powe-law egio η Shea ae log Fig. -3. Flow uve of a Coss model.

33 8 00 a b Shea sess 50 m B τ Shea ae Fig. -4. Flow uves of visoplasi fluids. a Casso o Heshel-Bulkle fluid. b Bigham plasi fluid.

34 9.3. Rheolog of Blood Blood behaves like a o-newoia fluid whose visosi vaies wih shea ae. The o-newoia haaeisis of blood ome fom he pesee of vaious ells i he blood piall makig up 45% of he blood s volume, whih make blood a suspesio of pailes [Fug, 993; Guo ad Hall, 996]. Whe he blood begis o move, hese pailes o ells iea wih plasma ad amog hemselves. Hemoheologi paamees of blood ilude whole blood visosi, plasma visosi, ed ell aggegaio, ad ed ell defomabili o igidi..3.. Deemias of Blood Visosi Muh eseah has bee pefomed o fomulae a heo ha aous ompleel fo he visous popeies of blood, ad some of he ke deemias have bee ideified [Dia, 98; Chie e al., 987; Guo ad Hall, 996]. The fou mai deemias of whole blood visosi ae plasma visosi, hemaoi, 3 RBC defomabili ad aggegaio, ad 4 empeaue. The fis hee faos ae paamees of phsiologi oe beause he peai o hages i whole blood visosi i he bod. Espeiall, he seod ad hid faos, hemaoi ad RBC aggegaios, mail oibue o he o-newoia haaeisis of shea-hiig visosi ad ield sess.

35 Plasma Visosi Plasma is blood fom whih all ellula elemes have bee emoved. I has bee well esablished ha plasma behaves like a Newoia fluid. Caeful ess odued usig boh oaig ad apilla ube visomees ove a age of shea aes i.e., fom 0. o 00 s - foud o sigifia depaues fom lieai. Theefoe, is visosi is idepede of shea ae. Figue -5 illusaes his leal i he hoizoal visosi lie fo plasma [Diefass, 97; Dia, 98]. Sie blood is a suspesio of ells i plasma, he plasma visosi affes whole blood visosi, paiulal a high shea aes Hemaoi Hemaoi is he volume peeage of ed blood ells i whole blood. Sie sudies have show omal plasma o be a Newoia fluid [Fug, 993], he o- Newoia feaues of huma blood udoubedl ome fom suspeded ells i blood. The heologial popeies of suspesios oelae highl wih he oeaios of suspeded pailes. I blood, he mos impoa suspeded pailes ae he ed blood ells RBC. Hemaoi is he mos impoa deemia of whole blood visosi [Beis e al., 970; Thuso, 978; Fug, 993; Pia e al., 998; Cia e al., 999]. The effe of hemaoi o blood visosi has bee well doumeed. All sudies have show ha he visosi of whole blood vaies diel wih

36 hemaoi a all ell oeaios above 0%. I geeal, he highe he hemaoi, he geae he value of whole blood visosi [Diefass, 97; Dia, 98; Chie e al., 987; Guo ad Hall, 996] RBC Defomabili Defomabili is a em used o desibe he suual espose of a bod o ell o applied foes. The effe of RBC defomabili i iflueig geeal fluidi of whole blood is leal evealed i Fig. -6. This figue shows he elaive visosi of blood a a shea ae >00 s - a whih paile aggegaio is egligible, isolaig RBC defomabili ompaed wih ha of suspesios wih igid sphees. A 50% oeaio, he visosi of a suspesio of igid sphees eahes almos ifii so ha he suspesio is o able o flow. O he oa, omal blood emais fluid eve a a hemaoi of 98%, o aou of he defomabili of is RBCs [Fug, 993] RBC Aggegaio - Majo Fao of Shea-Thiig Chaaeisi Sie ed ells do o have a uleus, he behave like a fluid dop [Dia, 98]. Hee, whe a umbe of ed ells luse ogehe as i he flow of a low shea ae, he aggegae ogehe. Aodigl, huma RBCs have he abili o

37 fom aggegaes kow as ouleaux. Rouleaux fomaio is highl depede o he oeaio of fibioge ad globuli i plasma. Noe ha bovie blood does o fom ouleaux beause of absee of fibioge ad globuli i plasma [Fug, 993]. Vaious degees ad umbes of ouleaux i liea aa ad bahed ewok ae piued i Fig. -7. Figue -8 shows he elaioship bewee blood visosi ad ouleaux fomaio. Rouleaux fomaio of healh ed ells ieases a deeasig shea aes. As ed ells fom ouleaux, he will umble while flowig i lage vessels. The umblig disubs he flow ad equies he osumpio of eeg, hus ieasig blood visosi a low shea [Fug, 993]. As shea ae ieases, blood aggegaes ed o be boke up, esulig i dop i blood visosi see Fig. -8. I sho, ouleaux fomaio ieases blood visosi, wheeas beakig up ouleaux deeases blood visosi Tempeaue Tempeaue has a damai effe o he visosi of a liquid, iludig whole blood ad plasma. As i mos fluids, blood visosi ieases as empeaue deeases [Fug, 993; Guo ad Hall, 996]. I blood, edued RBC defomabili ad ieased plasma visosi paiulal elevae whole blood visosi a low empeaues [Babee, 973]. Cosequel, peise ool of he sample empeaue is eessa o measue visosi auael i vio. I is

38 3 pefeable ad is a sadad i hemoheologi sudies o a ou blood visosi measuemes a bod empeaue of 37. Tpiall, blood visosi ieases less ha % fo eah deease i empeaue [Babee, 973]..3.. Yield Sess ad Thixoop.3... Yield Sess I addiio o o-newoia visosi, blood also exhibis a ield sess. The soue of he ield sess is he pesee of ells i blood, paiulal ed ells. Whe suh a huge amou 40-45% b volume of ed ells of 8-0 mios i diamee is suspeded i plasma, ohesive foes amog he ells ae o egligible. The foes exisig bewee pailes ae va de Waals-Lodo foes ad Coulombi foes [Cheg ad Evas, 965; Mewis ad Spaull, 976]. Hee, i ode o iiiae a flow fom es, oe eeds o have a foe whih is lage eough o beak up he paile-paile liks amog he ells. Howeve, blood oais 40-45% ed ells ad sill moves elaivel easil. The healh ed ells behave like liquid dops beause he membaes of ed ells ae so elasi ad flexible. Noe ha i a fluid wih o suspeded pailes, he fluid sas o move as soo as a ifiiesimall small amou of foe is applied. Suh a fluid is alled a fluid wihou ield sess. Examples of fluid wih o ield sess ilude wae, ai, mieal oils, ad vegeable oils. Examples of fluids havig he

39 4 ield sess ilude blood, kehup, salad dessigs, gease, pai, ad osmei liquids. The magiude of he ield sess of huma blood appeas o be a he ode of 0.05 de/m o 5 mpa [Shmid-Sh& o bei ad Wells, 97; Walawede e al., 975; Nakamua ad Sawada, 988; Fug, 993; Solz e al., 999] ad is almos idepede of empeaue i he age of 0-37 [Babee, 973] Thixoop - Time Depedee The pheomeo of hixoop i a liquid esuls fom he miosuue of he liquid ssem. Thixoop ma be explaied as a osequee of aggegaio of suspeded pailes. If he suspesio is a es, he paile aggegaio a fom, wheeas if he suspesio is sheaed, he weak phsial bods amog pailes ae upued, ad he ewok amog hem beaks dow io sepaae aggegaes, whih a disiegae fuhe io smalle fagmes [Baes, 997]. Afe some ime a a give shea ae, a dami equilibium is esablished bewee aggegae desuio ad gowh, ad a highe shea aes, he equilibium is shifed i he dieio of geae dispesio. The elaivel log ime equied fo he miosuue o sabilize followig a apid hage i he ae of flow makes blood hixoop eadil obsevable [How, 996]. This effe o visosi has bee sudied usig a sead flow [Huag e al., 975]. A high shea aes, suual hage ous moe apidl ha ha a low

40 5 shea aes. I hei sud, he fis sep was fom he o-flow odiio o a shea ae of 0 s -. The foud ha blood visosi deeased ove a peiod of appoximael 0 seods a he shea ae of 0 s - befoe he fial sae was aaied. Nex, whe he shea ae sepped fom 0 o 00 s -, almos o ime was equied o eah he miosuual equilibium afe he hage of shea ae. Gaspa-Rosas ad Thuso 988 also ivesigaed o ehoe aggegae heolog b vaig shea ae fom 500 s - o zeo. Based o hei esuls, i a be oluded ha he eove of quiese suue equies appoximael 50 seods while he high shea ae suue is aaied i a few seods. I ohe wods, i ode o miimize he effe of he hixoopi haaeisi of blood o he visosi measueme bewee he shea aes of 500 ad s -, a leas 50 seods should be allowed duig he es o have he full aggegaed quiese sae a a shea ae ea s -.

41 6 Visosi P 4 Whole blood Plasma 0 00 Shea ae s Fig. -5. Compaiso of Newoia plasma visosi ad shea-hiig whole blood visosi.

42 7 Relaive visosi 00 0 Suspesio wih igid sphees Nomal blood Paile volume faio Fig. -6. Vaiaio of he elaive visosi of blood ad suspesio wih igid sphees a a shea ae > 00 s - [Goldsmih, 97].

43 Fig. -7. Rouleaux fomaio of huma ed blood ells phoogaphed o a miosope slide showig sigle liea ad bahed aggegaes lef pa ad a ewok igh pa. The umbe of ells i liea aa ae, 4, 9, 5 ad 36 i a, b,, d, ad f, espeivel. [Fug, 993; Goldsmih, 97] 8

44 9 Relaive visosi 0 Nomal blood 0 Shea ae s Fig. -8. Elevaed blood visosi a low shea aes idiaes RBC aggegaio ouleaux fomaio. Blood visosi deeases wih ieasig shea aes as RBC aggegaios beaks up o idividual ed ells.

45 30 CHAPTER 3. CONVENTIONAL RHEOMETRY: STATE-OF-THE-ART This hape eviews lieaue o oveioal heomeies. Seio 3. biefl iodues oveioal heomees. I seios 3. ad 3.3, visomees ommol used fo he visosi measuemes of fluids, whih have bee used fo hemoheolog sudies, ae demosaed. Seio 3.4 povides oveioal mehods of measuig ield sesses of fluids. Seio 3.5 peses he dawbaks of oveioal visomees fo liial appliaios. 3.. Ioduio Numeous pes of heomees have bee used o measue he visosi ad ield sess of maeials [Tae, 985; Feguso ad Kemblowski, 99; Maosko, 994]. I he pese sud, heomee efes o a devie ha a measue boh visosi ad ield sess of a maeial, wheeas visomee a measue ol he visosi of he maeial. I addiio, ol shea visomees will be disussed i he sud sie he ohe pe, exesioal visomees, ae o ve appliable o elaivel low visous fluids, suh as wae ad whole blood. Tpiall, shea visomees a be divided io wo goups [Maosko, 994]: dag flows, i whih shea is geeaed bewee a movig ad a saioa solid sufae, ad pessue-dive flows, i whih shea is geeaed b a pessue diffeee ove a apilla ube. The ommol uilized membes of hese goups ae

46 3 show i Fig. 3-. Numeous ehiques have bee developed fo deemiig he ield sess of fluids boh diel ad idiel. Mos of hese visomees a podue visosi measuemes a a speified, osa shea ae. Theefoe, i ode o measue he visosi ove a age of shea aes, oe eeds o epea he measueme b vaig eihe he pessue i he esevoi ak of apilla ube visomees, he oaig speed of he oe o up i oaig visomees, o he desi of he fallig objes. Suh opeaios make visosi measuemes diffiul ad labo iesive. I addiio, hese visomees equie aioagulas i blood o peve blood loig. Hee, he visosi esuls ilude he effes of aioagulas, whih ma iease o deease blood visosi depedig o he pe of aioagula [Roseblum, 968; Couh e al., 986; Reiha e al., 990; Kamaeva e al., 994]. Dag-flow pe of visomees iludes a fallig obje ball o lide visomee ad a oaioal visomee. Howeve, he fallig obje visomee is o ve oveie o use fo liial appliaios. I he ase of he fallig obje visomee, he elaivel lage amou of a es fluid is equied fo he visosi measueme. I addiio, sie he esig fluid is a a saioa sae iiiall, he pe of visomee is o ve appliable o a hixoopi fluid like whole blood. The piiple of he fallig obje visomee is povided i Appedix B. Fo he ield measueme of blood, mos eseahes have used idie mehods ahe ha die mehods fo paial easos [Ngue ad Boge, 983; de Kee e al., 986; Magi ad Piau, 990]. Thus, he deails of die mehods will

47 3 o be disussed i his hape. As idie mehods, daa exapolaio ad exapolaio usig osiuive models ae iodued ad disussed i his hape.

48 33 Rheomees Visosi Measuemes Yield Sess Measuemes Dag Flows Pessue- Dive Flows Idie Mehods Die Mehods Capilla- Tube Visomee Daa Exapolaio Exapolaio usig Cosiuive Models Fallig/ Rollig Obje Visomee Roaioal Visomee Fig. 3-. Rheomees.

49 Roaioal Visomee I a oaioal visomee, he fluid sample is sheaed as a esul of he oaio of a lide o oe. The sheaig ous i a aow gap bewee wo sufaes, usuall oe oaig ad he ohe saioa. Two fequel used geomeies ae Couee Fig. 3- ad oe-ad-plae Fig Roaioal Coaxial-Clide Couee Tpe I a oaxial-lide ssem, he ie lide is ofe efeed o as bob, ad he exeal oe as up. The shea ae is deemied b geomeial dimesios ad he speed of oaio. The shea sess is alulaed fom he oque ad he geomeial dimesios. B hagig he speed of he oaig eleme, oe is able o olle diffee oques, whih ae used fo he deemiaio of he shea sessshea ae uve. Figue 3- shows a pial oaxial-lide ssem ha has a fluid Ri ofied wihi a aow gap bewee he ie lide oaig a Ω R o ad he saioa oue lide. Oe he oque exeig o eihe ie o oue lide is measued, he shea sess ad shea ae a be alulaed as follow [Maosko, 994]: M i M o τ Ri = o τ R o = 3- πr H πr H i o

50 35 ΩR Ri & γ Ri & γ Ro = whe > R R R o i o 3- whee R i ad R o = adii of ie ad oue lides, espeivel R = R i + R o M i ad M o = oques exeig o ie ad oue lides, espeivel H = heigh of ie lide Ω = agula veloi Coe-ad-Plae The ommo feaue of a oe-ad-plae visomee is ha he fluid is sheaed bewee a fla plae ad a oe wih a low agle; see Fig The oe-ad-plae ssem podues a flow i whih he shea ae is ve eal uifom. Le s oside a fluid, whih is oaied i he gap bewee a plae ad a oe wih a agle of β. Tpiall, he gap agle, β, is ve small o 4. The shea ae of he fluid depeds o he gap agle, β, ad he liea speed of he plae. Assumig ha he oe is saioa ad he plae oaes wih a osa agula veloi of Ω, he shea sess ad shea ae a be alulaed fom expeimeall measued oque, M, ad give geomei dimesios see Fig. 3-3 as follows [Maosko, 994]: 3M τ = ad 3 πr Ω & γ =. 3-3 β

51 36 Ω R i H R o Fig. 3-. Shemai diagam of a oei lide visomee.

52 37 Toque measueme devie Fluid Coe R β Plae Ω Fig Shemai diagam of a oe-ad-plae visomee.

53 Capilla-Tube Visomee The piiple of a apilla ube visomee is based o he Hage-Poiseuille Equaio whih is valid fo Newoia fluids. Basiall, oe eeds o measue boh pessue dop ad flow ae idepedel i ode o measue he visosi wih he apilla ube visomee. Sie he visosi of a Newoia fluid does o va wih flow o shea, oe eeds o have oe measueme a a flow veloi. Howeve, fo o-newoia fluids, i is moe ompliaed beause he visosi vaies wih flow veloi o shea ae. I a apilla-ube visomee, he fluid is foed hough a lidial apilla ube wih a smooh ie sufae. The flow paamees have o be hose i suh a wa ha he flow ma be egaded as sead-sae, isohemal, ad lamia. Kowig he dimesios of he apilla ube i.e., is ie diamee ad legh, oe a deemie he fuioal depedee bewee he volumei flow ae ad he pessue dop due o fiio. If he measuemes ae aied ou so ha i is possible o esablish his depedee fo vaious values of pessue dop o flow ae, he oe is able o deemie he flow uve of he fluid. Fo o-newoia fluids, sie he visosi vaies wih shea ae, oe eeds o va he pessue i he esevoi i ode o hage he shea ae, a poedue ha is highl ime-osumig. Afe eah u, he esevoi pessue should be ese o a ew value o obai he elaio bewee flow ae ad pessue dop. I ode o deemie he flow uve of a o-newoia fluid, oe eeds o esablish he fuioal depedee of shea sess o shea ae i a wide age of hese vaiables.

54 39 Figue 3-4 shows he shemai diagam of a pial apilla-ube visomee, whih has he apilla ube wih a ie adius of R ad a legh of L. I is assumed ha he aio of he apilla legh o is ie adius is so lage ha oe ma egle he so-alled ed effes ouig i he eae ad exi egios of he apilla ube. The, he shea sess a he ube wall a be obaied as follows: P τ = 3-4 L R P τ w = 3-5 L whee τ ad τ w = shea sesses a disae ad a ube wall, espeivel = disae fom he apilla axis P = pessue dop aoss a apilla ube. I is of oe ha he shea sess disibuio is valid fo fluids of a heologial popeies. I he ase of a Newoia fluid, he shea ae a ube wall a be expessed b akig advaage of he well-kow Hage-Poiseuille Equaio as: γ& = 4Q 4V w πr R 3-6 = 3 whee γ& w = wall shea ae 4 π R P Q = 8 µ L = πr V = volumei flow ae Hage-Poiseuille Equaio V = mea veloi.

55 40 Compessed ai Ai Tes fluid Capilla ube Resevoi ak L R Colleed es fluid Balae Fig Shemai diagam of a apilla-ube visomee.

56 Yield Sess Measueme Whehe ield sess is a ue maeial pope o o is sill a oovesial issue [Baes ad Wales, 985]. Howeve, hee is geeall a aepae of is paial usefuless i egieeig desig ad opeaio of poesses whee hadlig ad aspo of idusial suspesios ae ivolved. The miimum pump pessue equied o sa a slu pipelie, he levelig ad holdig abili of pai, ad he eapme of ai i hik pases ae pial poblems whee he kowledge of he ield sess is esseial. Numeous ehiques have bee developed fo deemiig he ield sess boh diel ad idiel based o he geeal defiiio of he ield sess as he sess limi bewee flow ad o-flow odiios. Idie mehods simpl ivolve he exapolaio of shea sess-shea ae daa o zeo shea ae wih o wihou he help of a heologial model. Die measuemes geeall el o some idepede assessme of ield sess as he iial shea sess a whih he fluid ields o sas o flow. The value obaied b he exapolaio of a flow uve is kow as exapolaed o appae ield sess, wheeas ield sess measued diel, usuall ude a ea sai odiio, is emed sai o ue ield value.

57 Idie Mehod Idie deemiaio of he ield sess simpl ivolves he exapolaio of expeimeal shea sess-shea ae daa a zeo shea ae see Fig The exapolaio ma be pefomed gaphiall o umeiall, o a be fied o a suiable heologial model epeseig he fluid ad he ield sess paamee i he model is deemied Die Daa Exapolaio Oe of mos ommo poedues is o exed he flow uve a low shea aes o zeo shea ae, ad ake he shea sess ieep as he ield sess value. The ehique is elaivel saighfowad ol if he shea sess-shea ae daa ae liea. Wih oliea flow uves, as show i Fig. 3-5, he daa ma have o be fied o a polomial equaio followed b he exapolaio of he esulig uve fi o zeo shea ae. The ield sess value obaied obviousl depeds o he lowes shea ae daa available ad used i he exapolaio. This shea ae depedee of he exapolaed ield sess has bee demosaed b Baes ad Wales 985 wih a well-kow ield sess fluid, Cabopol aboxlpolmehlee. The oluded ha his fluid would have o deeable ield sess eve if measueme was made a ve low shea aes of 0-5 s - o less. This fidig should be viewed wih auio, howeve, sie viuall all visomei isumes suffe wall slip ad

58 43 ohe defes whih ed o be moe pooued a low shea aes espeiall wih ield sess fluids ad paiulae ssems [Wildemuh ad Williams, 985; Magi ad Piau, 990]. Thus, i is impeaive ha some hekig poedue should be aied ou o aseai he eliabili of he low shea ae daa befoe exapolaio is made Exapolaio Usig Cosiuive Models A moe oveie exapolaio ehique is o appoximae he expeimeal daa wih oe of he visoplasi flow models. Ma wokes appea o pefe he Bigham model whih posulaes a liea elaioship bewee shea sess ad shea ae. Howeve, sie a lage umbe of ield sess fluids iludig suspesios ae o Bigham plasi exep a ve high shea aes, he use of he Bigham plasi model a lead o ueessa ovepediio of he ield sess as show i Fig. 3-5 [Ngue ad Boge, 983; de Kee e al., 986]. Exapolaio b meas of oliea Casso model a be used fom a liea plo of τ vesus γ&. The appliaio of Heshel-Bulkle model is less eai alhough ssemai poedues fo deemiig he ield sess value ad he ohe model paamees ae available [Hewood ad Cheg, 984]. Eve wih he mos suiable model ad appopiae ehique, he ield sess value obaied ao be egaded as a absolue maeial pope beause is aua depeds o he model used ad he age ad eliabili of he expeimeal

59 44 daa available. Seveal sudies have show ha a give fluid a be desibed equall well b moe ha oe model ad hee a have diffee ield sess values [Keeok, 98; Ngue ad Boge, 983; Uhlhe, 986] Die Mehod Vaious ehiques have bee iodued fo measuig he ield sess diel ad idepedel of shea sess-shea ae daa. Alhough he geeal piiple of he ield sess as he sess limi bewee flow ad o-flow odiios is ofe used, he speifi ieio emploed fo defiig he ield sess seems o va amog hese ehiques. Fuhemoe, eah ehique appeas o have is ow limiaios ad sesiivi so ha o sigle ehique a be osideed vesaile o auae eough o ove he whole age of ield sess ad fluid haaeisis. Usuall, he die mehods ae used fo fluids havig ield sesses of geae ha appoximael 0 Pa [Ngue ad Boge, 983]. Theefoe, as meioed ealie, he die mehod is o ve oveie o use fo he ield sess measueme of blood sie he ield sess of huma blood is appoximael o 30 mpa [Pia e al., 998].

60 Fig Deemiaio of ield sess b exapolaio [Ngue ad Boge, 983]. 45

61 Poblems wih Coveioal Visomees fo Cliial Appliaios Poblems wih Roaioal Visomees Ove he eas, oaioal visomees have bee he sadad i liial sudies ivesigaig heologial popeies of blood ad ohe bod fluids. Despie hei populai, oaioal visomees have some dawbaks ha limi hei liial appliabili i measuig whole blood visosi. The ilude he eed o alibae a oque-measuig seso, hadlig of blood, sufae esios effes, ad he age of eliabili. The oque-measuig seso a be a oveioal spig o a moe sophisiaed eleoi asdue. I eihe ase, he seso equies a peiodi alibaio beause epeaed use of he seso a ale is spig osa. The alibaio poedue is ofe aied ou a maufaue s laboao beause i equies a exemel aeful ad elaboae poool, equiig he visomee ui o be eued fo sevie. Aohe oe is he eed o wok wih oamiaed blood speimes. Afe eah measueme, he blood sample mus be emoved fom he es seio, ad he es seio mus be leaed mauall. No ol is his poedue imeosumig, bu also i poses a poeial isk fo oa wih oamiaed blood. Sufae esio effes aise i he use of he oaxial-lide visomee beause sufae esio is elaivel high fo blood ad maomoleula soluios. The oa aea bewee he blood ad a ie lide is o uifom alog he

62 47 peiphe. The bob ie lide is pulled i diffee dieios ad evealed i fluuaig oque eadigs, ioduig seious eos i visosi measueme. Aohe ihee diffiul i measuig whole blood visosi usig oaioal visomees is he limied shea ae age. I he exemes of he epued age whehe high shea o low shea, depedig o he isume, he deeed oque values do o have suffiie aua. Usuall, maufaues eommed disadig visosi daa if he oque is less ha 0% of he maximum value of he seso. This esiio is a majo oe. Fo example, i he ase of Bookfield oaioal visomee, he miimum shea ae is ofe limied a appoximael s - due o he 0% esiio. Thee ae ohe liial, paial osideaios i usig he oaioal visomee. Fo example, i is usuall eessa o ea he blood sample wih a measuable amou of aioagula, suh as ehleediamieeaaei aid EDTA o hepai, o peve oagulaio duig visosi measuemes. The easo fo his is ha he oa aea amog blood, oaioal visomee ompoe, ad ai is elaivel lage fo he size of he blood sample, ad i usuall akes a elaivel log ime o omplee visosi measuemes ove a age of shea aes. Teaig blood wih suh aioagulas esuls i a aleed sample, ad subseque visosi measuemes do o efle he iisi values of uaduleaed blood.

63 Poblems wih Capilla-Tube Visomees Thee ae some dawbaks i he use of oveioal apilla-ube visomees fo liial appliaios. The age of shea ae is limied o high sheas ove 00 s -. Alhough oe a podue visosi daa a lowe shea aes below 00 s - wih a sophisiaed vauum ssem, he apilla ube ssem is basiall desiged ad opeaed o obai visosi a he high shea age. Sie i is esseial o obai blood visosi a low shea aes below 0 s -, he adiioal apilla ube visomee is o suiable fo measuig he visosi a low shea aes. Howeve, apilla-ube visomee is simple i is desig ad uses gavi field o dive es fluid suh ha hee is o eed fo alibaio. I akes a elaivel log ime o omplee visosi measuemes ove a age of shea aes beause a eah shea ae, a suffiie quai of a fluid sample mus be olleed fo a auae measueme of flow veloi. Afe he measueme a oe shea ae, he pessue a he esevoi ak mus be eadjused o eihe iease o deease shea ae. The, he ex shea ae ase esumes. Thus, aioagulas mus be added o whole blood fo he visosi measueme ove a age of shea aes.

64 49 CHAPTER 4. THEORY OF SCANNING CAPILLARY-TUBE RHEOMETER Chape 4 peses he heo of saig apilla-ube heomee SCTR. Mahemaial poedues fo boh visosi ad ield-sess measuemes wee demosaed i deail usig powe-law, Casso, ad Heshel-Bulkle H-B models. Seio 4. povides a bief ioduio o he SCTR. I seio 4.., he desipio of a U-shaped ube se is epoed. I addiio, his seio shows how he dimesios of he disposable ube se wee deemied. Seio 4.. demosaes he equaios fo he eeg balae i he disposable ube se. Seio 4. povides he mahemaial deails of daa eduio fo boh visosi ad ield-sess measuemes. Seios 4.., 4.., ad 4..3 deal wih he mahemaial modelig i he daa eduio b usig he powe-law, Casso, ad H-B models, espeivel. Espeiall, i seios 4.. ad 4..3, he ield sess as well as he visosi of blood was osideed i he daa eduio. 4. Saig Capilla-Tube Rheomee SCTR Oe of he dawbaks of usig oveioal apilla visomees is ha oe eeds o hage he pessue i he esevoi ak i ode o measue he visosi a a diffee shea ae. Visosi a ol be measued a oe shea ae a a ime i he oveioal ssem. Similal, i ohe pes of visomees suh as oaig visomees ad fallig obje visomees, he oaig speed has o be haged o

65 50 he desi of he fallig obje has o be haged i ode o va shea ae as meioed i Chape 3. Suh opeaios a make visosi measuemes ime osumig ad labo iesive. Beause of he ime equied o measue visosi ove a age of shea aes, i is eessa o add aioagulas o blood o peve loig duig visosi measuemes wih hese oveioal visomees. The pese sud iodues a iovaive oep of a ew apilla ube heomee ha is apable of measuig ield sess ad visosi of whole blood oiuousl ove a wide age of shea aes wihou addig a aioagulas. 4.. U-Shaped Tube Se Figue 4- shows a shemai diagam of a U-shaped ube se, whih osiss of wo ise ubes, a apilla ube, ad a sopok. The iside diamee of he ise ubes i he pese sud is 3. mm. The iside diamee ad legh of he apillaube ae ad 00 mm, espeivel. The small diamee of he apilla ube, ompaed wih ha of he ise ubes, was hose o esue ha he pessue dops a he ise ubes ad oeig fiigs wee egligibl small ompaed o he pessue dop a he apilla ube [Kim e al., 000a, 000b, ad 00]. Fuhemoe, he iside diamee of he apilla ube was hose o miimize he wall effe whih is ofe kow as Fahaeus-Lidqvis effe [Fahaeus ad Ligqvis, 93]. The deails of he wall effe will be disussed i Chape 5. I he pese sud, he wall effe was foud o be egligibl small.

66 5 The legh of he apilla ube i.e., L = 00 mm i he U-shaped ube se was seleed o esue ha he ed effes would be egligible [Kim e al., 000a, 000b, ad 00]. The ed effes a he apilla ube will be also epoed i Chape 5. I addiio, he apilla-ube dimesios i he SCTR wee seleed o omplee oe measueme wihi -3 mi, a odiio ha is desiable whe measuig he visosi of uaduleaed whole blood i a liial eviome. Figue 4- shows skehes of he fluid levels i he U-shaped ube se as ime goes o. The fluid level i he igh-side ise ube deeases wheeas ha i he lefside ise ube ieases. As ime goes o ifii, he wo fluid levels eve beome equal due o he sufae esio ad ield sess effes as show i Fig. 4- i.e., h = > 0. While a es fluid avels hough he apilla ube bewee ise ubes ad, he pessue dop aused b he fiio a he apilla ube a be obaied b measuig he fluid levels a ise ubes ad. I Fig. 4-3, a pial fluid-level vaiaio measued b he SCTR is show. Pois a, b, ad epese he hee momes idiaed i Fig. 4- i.e., a = 0, > 0, ad =, espeivel. 4.. Eeg Balae Figue 4-4 shows he liquid-solid iefae odiio fo eah fluid olum of a U-shaped ube. A fallig olum igh side alwas has a full we sufae odiio, while a isig olum lef side has a almos pefel d sufae odiio a he liquid-solid iefae duig he eie es. Theefoe, he sufae

67 5 esio a he igh side was osisel geae ha ha a he lef side sie he sufae esio of a liquid is sogl depede o he weig odiio of he ube a he liquid-solid iefae [Jaobs, 966; Madles, 969; Kim e al., 00]. The heigh diffeee aused b he sufae esio a he wo ise ubes was oe ode of magiude geae ha he expeimeal esoluio desied fo auae visosi measuemes. Thus, i is exemel impoa o ake io aou he effe of he sufae esio o he visosi measueme usig he disposable ube se. The mahemaial model of he flow aalsis bega wih he equaio of he osevaio of eeg i he fom of pessue ui, whee he sufae-esio effe was osideed bewee he wo op pois of he fluid olums a he ise ubes see Fig Assumig ha he sufae esio fo he liquid-solid iefae a eah ise ube emais osa duig he es, oe ma wie he goveig equaios as [Bid e al., 987; Muso e al., 998]: P s V V gh P V gh P g h ρ + ρ = + ρ + ρ + + ρ + ds = ρ s, 4- + whee P ad P = sai pessues a wo op pois ρ = desi of fluid g = gaviaioal aeleaio V ad V = flow veloiies a wo ise ubes h ad h = fluid levels a wo ise ubes P = pessue dop aoss apilla ube h = = addiioal heigh diffeee

68 53 V = flow veloi = ime s = disae measued alog seamlie fom some abia iiial poi. I Eq. 4-, he eeg emied fom LEDs was igoed sie he eeg asfeed fom he LEDs, whih a affe he empeaue of a es fluid, was egligible small. I ode o esue ha he amou of he hea emied fom he LEDs is ve small, he empeaue of bovie blood was measued duig a oom-empeaue es. The esuls showed o hages i empeaue duig he es, idiaig ha he eeg emied fom LEDs migh be egligibl small. Fo he oveiee of daa-eduio poedue, he usead em i Eq. 4- s V, ρ ds, ma be igoed ude he assumpio of a quasi-sead sae. I ode s o make he assumpio, oe should make sue ha he pessue dop due o he usead effe is ve small ompaed wih ha due o he fiio esimaed fom he sead Poiseuille flow i a apilla ube. The usead em a be boke io hee iegaios ha epese he pessue dops due o he usead flow alog he seamlies a ise ube, apilla ube, ad ise ube as [Muso e al., 998]: s V s dv s s dv dv ρ ds = ρ + + ds ds ds, 4- s s s s d d d whee V ad V ae mea flow veloiies a ise ad apilla ubes, espeivel. Sie he em of V is idepede of seamlies, oe a simplif he equaio as:

69 54 ρ s s V dv ds = ρ d l dv + d L dv + d l = ρl dv d + ρ dv l + l d, 4-3 whee l ad l ae leghs of he liquid olums wheeas L is he legh of he apilla ube as show i Fig Usig he mass osevaio, π R V = πr V, he pessue dop due o he usead effe a be edued as: s V R dv Pusead = ρ ds = ρ L + l + l s R, 4-4 d whee P usead = pessue dop due o he usead flow R ad R = adii of ise ad apilla ubes, espeivel. I he pese expeimeal se up, l, l, ad L ae measued o be appoximael, 4, ad 0 m, espeivel. Sie h ad h ae sogl depede o eah ohe b he osevaio of mass fo iompessible fluids, V mus be equal o dh d ad dh. I ode o alulae he em of d dv d fom he expeimeal values, oe ould use he followig eal diffeeial mehod: dv d [ h + h + h ] [ h + h + h ] =. 4-5 = Fo he ompaiso of Pusead wih P, Pusead was esimaed hough a uvefiig poess. I ode o obai a smooh uve fom aw daa, he followig expoeial equaio was used. dv b Eo = a e. 4-6 d

70 55 Two osas, a ad b, wee obaied hough a uve-fiig poess, a leassquae mehod, whih miimized he sum of eo fo all expeimeal daa pois obaied i eah es. usead flow, ube, Tpial esuls showed ha he magiude of he pessue dop due o he Pusead, was alwas less ha % of ha of pessue dop a apilla P, ove he eie shea-ae age. This ofims ha he assumpio of a quasi-sead sae ould be used fo he pese daa poedue. The deails of expeimeal esuls will be disussed i Chape 5. Assumig a quasi-sead flow behavio, oe ma ewie Eq. 4- as follows [Bid e al., 987; Muso e al., 998]: P + ρ V + ρgh = P + ρv + ρgh + P + ρg h =. 4-7 Sie P = = P Pam ad V = V, Eq. 3-7 a be edued as: [ h h h ] P = ρ g. 4-8 Noe ha h a = = oais a heigh diffeee due o he sufae esio, hs, ad a addiioal heigh diffeee due o he ield sess, h, fo he ase of blood i.e., see Fig The ex seio addesses he mahemaial poedue of hadlig he ield sess.

71 56 Ope o ai 3. mm Rise ubes Capilla ube mm Sopok 00 mm Fig. 4-. Shemai diagam of a U-shaped ube se.

72 57 a a = 0 Rise ube Rise ube b a > 0 h = a = Fig. 4-. Fluid-level vaiaio i a U-shaped ube se duig a es.

73 58 Heigh h h = h a b Time Fig Tpial fluid-level vaiaio measued b a SCTR. a a = 0, b a > 0, ad a =.

74 59 We sufae odiio D sufae odiio l l ' ' L Fig Liquid-solid iefae odiios fo fluid olums of a U-shaped ube se.

75 60 4. Mahemaial Poedue fo Daa Reduio I Chape, we disussed he o-newoia haaeisis of whole blood. This seio deals wih o-newoia osiuive models fo blood ad hei appliaios o he SCTR. Sie blood has boh shea-hiig pseudo-plasi ad ield sess haaeisis, hee diffee osiuive models wee used fo he visosi ad/o ield-sess measuemes of blood i his sud. Powe-law model was hose o demosae he shea-hiig behavio of blood. Casso ad Heshel-Bulkle H-B models wee seleed o measue boh shea hiig visosi ad ield sess of blood. Fo he pupose of liial appliaios, disposable ube ses a be used fo he visosi ad ield-sess measuemes of blood. Sie he disposable ube ses have diffee sufae odiios a ise ube ad duig he es, oe eeds o mahemaiall hadle sufae esio ad ield sess effes i ode o measue he visosi ad ield sess of blood usig Casso o H-B model. The deails of mahemaial mehod of isolaig hose wo effes ae show i his seio. 4.. Powe-law Model I is well kow ha powe-law model does o have he apabili o hadle ield sess. As povided i Chape, he elaio amog shea sess, shea ae, ad visosi i powe-law fluids ma be wie as follows:

76 6 τ mγ& =, 4-9 η = mγ&. 4-0 Sie < fo pseudo-plasis, he visosi fuio deeases as he shea ae ieases. This pe of behavio is haaeisi of high polmes, polme soluios, ad ma suspesios iludig whole blood. We oside he fluid eleme i he apilla ube a ime as is show i Fig The Hage-Poiseuille flow ma be used o deive he followig elaioship fo he pessue dop a he apilla ube as a fuio of apilla ube geome, fluid visosi, ad flow ae [Fug, 990; Muso e al., 998]: l L µ L & γ w 8µ LQ 8µ L R P = τ = τ w = = = 4 4 R R πr R whee = adial disae l = legh of fluid eleme dh d, 4- τ ad τ w = shea sess ad wall shea sess, espeivel 4Q & γ w = = wall shea ae πr 3 µ = Newoia appae visosi L = legh of apilla ube dh dh dh Q = π R = πr = πr = volumei flow ae. d d d The above elaioship is valid fo Newoia fluids whose visosiies ae idepede of shea ae. Fo o-newoia fluids, he visosiies va wih shea

77 6 ae. Howeve, he Hage-Poiseuille flow wihi he apilla ube sill holds fo a quasi-sead lamia flow. Whe applig a o-newoia powe-law model o whole blood, he pessue dop a he apilla ube a be desibed as follows [Middlema, 968; Bid e al., 987; Fug, 990]: P = η wl & γ R w = ml & γ R w = ml R 3 + Q πr 3, 4- = ml R 3 + R R 3 dh d whee η w = powe-law appae visosi 3 + Q & γ w =. πr 3 I is of oe ha if =, Eq. 4- ields o Eq.4-. Applig Eqs. 4-8, 4-, ad 4-, oe a ewie he eeg osevaio equaio as follows: 8µ L R dh ρ g{ h h h = } = fo Newoia fluids, R d ρ g { h h h } ml = R 3 + R R = 3 dh d fo powe-law fluids. 4-4 Fo oveiee, oe ma defie a ew fuio, θ h h h so ha Eqs. 4-3 ad 4-4 beome as follows: = = dθ = α d fo Newoia fluids, 4-5 θ

78 63 dθ = d fo powe-law fluids, 4-6 θ β whee θ dh = d d dh d dh = d d α = ρgr 4 4µ L R ρgr ml β =. 3 + R 3 R The above equaios ae he fis-ode liea diffeeial equaios. Sie α ad β ae osas, hese equaios a be iegaed as follows: α θ = θ 0 e fo Newoia fluids, 4-7 θ = θ 0 β fo powe-law fluids, 4-8 whee θ 0 = h 0 h 0 h = : iiial odiio. Equaio 4-8 a be used fo uve fiig of he expeimeal daa i.e., h ad h o deemie h =, he powe-law idex,, ad he osise idex, m. A leas-squae mehod was used fo he uve fiig. The daa eduio poedue adoped is as follows:. Codu a es ad aquie all daa, h ad h.. Guess values fo m,, ad h =. 3. Calulae he followig eo values fo all daa pois:

79 [{ θ } { θ } ] Eo =. 4-9 Expeimeal value Theoeial value 4. Sum he eo values fo all daa pois. 5. Ieae o deemie he values of m,, ad h = ha miimize he sum of eo. 6. Le he ompue deemie whehe a es fluid is Newoia o o. 7. Calulae shea ae ad visosi fo all daa pois as follows: R ρgr & γ w = P = θ fo Newoia fluids, 4-0 µ L µ L 64 R ρgr w = P = ml θ ml γ& fo powe-law fluids. 4- Whe beomes ± 0.00, µ is equal o m, wheeas whe 0< <, he visosi is alulaed fom Eq I ode o obai he veloi pofile a he apilla ube, whih hages wih dv ime, usig a powe-law model, Eq. 4- a be used o deive i. Sie γ& =, d he veloi pofile a be expessed as follows: dv, d = P ml, P P + V, = d = + C ml ml, 4- + whee C is a osa. Usig o-slip odiio o he apilla wall, V, = 0, he osa a be obaied as: R

80 65 R ml P C + + =. 4-3 Fiall, he veloi pofile wihi he apilla ube a be expessed as follows: + = + = + + = + + R ml h h h R ml P V, 4-4 whee [ ] = = h h h g P ρ. Noe ha if powe-law idex beomes zeo, =, he he above equaio ields o he equaio fo he Newoia veloi pofile as: 4, R L P V = µ. 4-5 I ode o deemie he mea flow veloi a he ise ube, oe has o fid he flow ae a he apilla ube fis. The flow ae a be obaied b iegaig he veloi pofile ove he oss-seioal aea of he apilla ube as follows: [ ] R R ml h h h g R ml P d V Q , + = + + = + = = ρ π π π 4-6 Sie V R Q π =, he mea flow veloi a he ise ube a be deemied b he followig equaio:

81 66 [ ] R R ml h h h g R R ml P V + = + + = + = ρ 4-7 whee R is he adius of he ise ube. 4.. Casso Model The Casso model a hadle boh ield sess ad shea-hiig haaeisis of blood, ad a be desibed as follows [Babee ad Cokele, 97; Beis e al., 97; Reiha e al., 990]: γ τ τ & k + = whe τ τ, 4-8 = 0 γ& whe τ τ, 4-9 whee τ ad γ& = shea sess ad shea ae, espeivel τ = a osa ha is iepeed as he ield sess k = a Casso model osa. Wall shea sess ad ield sess a be defied as follows: w L R P = τ, 4-30 L P = τ, 4-3

82 67 whee is a adial loaio below whih he veloi pofile is uifom as show i Fig. 4-6, i.e., plug flow, due o he ield sess. Now, fo he Casso model, Eq. 4-8 beomes [ ] h s h h g P = ρ, idiaig ha he effe of he sufae esio is isolaed fom he pessue dop aoss he apilla ube. Usig Eqs. 4-8 ad 4-9, oe a obai he expessios of shea ae ad veloi pofile a he apilla ube as follows: = = L P L P k d dv γ&, = 3 8 4, 3 3 R R R L P k V fo R, R R L P k V + = fo Fo he pupose of simplii, oe ma defie wo ew paamees, R C = ad R C =, so ha Eqs ad 4-34 beome as follows: + = R R R R R R L P k V 3 8 4, 3 + = C C C C C kl P R fo R, 4-35

83 68 + = + = C C kl P R R R R R kl P V fo, 4-36 whee P P R C w = = = τ τ. I ode o deemie he mea flow veloi a he ise ube, oe has o fid he flow ae a he apilla ube fis. The flow ae a be obaied b iegaig he veloi pofile ove he oss-seioal aea of he apilla ube as follows: + = + = + = = ] [ 8 w w w R C C C kl P R kl P R L P R R L P R L P k R d V Q π τ τ τ τ τ τ π τ τ τ π π 4-37 Sie V R Q π =, he mea flow veloi a he ise ube a be deemied b he followig equaio:

84 69 4 R V = 8kR P 6 τ [ L 7 R τ R P L τ 4 P R L 3 ] R P = 8kR L 6 [ C C 3 C 4 ] whee R is he adius of he ise ube. Fo he pupose of simplii, Eq a be ewie o leal displa he ukows ad he obseved vaiables as: 4 R ρg V = 8kR L [ h h 4 + h 3 h h 4 s 6 h 7 h h h h h s 3 h ] s 4-39 whee C = P P = h h h h s. Noe ha Eq oais wo idepede vaiables, i.e., h ad h, ad oe depede vaiable, i.e., V. Thee ae hee ukow paamees o be deemied hough he uve fiig i Eq. 4-39, amel hs, k, ad h. hs is h due o he sufae esio, k is he Casso osa, ad h is h due o he ield sess. Oe he equaio fo he mea flow veloi, V, was deived, oe ould deemied he ukow paamees usig he expeimeal values of h ad h. A leas-squae mehod was used fo he uve fiig. Fo he Casso model, hee wee hee ukow values, whih wee k, hs, ad τ. Noe ha he ukow values wee assumed o be osa fo he uve-fiig mehod. Sie h ad

85 70 h ae sogl depede o eah ohe b he osevaio of mass fo iompessible fluids, dh d mus be equal o dh. Theefoe, i was moe d oveie ad auae o use he diffeee bewee he veloiies a he wo ise ubes, i.e., d h h, ha o use d dh d dh ad diel. I ode o ge d he diffeee bewee he wo veloiies fom he expeimeal values, oe ould use he eal diffeeial mehod as follows: d h h [ h + h + ] [ h h ] d = Usig Eq. 4-39, he deivaive of he veloi diffeee a be deemied heoeiall as follows: d h h d = V = 4 R ρ g 6 [ h h h s h h h h 4kR L h h h h hs ] 3 s 4-4 whee V is he mea flow veloi a he ise ube. I ode o exeue he uve-fiig poedue, oe eeds o have a mahemaial equaio of V fo he Casso model. Eq ad 4-4 wee used fo he uve fiig of he expeimeal daa o deemie he ukow osas, i.e., k, hs, ad h. Noe ha Eq. 4-4 ould be appliable fo boh Casso-model

86 7 fluids ad Newoia fluids egadless of he exisee of he ield sess. The daa eduio poedue adoped is as follows:. Codu a es ad aquie all daa, h ad h.. Guess values fo he ukows, k, hs, ad h. 3. Calulae he followig eo values fo all daa pois. [{ V } { V } ] Eo = 4-4 Expeimeal values Theoeial values 4. Sum he eo values fo all daa pois. 5. Ieae o deemie he ukows ha miimize he sum of he eo. 6. Calulae wall shea ae ad visosi fo all daa pois as follows: h h h h gr γ& = ρ, 4-43 w s kl η w Noe ha whe ρgr [ h h h ] s = & γ L w h beomes appoximael zeo i.e., esoluio of , he o-newoia visosi, η, is edued o k, a Newoia visosi. Fuhemoe, he elaio bewee wall visosi ad shea-ae a be obaied fom Eqs ad 4-44 as follow: τ ηw = k + + & γ w ρgr h L = k + & γ w 4kτ & γ w + kρgr h L & γ w 4-45 whee k ad h ae he fluid popeies o be deemied usig he Casso model.

87 7 Yield sess ould be also deemied hough he uve-fiig mehod fom he expeimeal daa of h ad h b usig he Casso model. Sie he pessue dop aoss he apilla ube,, ould be deemied usig Eq. 4-8, P P epeses he effe of he ield sess o he pessue dop. The elaioship bewee he ield sess, τ, ad P a be wie b he followig equaio: P R ρg h R τ = = L L Theefoe, oe auomaiall deemied. h is obaied usig a uve-fiig mehod, he ield sess a be 4..3 Heshel-Bulkle H-B Model Fo a Heshel-Bulkle H-B model, he shea sess a he apilla ube a be desibed as follows [Tae, 985; Feguso ad Kemblowski, 99; Maosko, 994]: τ + = m & γ τ whe τ τ, 4-47 γ& = 0 whe τ τ, 4-48 whee τ ad γ& = shea sess ad shea ae, espeivel τ = a osa ha is iepeed as ield sess m ad = model osas.

88 73 Sie he H-B model edues o he powe-law model whe a fluid does o have a ield sess, he H-B model is moe geeal ha he powe-law model. Fo he H-B model, wall shea sess ad ield sess a also be defied as follows: w L R P = τ, 4-49 L R h g L R P L P = = = ρ τ, 4-50 whee is a adial loaio below whih he veloi pofile is uifom due o he ield sess see Fig Usig Eqs , oe a obai he expessios of shea-ae ouside of he oe egio as: ml P d dv = = γ& fo R. 4-5 The veloi pofile ouside of oe egio a be obaied b iegaig Eq. 4-5 as: + = + + R ml P V, fo R. 4-5 Sie he veloi pofile iside of he oe egio is a fuio of ime,, ol, he pofile a be obaied usig a bouda odiio,, V V = a =. R ml P V + + = fo. 4-53

89 74 Agai, fo he pupose of simplii, oe ma defie wo ew paamees, R C = ad R C =, so ha Eqs. 4-5 ad 4-53 beome as follows: + = + = C C C ml P R R R R ml P R V, fo R, 4-54 C ml P R R ml P R V = + = fo I ode o deemie he mea flow veloi a he ise ube, oe has o fid he flow ae a he apilla ube fis. The flow ae a be obaied b iegaig he veloi pofile ove he oss-seioal aea of he apilla ube as follows: ] 3 [ 3 0 R R R R R R ml P d V Q = = π π 4-56

90 75 ] 3 [ ] 3 [ C C C C C C C ml P R R R R R R R R R R R R ml P = = π π whee s w h h h h P P R C = = = = τ τ. Sie V R Q π =, he mea flow veloi a he ise ube a be deemied b he followig equaio: ] 3 [ 3 3 C C C C C C C ml P R R V = 4-57 Equaio 4-57 a be ewie o leal displa he ukows ad he obseved vaiables as follows:

91 76 [ ] ] 3 [ 3 3 s s s s s s s s h h h h h h h h h h h h h h h h h h h h h h h h h h h h ml h h h g R R V = ρ 4-58 Noe ha Eq oais wo idepede vaiables, i.e., h ad h, ad oe depede vaiable, i.e., V. Thee ae fou ukow paamees o be deemied hough he uve fiig i Eq. 4-58, amel m,, s h, ad h. Oe he equaio fo he mea flow veloi, V, was deived, oe ould deemied he ukow paamees usig he expeimeal values of h ad h b usig he same uve-fiig mehod of deemiig ukows as i he ase of he Casso model. I he ase of he H-B model, hee wee fou ukow values, whih wee m,, s h, ad h. Noe ha he ukow values wee assumed o be osa fo he uve-fiig mehod. Usig Eq. 4-58, he deivaive of he veloi diffeee a be deemied heoeiall as follows:

92 77 [ ] ] 3 [ 3 3 s s s s s s s s h h h h h h h h h h h h h h h h h h h h h h h h h h h h ml h h h g R R V d h h d = = ρ 4-59 whee V is he mea flow veloi a he ise ube. I ode o exeue he uvefiig poedue, oe eeds o have a mahemaial equaio of V fo he H-B model. Eq ad 4-59 wee used fo he uve fiig of he expeimeal daa o deemie he ukow osas, i.e.,, m, s h, ad h. Noe ha Eq ould be appliable fo H-B fluids, Shea-hiig fluids, ad Newoia fluids egadless of he exisee of he ield sess. Afe ieaios fo he deemiaio of he ukows ha miimize he sum of he eo, wall shea ae ad visosi fo all daa pois a be alulaed as follows: [ ] s w h h h h ml gr = ρ γ&, 4-60

93 η w ρgr [ h h h ] s =. 4-6 Noe ha whe & γ L w h beomes appoximael zeo i.e., esoluio of , he H-B model is edued o powe-law model. I addiio, whe beomes, he mahemaial fom of he H-B model ields o Bigham plasi [Tae, 985], whih a be desibed as follows: τ m γ + τ = & B whe τ τ, 4-6 γ& = 0 whe τ τ, 4-63 whee τ ad γ& = shea sess ad shea-ae, espeivel τ = a osa ha is iepeed as he ield sess m B = a model osa ha is iepeed as he plasi visosi. Simila o he Casso model, he elaioship bewee wall visosi ad shea-ae usig he H-B a be expessed as follows: η = m & γ w w = m & γ w τ + & γ w ρgr h L + & γ w 4-64 whee m,, ad h ae he fluid popeies o be deemied usig he H-B model.

94 79 Capilla ube R l a Moio of a lidial fluid eleme wihi a apilla ube. τ πl Pπ Flow dieio P P π l b Fee-bod diagam of a lide of fluid. Fig Fluid eleme i a apilla ube a ime.

95 80 Capilla ube R Fig Veloi pofile of plug flow of blood i a apilla ube.

96 8 CHAPTER 5. CONSIDERATIONS FOR EXPERIMENTAL STUDY Chape 5 peses he issues ad osideaios i he expeimeal sud wih a saig apilla-ube heomee SCTR. Theoeial ad expeimeal issues ivolved i he visosi ad ield sess measuemes of fluids, suh as disilled wae, bovie blood, ad huma blood, ae examied. Seios 5., 5., ad 5.3 addess he majo assumpios i he sud ha ma affe he heologial measuemes i he SCTR: usead effe, ed effe, ad wall effe, espeivel. I addiio, seio 5.4 epos ohe possible faos ha ilude pessue dop a ise ubes, effe of desi vaiaio of blood, ad hixoopi effe. I seio 5.5, he empeaue osideaio fo he visosi measueme of huma blood i he SCTR duig a es is disussed. The empeaue of huma blood was heked o see if i ould be maiaied a a bod empeaue of 37 duig a visosi measueme. I seio 5.6, he sud o he effe of de oeaio o he visosi of disilled wae is peseed. The objeive of he sud was o see whehe o o he visosi of disilled wae ould be aleed b he addiio of de.

97 8 5.. Usead Effe I ode o make he assumpio of a quasi-sead flow behavio duig a es wih he SCTR, oe eeds o make sue ha he pessue dop due o he usead sae is egligibl small ompaed o ha due o he fiio hough a apilla ube. Disilled wae ad bovie blood wee aalzed fo he usead effes o he visosi measuemes of he fluids. Figue 5- shows he pessue dops due o boh usead flow ad fiio a he apilla ube obaied b usig Eqs. 4-4, 4-6, ad 4-8 i he ase of disilled wae. Usuall, he pessue dop due o he usead flow was less ha 3 Pa a he begiig of a es while pessue dop due o he fiio a he apilla ube was geae ha 50 Pa see Table 5-. As show i Fig. 5-, i he ase of bovie blood, he pessue dop due o he usead flow was also muh smalle ha ha a he apilla ube. Tpiall, he pessue dop due o he usead flow was less ha. Pa a he begiig of a es while pessue dop due o he fiio a he apilla ube was geae ha 700 Pa. Fuhemoe, as show i Table 5-, he magiude of he pessue dop due o he usead flow, Pusead, was alwas less ha % of ha of he pessue dop a he apilla ube, P, ove he eie shea-ae age. This ofims ha he assumpio of a quasi-sead sae ould be used fo he pese daa eduio poedue.

98 83 a Pessue dop Pa P usead Time s b Pessue dop Pa P Time s Fig. 5-. Pessue dop esimaio fo disilled wae. a Pessue dop due o a usead flow i a es wih disilled wae. b Pessue dop a a apilla ube i a es wih disilled wae.

99 84 Table. 5-. Compaiso of Pusead ad P fo disilled wae. Time s Pusead Pa P Pusead Pa 00 P %

100 85 a Pessue dop Pa P usead Time s b Pessue dop Pa P Time s Fig. 5-. Pessue dop esimaio fo bovie blood. a Pessue dop due o a usead flow i a es wih bovie blood. b Pessue dop a a apilla ube i a es wih bovie blood.

101 86 Table. 5-. Compaiso of ad P fo bovie blood. Pusead Time s Pusead Pa P Pusead Pa 00 P %

102 Ed Effe Figue 5-3 shows he flow-pae hages due o ed effes a boh a eae ad b exi of a apilla ube. Due o he sudde oaio ad expasio, addiioal pessue dops a ou a he boh eds. The mos ommo mehod used o esimae hese mio pessue dops is o use he loss oeffiie, defied as [Muso e al., 998]: K L, whih is K L PEd = 5- ρv so ha PEd = K L ρv 5- whee PEd is he pessue dop due o he ed effes ad V is he mea veloi a he apilla ube. Wih he pese expeimeal se-up, he veloi i he apilla ube was appoximael 6 imes geae ha ha i he ise ube. Theefoe, he eeg loss b seoda flow paes o eddies i he eae ad exi of he apilla ube ma appea o be sigifia i a high shea zoe. I he ase of a lamia flow, he loss oeffiie was epoed o be appoximael.4 [Feguso ad Kemblowski, 99]. Usig he value of he loss oeffiie, he pessue loss due o he sudde hages i geome, PEd, beame ol.79 Pa fo disilled wae ad.88 Pa fo bovie blood fo he maximum shea ae of 400 s - a a oespodig veloi of 0.04 m/s. I oas, he pessue dops aoss he apilla ube a he maximum

103 88 shea ae wee 45 Pa fo disilled wae ad 705 Pa fo bovie blood, idiaig ha he loss due o he seoda flow paes o eddies a boh eae ad exi ould be egleed. I hese ed egios see Fig. 5-3, he flow is hagig fom o o is pevious o fuue disibuio ouside he apilla ube. The legh of a ed egio is geeall a fuio of ube geome ad some dami paamees. The eae legh, he legh of ube equied o ahieve he full developed simple shea flow, a be esimaed b usig he followig equaio [Middlema, 968]: L e D Re 5-3 whee L e is he eae egio, D 0.8 mm is he ie diamee of a apilla ube, ad Re is he Reolds umbe. The maximum Reolds umbe fom a pial u i he pese sud was appoximael 8.6. The eae legh i he apilla ube used fo he pese sud was esimaed o be m usig he above equaio. Geeall, he aio of he eae legh o he apilla-ube legh, L e, should be he ode of 0.0 i ode o assume he effe of eae L legh o be egligible [Middlema, 968]. Sie he aio was i he pese sud, i is easoable o assume ha he eae legh effe is egligibl small.

104 89 a Sudde oaio a eae of a apilla ube b Sudde expasio a exi of a apilla ube Fig Flow-pae hages due o ed effes [Muso e al., 998].

105 Wall Effe Fahaeus-Lidqvis Effe Apa fom ed effes, ohe soues of eo i a apilla-ube heome should be osideed. The wall effe is oe of he mos impoa eo soues [Baes, 995; Missilis e al., 00]. Fo example, duig he flow of a suspesio, a hi lae of he solve whose visosi is lowe ha he visosi of he suspesio soluio ma be fomed ea he apilla wall, ad his wall effe beomes moe sigifia wih he deease i he apilla diamee [Dia, 98; Feguso ad Kemblowski, 99; Fug, 993]. I he ase of blood flow, as show i Fig. 5-4, he wall effe a be desibed as a ede fo RBCs o move owad he ee of he ube o blood vessel [Thomas, 96; Pia e al., 998]. The plasma-ih zoe ex o he solid wall, alhough ve hi, has a impoa effe o blood heolog. I ohe wods, he plasma-ih lae ea he wall mus affe he measueme of blood visosi b a isume wih a solid wall. The eduio i he RBC oeaio i his lae ea he wall deeases he measued value of blood visosi, esulig i eoeous visosi esuls. Thus, he appae visosi of whole blood deeases wih he deease i ube diamee. Howeve, as show i Fig. 5-5, he wall effe is epoed o be egligibl small whe he ube diamee is geae ha appoximael 0.4 mm [Fahaeus R ad Lidquis, 93; Diefass, 97; Dia, 98; Sadle e al., 990; Pies e al., 99] o 0.8 mm [Haes, 960; Babee, 97]. Noe ha he

106 9 appae visosi of blood deeases o a value lose o plasma visosi if he diamee of he apilla ube deeases below 0. mm [Beis e al., 970]. I ode o hek whehe o o he pese apilla ube diamee wih mm ID was lage eough o peve he wall effe, wo addiioal apilla ubes, whose diamees wee.0 mm wih legh = 30 mm ad. mm wih legh = 56 mm, wee used fo he visosi measuemes of bovie blood wih 7.5% EDTA a a oom empeaue of 5. As show i Fig. 5-6, he expeimes pefomed wih hee diffee apilla ubes wih ID of mm he sadad size of he SCTR,.0 mm, ad. mm povided almos ideial visosi esuls, ofimig ha he wall effe was egligibl small fo he pese apilla ube wih ID equal o mm.

107 9 Aeial wall Flow RBCs Cell-fee egio Fig Migaio of ells owad o he ee of lume wall effe.

108 93 Blood visosi P Tube diamee mios Fig Fahaeus-Lidquis effe due o he eduio i hemaoi i a ube wih a small diamee ad he ede of ehoes o migae owad he ee of he ube [Fahaeus ad Lidquis, 93; Diefass, 97; Dia, 98; Sadle e al., 990; Pies e al., 99]

109 94 Visosi P mm.0 mm. mm Shea ae s - Fig Visosi measuemes fo bovie blood wih hee diffee apilla ubes wih ID of mm wih legh = 00 mm,.0 mm wih legh = 30 mm, ad. mm wih legh = 56 mm.

110 Ohe Effes Pessue Dop a Rise Tube Sie he small diamee of a apilla ube was seleed o make sue ha he pessue dop a he apilla ube ould be domia, he pessue dops a ise ubes should be egligibl small. I has bee suggesed ha he pessue dop i he esevoi should be esimaed b usig a powe-law model as [Mashall ad Rile, 96; Mezge ad Kox, 965; Maosko, 994]: P L 5-4 P = + R 3 L R whee P = pessue dop i esevoi L = weed legh i esevoi R = adius of esevoi. The powe-law model is oe of he simples models, whih a be used o show o-newoia behavio of blood. Fuhemoe, he powe-law model geeall povides almos ideial visosi esuls wih boh Casso ad Heshel- Bulkle models a he shea aes bewee appoximael 300 ad 30 s -. The visosi esuls of blood obaied wih hose models will be disussed i Chape 6 i deail. Tpiall, he powe-law idex,, fo healh huma blood is a a bod empeaue of 37.

111 96 Cosideig he esevoi i Eq. 5-4 as he ise ubes i he pese ssem ad = 0.8 fo huma blood, oe a obai he followig elaio bewee pessue dops a apilla ad ise ubes usig Eq P 500 P 5-5 Theefoe, i he ase of huma blood, he sum of he pessue dops a ise ubes is appoximael 0. Pa a a shea ae of 30 s - while he pessue dop a he apilla ube is appoximael 93 Pa. I ould be agued ha Casso o Heshel-Bulkle model would have a lage pessue dop ha he powe-law model a a lowe shea ae. Theefoe, we wa o examie whehe o o he pessue dop a he ise ube is sill egligibl small fo Casso o Heshel-Bulkle model ompaed o ha a he apilla ube a a ve low shea ae b lookig a he uppe boud of he eo. I is ahe obvious ha he pessue dop a he ise ube a a low shea ae i.e., below 30 s - should be smalle ha 0. Pa. Le s oside a shea ae of s -. The pessue dop a he apilla ube a γ& = s - is appoximael 5 Pa. Theefoe, he pessue dop a he ise ube 0. is less ha.33% i.e., = Hee, i is easoable o assume ha he 5 pessue dops a he ise ubes a be igoed ompaed o he pessue dop a he apilla ube.

112 Effe of Desi Vaiaio I ode o measue he visosi of blood b usig he SCTR, oe eeds o kow he desi of blood. Howeve, i he ase of huma blood, i is o ve oveie o measue he desi of blood fo eah visosi measueme. Theefoe, he followig elaio [Chie e al., 987] bewee hemaoi H as a dimesioless faio ad blood desi ρ i kg/m 3 was used fo he esimaio of he desi of huma blood. ρ = H 5-6 Table 5-3 shows he desi of blood oespodig o hemaoi. I omal hemaoi oeaios, i.e., 35-45% [Guo ad Hall, 996], he desi vaiaio is less ha %, whih bael affes he visosi esuls of blood Aggegaio Rae of RBCs Thixoop As disussed i Chape, he hixoopi effe o blood visosi ma be moe sigifia a low shea aes ha high shea aes. I he SCTR, he shea ae vaies fom high appoximael 400 s - o low s - values. A leas 50 seods is equied duig a es o have he full aggegaed quiese sae a a shea ae ea s - [Gaspa-Rosas ad Thuso, 998]. I he visosi measueme of huma blood wih he SCTR, a pial es duaio i whih he shea ae deeased fom 0 o s - was loge ha 60 seods.

113 98 I is easoable o assume ha he 60-seod peiod is log eough o ause aggegaios if he aggegaios wee goig o ake plae. To fuhe validae he above assumpio, a loge apilla ube 5-mm legh was used. Sie he es duaio ieased i he loge apilla ube, a aioagula 7.5% EDTA was added o avoid he blood loig. As show i Fig. 5-7, he visosi esuls obaied b usig he loge apilla ube showed exelle ageemes wih hose obaied b usig he apilla ube wih 00-mm legh also wih 7.5% EDTA. Theefoe, i is oluded ha, i he pese ssem, he hixoopi effe of blood o he visosi measueme is egligibl small.

114 99 Table Desi esimaio Hemaoi % Desi kg/m

115 00 Visosi P mm 5 mm Shea ae s - Fig Visosi esuls fo huma blood wih wo diffee apilla ubes wih legh of 00 mm wih ID = mm ad 5 mm ID = mm.

116 Tempeaue Cosideaios fo Visosi Measueme of Huma Blood Fo uaduleaed huma blood, he empeaue of a SCTR was oolled duig he es a a bod empeaue of 37 C b usig peheaed disposable ube ses ad a heaig pad isalled iside he SCTR. I ode o hek whehe o o he empeaue of blood was maiaied a a bod empeaue, a speial U-shaped ube se was pepaed fo he expeime. Figue 5-8 shows he speial U-shaped ube se whih is basiall he same as a sadad U-shaped ube se exep hee addiioal hemoouples plaed a boh eds ad o he ouside sufae of he apilla ube. The empeaues of blood a hee pedeemied pois wee measued duig a visosi es. Figue 5-9 povides he empeaue measueme esuls fo huma blood duig he es. The empeaue of blood a he exi of he apilla ube was maiaied a appoximael 38, wheeas ha a he eae was gaduall ieased fom abou 36 a he begiig of he es ad eahed 37.5 a he ed of he es. Theefoe, i is easoable o sa ha he empeaue of huma blood flowig hough he apilla ube duig he es was maiaied a a bod empeaue of 37 wih ±.

117 0 Capilla Sufae Themoouple Exi Themoouple Eae Themoouple Themomee Fig Shemai diagam of a U-shaped ube se fo empeaue measueme.

118 03 Tempeaue Time s Eae Exi Capilla Sufae Fig Tempeaue measueme a a apilla ube duig a visosi es.

119 Effe of De Coeaio o he Visosi of Wae Ioduio Figue 5-0 shows a shemai diagam of a SCTR, whih osiss of wo hage-oupled devies CCDs ha ae posiioed veiall, wo ligh-emiig diodes LEDs, wo ise ubes ad a apilla ube, a sopok, ad a daa-aquisiio ssem. The esseial feaue i he SCTR is o use wo ise ubes, whee iiial fluid levels ae diffee: oe ise ube has a highe fluid level ha he ohe oe. Thus, a = 0, he fluid begis o fall fom he ise ube wih he high level o he ise ube of low level b gavi. Sie he flow ae depeds o he pessue head bewee he wo fluid levels, he flow ae gaduall deeases wih ime as he diffeee bewee he wo fluid level deeases wih ime. Sie he flow ae a be esimaed fom he ime ae of hage of he fluid level, oe a esimae boh flow ae ad pessue dop fom he measueme of wo fluid levels. The, oe a alulae shea ae fom he flow ae daa ad shea sess fom he pessue dop daa, espeivel. Fom he shea ae ad shea sess, oe a deemie he visosi of he liquid. Thus, he mos impoa expeimeal vaiable i he opeaio of he SCTR is he measueme of wo fluid levels i he ise ubes. As show i Fig. 5-0, he pese SCTR uses a opial deeo i.e. CCD sesos ad LED aa o measue he fluid-level vaiaios i he ise ubes. The opial deeo woks as follows: as a opaque fluid level ises i he ise ube, he opaque fluid bloks he passage of he ligh emied b he LED. Aodigl, he umbe of he CCD sesos ha eeive

120 05 he ligh fom he LED beomes smalle. Compue sofwae eods he hages i he umbe of CCD sesos ha eeive he ligh fom he LED. Sie he umbe of he CCD sesos ha do eeive he ligh fom he LED is diel popoioal o he fluid level, oe a deemie he fluid level. I ohe wods, he isaaeous fluid levels ae eoded i he fom of pixel umbes i.e., CCD sesos vesus ime i a ompue daa file hough a aalog-o-digial daa aquisiio ssem. The fluid level daa fom he wo ise ubes wee aalzed o deemie he visosi of he fluid. Theefoe, i is esseial o have a opaque fluid fo he pese SCTR opeaio so ha he ligh fom he LED a be bloked b he opaque fluid as he fluid level ieases, ad vie vesa. Of ouse, oe a use a lase ligh so ha a aspae fluid a be used as demosaed b Kim e. al. 000b. Howeve, he os of a SCTR usig suh a lase-based ssem beame pohibiivel expesive, makig suh a ssem eoomiall uaaive. I ode o use he SCTR usig CCD-LED aagemes fo he visosi measueme of a aspae fluid, oe ma add de o he fluid i ode o make he fluid opaque. Howeve, he addiio of a de o a aspae fluid ma ale he visosi of he fluid. Fuhemoe, he addiio of he de ma make a aspae Newoia fluid suh as wae a o-newoia fluid if he oeaio of he de is suffiiel lage [Kim ad Cho, 00]. Theefoe, he objeive of he sud is o ivesigae he effe of de oeaio o he visosi of disilled wae i he SCTR. Moe speifiall, he

121 06 pese sud plas o deemie he maximum oeaio of de below whih he visosi of he de-wae soluio is o aleed Expeimeal Mehod Alhough disilled wae is a Newoia fluid, he aqueous soluio of dewae ma exhibi he o-newoia haaeisis fo a suffiiel lage de oeaio. Thus, i ode o ivesigae he visosi haaeisis of a dewae soluio, he pese sud used a o-newoia model o edue expeimeal daa. I he pevious hapes, vaious o-newoia models have bee iodued fo he deemiaio of blood visosi wih he SCTR, whih ilude powe-law model, Casso model, ad Heshel-Bulkle H-B model. Howeve, i is o ve oveie o use he Casso model whe a fluid shows ol shea-hiig haaeisis wihou ield sess. The H-B model is edued o a powe-law model fo he ase of fluids wih o ield sess. Thus, i he pese sud, a powe-law model was used fo he visosi aalsis of he de-wae soluio. The poedue of daa eduio wih powe-law model will be disussed i Chape 6. Theefoe, ol he expeimeal esuls will be povided ad disussed i he ex seio.

122 Resuls ad Disussio I his sud, six diffee oeaios 0.5,,, 3, 4, ad 7% b volume of de wee used fo he visosi measueme of de-wae soluio a 5. The de i a liquid fom was puhased a a goe soe, whih was a vegeable de podued fom bad ame, MComik. Fo he validaio of he mehod o edue daa fo he SCTR, he visosiies of de-wae soluio wih diffee de oeaios wee ompaed wih well-aeped efeee daa fo wae a 5 [Muso e al., 998]. Figue 5- shows he vaiaios of boh powe-law ad osise idies of he de-wae soluio fo six diffee de oeaios. Boh idies wee deemied hough a uve-fiig mehod. Reagula smbols idiae he powelaw idex wheeas iagula smbols idiae he osise idex. As show i he figue, boh idies saed o va whe he amou of de used beame geae ha % b volume. Whe he de oeaio was less ha %, he powe-law idex was exal oe. The values of he osise idex fo 0.5%, %, ad % of de oeaio ases wee 0.890, 0.878, ad 0.888, espeivel. The disilled wae visosi, whih is give i he lieaue as a fuio of empeaue, was esimaed o be 0.89 P a 5 [Muso e al., 998; Kim e al., 00]. Whe he de oeaio was geae ha %, he powe-law idex deeased fom = a % o = 0.93 a 7%, wheeas he osise idex ieased fom k = 0.89 a % o k =.68 a 7%. The pese esuls idiaed ha he effe of de oeaio

123 08 o he visosi of he de-wae soluio was egligibl small whe he amou of de used was less ha % b volume. Figue 5- shows he visosi daa fo he de-wae soluio wih six diffee de oeaios. A a high shea-ae of 500 s -, eve wih high oeaios i.e., 3, 4, 7% of de, he esuls showed ha he effe of de oeaio o he visosi of wae was ve small. Howeve, a low shea-aes suh as ad 0 s -, he visosi of he de-wae soluio damaiall ieased wih ieasig de oeaio. I he pese expeime, he maximum oeaio of de, ude whih he visosi of he de-wae soluio did o hage, was appoximael % b volume. Compaed wih he efeee daa fo wae a 5 [Muso e al., 998], he es esuls obaied wih 0.5%, %, ad % of de oeaios gave less ha % eo i he eie shea-ae age.

124 09 LED aa CCD Rise ube Rise ube CCD Compue ssem fo daa olleio Tes fluid Capilla ube Thee-wa sopok Fig Shemai diagam of a saig apilla-ube heomee SCTR ssem.

125 0 Powe-law idex, Cosise idex, k Ps De oeaio % 0.6 Fig. 5-. Vaiaios of boh powe-law idex ad osise idex of de-wae soluio due o he effes of de oeaios.

126 Visosi P a 500 /s a 00 /s a 0 /s a /s De oeaio % Fig. 5-. Visosi daa fo de-wae soluio wih 6 diffee de oeaios a 5.

127 CHAPTER 6. EXPERIMENTAL STUDY WITH SCTR Chape 6 peses he esuls of visosi ad ield sess measuemes wih he saig apilla-ube heomee SCTR. Expeimeal ess wee pefomed wih mieal oil, disilled wae, bovie blood wih 7.5% EDTA, ad uaduleaed huma blood. Seio 6. povides he visosi esuls of boh mieal oil ad huma blood podued wih he SCTR wih peisio glass ise ubes usig he powe-law model fo daa eduio. Seio 6. gives he es esuls of disilled wae, bovie blood, ad huma blood obaied wih he SCTR wih plasi ise ubes. Casso ad Heshel- Bulkle models wee used fo daa eduio o hadle he ield sess of blood. Seio 6.3 epos he effe of he hee models o he visosi ad ieldsess measuemes of blood wih he SCTR as well as o he flow paes of blood suh as veloi pofile ad wall shea sess i a apilla ube. 6.. Expeimes wih SCTR wih Peisio Glass Rise Tubes The pese sud measued he visosi of uaduleaed blood a bod empeaue, 37. Blood is a fluid osisig pimail of plasma ad ells suh as ehoes, leukoes ad plaeles. Ehoes i.e., ed blood ells, RBC osiue he majoi of he ellula oe ad aou fo almos oe half of he

128 3 blood volume. The pesee of suh a high volume of ed blood ells makes blood a o-newoia fluid whose visosi vaies wih shea ae. Whole blood visosi deeases as shea ae ieases, a pheomeo alled shea-hiig haaeisis. I ohe wods, whole blood behavio ma be desibed usig a powe-law model, a Casso model, o a Heshel-Bulkle model. I he pese sud, he powe-law model was hose fo simplii. I ode o demosae he validi of he saig apilla-ube heomee, he visosi daa wee ompaed wih daa obaied usig a oe-ad-plae oaig visomee. Sie he oaig visomee podues ol 7 daa pois a elaivel high shea aes due o he oque equieme, he aua of he ew saig heomee a a low shea ae age was demosaed b ompaiso wih he visosi of a sadad-visosi oil a Newoia fluid fom Cao Isume Compa Sae Pak, PA Desipio of Isume Figue 6- shows a shemai diagam of he saig apilla-ube heomee, whih osiss of wo hage-oupled devies CCDs ha ae posiioed veiall, wo ligh emiig diodes LEDs, wo ise ubes ad a apilla ube boh made of peisio glass, wo sopoks, a asfe ube made of go, ad a ompue aquisiio ssem. The iside diamee of boh he asfe ad ise ubes

129 4 used i he pese ess wee 3 mm. The iside diamee ad legh of he apilla ube wee mm ad 00 mm, espeivel. The esseial feaue i he saig apilla-ube heomee is he use of a opial deeo i.e., CCD sesos ad LED aa o measue he fluid level vaiaios i he ise ubes, h ad h, eve 0.0 s. The isaaeous fluid levels wee eoded i a ompue daa file hough a aalog-o-digial daa aquisiio ssem i he fom of pixel umbes vs. ime. Sie pixels ae equal o mm, oe ould deemie he aual heigh hages i he ise ube wih a aua of mm Tesig Poedue Tpial ess ae odued as follows: The ssem was ued o ad oeed o a ompue. The sofwae o he ompue was exeued, ad ommuiaio wih he visosi measueme ssem was popel esablished. A ha poi, he ompue was ead o aquie daa fom he CCD sesos i he ssem. The expeimeal es u was iiiaed wih a veipuue o he paie usig a 9-gauge sailess seel eedle. Fesh blood was fis dieed fom he fis sopok o he seod sopok o olle blood io he sige. Abou 5 ml of blood was olleed i he sige fo ess wih a oe-ad-plae visomee Bookfield DV-III ad hemaoi measuemes, ad he sige was he emoved fom he ssem. Appoximael 0.5 ml of his fesh blood fom he sige was

130 5 immediael asfeed o he sample up of he Bookfield oaig visomee ha was maiaied a a osa empeaue of 37 b a wae bah oeed o he up. The visosi measuemes wih he oaig visomee wee ompleed wihi appoximael miue fom he ime whe he blood lef he huma bod. Blood loig apidl developed iside he oe-ad-plae es seio. The ae of blood loig wih ime iiall depeds o he homboi ede of a paiula idividual s blood. As soo as blood bega o lo, he oaig visomee flashed a EEEE sig idiaig a oveloaded oque, ad hus ess wee sopped. This usuall happeed wihi miues of he es. Duig he visosi measueme wih he Bookfield oaig visomee, hemaoi values wee deemied wih a miohemaoi eifuge Ieaioal Cliial Ceifuge. Immediael followig he emoval of he sige, he expeime wih he saig apilla-ube heomee was oiued wih he seod sopok ued o a posiio o allow blood flow o boh he apilla ube ad ise ube. Whe blood eahed a pedeemied heigh of 300 pixels i he ise ube, he seod sopok was shu o sop fuhe blood flow io he ise ube, ad he fis sopok was he ued o die blood flow io he ise ube up o a heigh of 000 pixels. A = 0, he daa aquisiio ssem was eabled, ad boh sopoks wee adjused o allow blood o flow fom he ise ube o ube as dive b he gavi head. Of oe is ha he iiial pixel diffeee of 700 was hose o podue he maximum shea ae of appoximael 400 s -. If a highe shea ae is desied, a iiial pixel diffeee geae ha 700 a easil be seleed.

131 6 Fo he pupose of alibaio, he pese sud used he saig apillaube heomee o measue he visosi of mieal oil, whih had a sadad Newoia visosi of 9.9 P a 5. I he ess wih huma blood ad mieal oil, he apilla ube ad majo poios of he asfe ube i whih es fluids wee auall flowig hough he apilla ube wee plaed i a wae bah maiaied a 37 ad 5, espeivel Daa Reduio wih Powe-law Model The mahemaial poedue fo daa eduio usig a powe-law model was disussed i Chape 4. The leas-squae mehod was used fo uve fiig of he expeimeal daa ad Eq. 4-8 i ode o deemie he powe-law idex,, ad he osise idex, m. A sadad sofwae pakage Exel-Solve, Miosof; see Appedix E, whih has a fomula kow as a Newo s mehod see Appedix F [Miosof Copoaio, ; Hais, 998; Joh, 998; Bow, 00], was used fo ieaios o deemie he values of ad m ha miimize he sum of eo see Eq The aalsis of daa eduio fo a mieal oil is iodued i Fig. 6-. Figue 6-a shows boh expeimeal values of θ ad heoeial values of θ ha wee obaied wih iiial guesses of he wo ukows, wheeas Figue 6-b shows he uve-fiig esul afe ieaios o miimize he sum of eo. The iiial guesses fo ad m wee 0.8 ad 8 P s -, espeivel, i he ase of he mieal

132 7 oil see Fig. 6-a. The esulig values of ad m wee deemied o be ad 9.9 P s -, espeivel, b he ieaios usig he Exel-Solve. The aalsis of daa eduio fo huma blood is show i Fig Fo he huma blood ase, iiial guesses of he wo ukows of ad m wee 0.8 ad 6 P s -, espeivel see Fig. 6-3a. Afe ieaios o miimize he sum of eo, he ukows, ad m, wee deemied o be 0.83 ad 9.7 P s -, espeivel see Fig. 6-3b. The iiial guesses ad esulig values of, m, ad boh mieal oil ad huma blood wee epoed i Table 6-. h = fo Resuls ad Disussio Boh mieal oil ad uaduleaed huma blood wee used i he pese sud. The fome was speiall odeed as a ded visosi-sadad fluid i.e., 9.9 P a 5 fom Cao Isume Compa Sae Pak, PA, ad he lae was obaied fom doos. Fo ompaiso pupose, he visosi of he huma blood was also measued b usig a oe-ad-plae oaig visomee Bookfield model DV- III a 37. The oaig visomee used i he pese sud had a LV-pe spig oque wih a CP-40 spidle. I ode o maiai he pese empeaues, a wae bah PolSiee model LS-M was used, whih oolled he empeaue wih a aua of 0.. Figues 6-4 ad 6-5 show es esuls obaied wih he mieal oil a 5. Figue 6-4 shows he fluid level vaiaios i he ise ubes, h ad h. Boh

133 8 fluid levels ovege gaduall fom he iiial fluid level diffeee ad eveuall eah a equilibium fluid level. I he ase of mieal oil, 4.5 mm of a iiial fluid level diffeee was used o esue ha visosi measuemes a a low shea ae age wee auae. I is of oe ha, fo mieal oil, h = was foud o be zeo. Figue 6-5 shows visosi esuls fo he mieal oil a 5 obaied wih he SCTR. The powe-law idex of he mieal oil was deemied o be.0 b a ompue pogam Exel-solve, ofimig ha i was a Newoia fluid. Based o he pese visosi measueme mehod, he visosi of he mieal oil was foud o be bewee 9.86 ad 9.9 P a 5, whih was a 0.5% diffeee i he whole age of shea aes fom he sadad visosi of 9.9 P a he same empeaue. Figue 6-6 shows heigh vaiaios i eah ise ube as a fuio of ime fo fesh huma blood a 37. I he ase of huma blood, abou 58 mm of iiial fluid level diffeee was used fo he visosi measueme so ha oe ould obai he auae visosi of huma blood ove a wide shea ae age as low as s -. I ode o fiish a es wihou usig aioagulas, he es should be ompleed wihi 3-4 miues. Ohewise, blood ma begi o lo. I he pese sud, oe es u ook less ha miues. Fo huma blood, he eds of fluid level vaiaios wee ve simila o hose fo mieal oil. Howeve, h = fo huma blood was o zeo bu a fiie value, whih depeded o he idividual doo. The miimum ad maximum values of h = wee foud o be 3.86 mm ad 6. mm, espeivel,

134 9 amog 8 doos. These values of blood ha esul i he ield sess. h = epese he hixoopi haaeisis of Figue 6-7 shows he visosi of uaduleaed huma blood a 37, whih was measued wih boh he SCTR ad he oe-ad-plae oaig visomee RV. Closed ile smbols idiae visosi daa measued wih he SCTR while iagle smbols idiae hose measued wih he RV. The visosi of he uaduleaed huma blood measued wih he pese SCTR was based o a alulaio mehod ha deemied he powe-law idex,, ad osise idex, m. I he ase show i Fig. 5, he values of ad m wee 0.88 dimesioless ad 9.67 P s -, espeivel. Compaed wih he measued daa usig he RV, he pese es esuls fom he SCTR gave exelle ageeme wih hose measued b he RV i.e., less ha 5% diffeee i a shea ae age bewee 30 ad 375 s -. Howeve, as he shea ae deeased below 30 s -, he RV was o eommeded b Bookfield fo he measueme of blood visosi. Moe speifiall, he shea sess should va fom a miimum of 0% o 00% of he full age of he oque seso used i he oaioal pe visomee a a give shea ae fo easoabl auae visosi measuemes [Bookfield, 999]. Theefoe, he miimum shea ae a whih he RV ould be used fo he visosi measueme of huma blood was 30 s -. Blood loig i he RV was he ohe easo ha oe ould o obai moe ha 7 daa pois. Oe ould see he effes of blood loig o visosi as esig ime passed beod miue wih he RV. Sie ol 0.5 ml was used fo he RV es, he blood oa aea wih he sufae of he oe-ad-plae was muh bigge

135 0 ha ha i he ase of he SCTR, a odiio ha migh have aused apid blood loig. Figue 6-8 shows he visosi of uaduleaed huma blood fo wo diffee doos a 37, whose hemaois wee H = 4 ad Fuhemoe, huma blood fom 8 doos was esed fo visosi measuemes i he pese sud. Eve esul usig SCTR gave good ageeme wih ha fom he RV a high shea aes bu had a diffee slope wih espe o shea ae idividuall. The visosi fo he ase wih H = 46.5 was osisel geae ha ha fo he ase wih H = 4. The diffeee bewee he wo visosi daa was ve small a high shea aes geae ha 300 s - wheeas he diffeee was sigifia i.e., geae ha 00% a a low shea age, idiaig he sigifiae of low shea visosi daa. I fa, i is well kow ha slip a he wall ous i he flow of wo-phase ssems beause of he displaeme of he dispese phase awa fom solid sufaes [Baes, 995; Pia e al., 998a, 998b]. I he ase of blood, a sigifia amou of slip appeas a low shea aes whe he size of RBC ed blood ells is elaivel lage ompaed o wall oughess. Fo a smooh geome like a glass ube, howeve, he slip effe begis o be osideable fom as low as 0.5 s - [Pia e al., 998a]. Theefoe, whole blood ha was used i he pese sud did o show lage slip effes sie he lowes shea ae daa used was s -. I ode o ge eliable visosi daa below 0.5 s -, i ma be eessa o use a ough sufae apilla.

136 LED Aa CCD CCD Rise ube Rise ube Compue ssem Tasfe ube Fis sopok Blood fom vei Blood Wae bah Seod sopok Capilla ube Fig. 6-. Shemai diagam of he saig apilla-ube heomee wih peisio glass ise ubes.

137 6 θ mm Expeimeal daa Theoeial daa = 0.8 m = 8 P s Time s a Wih iiial guess values 6 θ mm 8 4 Expeimeal daa Theoeial daa = m = 9.9 P s Time s b Wih fial esulig values Fig. 6-. Cuve-fiig poedue wih powe-law model fo mieal oil.

138 3 60 θ mm 40 0 = 0.8 m = 6 P s - Expeimeal daa Theoeial daa Time s a Wih iiial guess values 60 Expeimeal daa 40 θ mm 0 Theoeial daa = 0.83 m = 9.7 P s Time s b Wih fial esulig values Fig Cuve-fiig poedue wih powe-law model fo huma blood.

139 4 Table. 6-. Compaiso of iiial guess ad esulig value usig powe-law model. Disilled Wae Huma Blood Iiial Guess = 0.8 m = 8 P s - h = 0.03 mm = = 0.8 m = 6 P s - h = = 3 mm Resulig Value = m = 9.9 P s - h = = 0.07 mm = 0.83 m = 9.7 P s - h = = 3.86 mm

140 5 60 Heigh mm 40 0 Rise ube Rise ube Time s Fig Heigh vaiaio i eah ise ube vs. ime fo mieal oil 9.9 P visosisadad oil.

141 6 Visosi P 0 8 SCTR Shea ae s - Fig Visosi measueme fo mieal oil a 5 wih a saig apillaube heomee SCTR.

142 7 Heigh mm Rise ube Rise ube Time s Fig Heigh vaiaio i eah ise ube vs. ime fo huma blood a 37.

143 8 00 Visosi P 0 Hemaoi : 40.5 SCTV RV Shea ae s - Fig Visosi measueme log-log sale fo huma blood a 37 wih oaig visomee RV ad saig apilla-ube heomee SCTR.

144 9 00 Visosi P 0 Hemaoi : 46.5 SCTV RV Hemaoi : Shea ae s - Fig Visosi measueme log-log sale of uaduleaed huma blood a 37, measued wih saig apilla-ube heomee SCTR ad oe-ad-plae oaig visomee RV, fo wo diffee doos.

145 Expeimes wih SCTR wih Plasi Rise Tubes A ew U-shaped saig apilla-ube heomee SCTR has bee developed fom he oep of a oveioal apilla-ube visomee. I geeal, he apilla-ube visomee is a aaive ehique fo seveal easos. The basi isume is elaivel iexpesive, eas o osu ad simple o use expeimeall. Tempeaue ool is elaivel eas. The flow i a apilla ube mos losel simulaes he blood flow i phsiologial odiios ompaed wih he flows i oaig visomees ad fallig-obje visomees. Mos of all, sie he apilla-ube visomee uses he gavi as he divig foe, i does o equie peiodi alibaio of a ompoes. Howeve, sigifiae of ed effe, wall effe, ad sufae-esio effe should be aefull osideed. The ed ad wall effes a be made egligibl small b seleig appopiae dimesios fo he apilla ad ise ubes. Howeve, ulike he ase of he SCTR wih peisio glass ise ubes, he effe of he sufae esio is a uique ad iial fao i usig U-shaped disposable ube ses. Sie iexpesive disposable apilla-ise ube ses should be used fo liial appliaios, i ma o be eas o sil ool he sufae quali of ise ubes wihi a eai limi. Theefoe, he effes of he sufae esio a he ise ubes as well as he popeies of a esig fluid had o be osideed i he visosi ad ield sess measuemes wih he SCTR. The esisae assoiaed wih ai-liquid iefaes i plasi ise ubes of a small diamee i he SCTR a be a sigifia pa of he pessue head applied o

146 3 he SCTR, paiulal a low shea aes [Jaobs, 966; Madles, 969; Eifeld ad Shmelze, 98]. The meisus esisae depeds o he sufae esio of he fluid-ai iefae ad o he eipoal of he ieal adius of he ise ube. Thoughou he developme of a U-shaped saig apilla-ube heomee oep, he fous has bee o how o isolae he effes of sufae esio ad ield sess i obaiig low-shea-ae visosi fo o-newoia fluids like blood. This sud aemped o measue he visosi of uaduleaed blood a a bod empeaue of 37. I he pese sud, boh Casso ad Heshel-Bulkle models wee seleed fo he visosi ad ield sess measuemes of blood sie boh models have a ield sess em Desipio of Isume Figue 6-9 shows a phoogaph of he SCTR wih plasi ise ubes, whih osiss of wo hage-oupled devies CCD ad CCD ha ae posiioed veiall, wo ligh-emiig diodes LEDs, wo ise ubes made of ali plasi ad a apilla ube made of glass, a sopok, ad a daa-aquisiio ssem. The iside diamee of he ise ubes used i he sud was 3. mm. The iside diamee ad legh of he apilla ube wee mm ad 00 mm, espeivel. The small diamee of he apilla ube, ompaed wih ha of he ise ubes, was hose o esue ha he pessue dop a he apilla ube was sigifial geae ha hose a he ise ubes ad oeig fiigs.

147 Tesig Poedue Tess wih disilled wae ad bovie blood wee pefomed a he oom empeaue of 5. Rise ube was fis filled wih he es fluid o he pedeemied heigh of appoximael 550 pixels b usig a sige. Oe he desied level was eahed, he sopok was ued o a posiio o allow es fluid o flow o he apilla ube. Whe he fluid eahed he pedeemied heigh of 00 pixels i ise ube, he sopok was shu o sop fuhe fluid moveme io ise ube. Nex, he sige was emoved fom he SCTR ssem, ad he he sopok was ued o allow fluid o move fom ise ube o ise ube b gavi. As show i Fig. 6-9, wo CCD sesos wee used: oe loaed a he lowe lef side ad he ohe loaed a he uppe igh side. The diffeee bewee he loaios of he wo CCD sesos was 500 pixels, a umbe ha was ake io aou i he heigh measuemes. Fo he pupose of ompaiso, appoximael 0.5 ml of bovie blood fom he sige was immediael asfeed o a oe-ad-plae es up of a oaig visomee Bookfield model DV-III wih LV-pe spig oque wih CP-40 spidle ha was maiaied a a osa empeaue of 5 b a wae bah oeed o he up. Fo uaduleaed huma blood, he empeaue of he SCTR was oolled duig he es a a bod empeaue of 37 b usig peheaed disposable ube ses ad a heaig pad show i Fig. 6-0 isalled iside he SCTR. Afe he empeaue i he SCTR was sabilized, he visosi measueme was iiiaed wih a veipuue usig a 9-gauge sailess seel eedle. Abou 5 ml of

148 33 exa blood was olleed fo hemaoi measuemes, whih wee deemied wih a miohemaoi eifuge Ieaioal Cliial Ceifuge fo boh bovie blood ad huma blood. Visosiies of disilled wae a Newoia fluid, bovie blood oaiig 7.5% EDTA, ad uaduleaed huma blood wee measued ove a age of shea aes. Beause he CCD seso equies a opaque fluid, de was added o he disilled wae. The amou of de used fo disilled wae was less ha % oeaio b volume, ad he de-effe o he visosi of disilled wae was egligibl small a his oeaio. Bovie blood was puhased fom Lampie Biologial Laboaoies, I., ad huma blood was obaied fom wo healh male doos who wee 9 ad 5 eas of age. Fo ompaiso puposes, a efeee value was used fo he disilled wae while he visosi of he bovie blood was idepedel heked b usig he oe-ad-plae oaig visomee Daa Reduio wih Casso Model The fluid level daa fom he wo ise ubes wee aalzed o deemie he visosiies of disilled wae a Newoia fluid ad blood a o-newoia fluid. I ode o measue blood visosi usig a U-shaped SCTR, oe eeds o isolae he effes of boh sufae esio ad ield sess o he visosi of blood. The deails of mahemaial poedue fo uve-fiig usig he Casso model have alead

149 34 bee iodued i Chape 4. Thus, i his seio, he poedue o deemie he ukow values fo he Casso model is disussed Cuve Fiig As disussed i Chape 4, hee ae hee ukow values, i.e., k, hs, ad h, o be deemied hough he ieaios usig he same sofwae pakage Exel Solve; see Appedix E used i he powe-law model ase. The leas-squae mehod was used fo uve fiig of he expeimeal daa ad Eq. 4-4 o obai he hee ukows ivolved i he Casso model. The poedue of daa eduio fo disilled wae is show i Fig. 6-. Figue 6-a shows mea-veloi vaiaios a a ise ube whih wee obaied expeimeall ad heoeiall. I he ase of heoeial values, he iiial guesses fo he hee ukows wee used o esimae he values. I Fig. 6-b, he uvefiig esuls afe ieaios o miimize he sum of eo ha wee alulaed b Eq. 4-4 ae show. The iiial guesses ad fial values of k, hs, ad h fo disilled wae ae show i Table 6-. Figues 6- ad 6-3 show he uve-fiig poedues fo huma blood obaied fom wo doos. As show i Table 6-, he same iiial guesses of he hee ukows wee used fo he wo diffee bloods. Howeve, he esulig values of he hee ukows i he Casso model fo he wo doos wee ve diffee, validaig he pese uve-fiig mehod.

150 Resuls ad Disussio Figues 6-4 ad 6-5 show es esuls obaied wih disilled wae a 5. Figue 6-4 shows he fluid-level vaiaios i he wo ise ubes, h ad h. Boh fluid levels oveged gaduall fom he iiial diffeee o a equilibium sae. Eve fo he disilled wae, h = was o zeo due o he diffeee i he sufae esio bewee he wo ise ubes. Uless he weig odiios of he liquid-solid iefae a he wo ise ubes ae exal same, he sufae-esio diffeee alwas exiss. Figue 6-5 shows visosi esuls fom wo ess fo disilled wae a 5 obaied wih he SCTR, ogehe wih he efeee daa fo ompaiso. The values of of hs wee deemied o be appoximael 4 mm fo boh ess wheeas he values h wee deemied o be zeo b a ompue pogam Miosof Exel-solve, validaig he daa eduio poedue ivolvig he ield sess. Based o his visosi measueme mehod, he visosi of he disilled wae was foud o be bewee ad P a 5. The solid lie idiaes he visosi of he disilled wae alulaed b usig he so-alled Adade s equaio. Sie he wae visosi daa ae give i he lieaue as a fuio of empeaue, he exa visosi of wae a 5 was alulaed usig he Adade s equaio [Muso e al., 998]: B T µ = D e 6-

151 36 whee D ad B ae give as mpa s ad K, espeivel, fo wae i a empeaue age bewee 0 ad 30. Based o Eq. 6-, he wae visosi was esimaed o be 0.89 P a 5. The es esuls obaied wih he SCTR gave less ha % eo i he eie shea ae age, validaig he es mehods ad daa eduio poedue. Thus, i is oluded ha i is exemel impoa o oside he effe of he sufae esio o he visosi measueme usig a gavi dive, U-shaped apilla-ube ssem. Figue 6-6 shows heigh vaiaios a he wo ise ubes as a fuio of ime fo bovie blood wih 7.5 % EDTA a a oom empeaue of 5. The eds of fluid-level vaiaios fo he bovie blood wee ve simila o hose fo he disilled wae. As expeed, h = fo he bovie blood was o zeo bu a fiie value ha is slighl geae ha ha fo he disilled wae. The heigh diffeee due o sufae esio, hs, ad he heigh diffeee due o ield sess, h, wee deemied o be i he age of mm ad mm, espeivel. The hemaoi of he bovie blood was measued o be 35 pee. Figue 6-7 shows he visosi of he bovie blood wih 7.5% EDTA a 5, whih was measued wih boh he SCTR idiaed b iles ad iagles ad he oaig visomee RV; idiaed b diamods. Compaed wih he measued daa usig he RV, he es esuls fom he SCTR gave exelle ageeme wihi 3% i a shea ae age bewee 5 ad 300 s -. Howeve, as he shea ae deeased below 5 s -, he visosi daa measued fom he RV seemed o be ioe. Moe speifiall, he oque fo visosi measuemes wih he RV should be geae ha 0% of he full sale as suggesed b Bookfield a a give shea ae fo

152 37 easoabl auae visosi measuemes. I he ase of he bovie blood, he miimum shea ae ha Bookfield eommeded, based o he 0% ieio, was appoximael 30 s -. I oas, he SCTR gave a osise visosi measueme ove a age of shea aes as low as a shea ae of s -. Relaed o he ueai i measuig blood visosi a low shea aes, wall slip is a issue. Sie he miimum shea ae i his sud was s -, as disussed ealie, oe ould assume ha he slip effe was egligibl small [Pia e al., 999a]. Figues 6-8 ad 6-9 show es esuls of fesh, uaduleaed huma blood a a bod empeaue of 37. The es was ompleed wihi -3 mi o avoid blood loig, whih migh have aleed he visosi of he blood. Figue 6-8 shows heigh vaiaios i he wo ise ubes as a fuio of ime fo he fesh huma blood a 37. The value of depeded o idividual doos. The values of be appoximael 8.5 ad 9.6 mm, espeivel. h = fo he fesh huma blood had a fiie value, whih hs fo doos ad wee foud o I he use of he SCTR, wo pheomea of paiula impoae should be poied ou i egads o liial hemoheolog: oe is he a-ove effe ad he ohe is he sufae esio effe. Fis, a he ompleio of a measueme, a hi lae of he es blood sample was alwas eaied o he ube wall, uless he ube was ve aefull washed ad died. This esidual lae a be alled a-ove. Hee, fo uaduleaed blood-visosi measuemes, i was eessa o use disposable apilla-ise ube ses o avoid he a-ove pheomeo. Seod, he diffeee bewee sufae esios a he wo ise ubes ma va fom oe

153 38 disposable se o aohe. Alhough he ise ubes wee made of he same maeial ali plasi, he sufae esios wee slighl diffee fom se o se. The values of h epeseig he effe of he ield sess fo doos ad wee foud o be 0.7 ad 0. mm, espeivel. These esuls wee osise wih hemaoi daa fo doos ad, whih wee 4 ad 35 pee, espeivel. Doo a phsiia paies heapeui bloodleig peiodiall, whih explais wh he hemaoi of doo was uusuall low. I is of oe ha he value of epeses he hixoopi haaeisis of fesh huma blood ha is losel elaed o he ield sess. h A hixoopi blood exhibis a high visosi whe fis sheaed fom es. The visosi oiues o deease as sheaig oiues. Thixoop is usuall a esul of he paial desuio, b sheaig, of he ieal liquid suue. While a es, he ieal suue made of suspeded ells ad plasma ma fom o eae aggegaios of RBCs, fo example. This pheomeo is geeall efeed o as suue visosi. I fa, he pheomeo of RBCs aggegaios a low shea aes is well kow bu o well udesood so fa. The foes leadig o aggegaios ae weak, so if a sample of omal blood is subjeed o ieasig shea ae, he aggegaes pogessivel beak up ad ae geeall moodispesed a a shea ae geae ha 0 s -. Howeve, i is impoa o oe ha hee ould be wo kids of ield sesses: a sa-up ield sess ad a soppig ield sess [Cho ad Choi, 993]. The ield sess deemied i his sud was he soppig ield sess, a impoa pheomeo i liial hemoheolog ad sudies of adiovasula disease. I he

154 39 visosi measueme wih whole blood, a pial es duaio i whih he shea ae deeased fom 0 o s - was loge ha 60 seods. I is easoable o assume ha he 60-seod peiod is log eough o ause aggegaios if he aggegaios wee goig o ake plae. Figue 6-9 shows he visosiies of he wo doos a 37 measued wih he SCTR. The visosiies fo doo wee sigifial lowe ha hose fo doo due o he diffeee i hemaoi. I addiio, he visosi uve fo doo was flae ha ha fo doo sie doo had a smalle value of h ad a lowe hemaoi. Figue 6-0 shows shea sess vaiaios agais shea ae fo boh doos. Like he ase of visosi, shea sess fo doo was sigifial lowe ha ha fo doo due o diffeees i hemaoi ad ield sess. The values of he ield sess deemied fom Casso model wee appoximael 4 mpa ad 5 mpa fo doo ad, espeivel. The diffeee bewee he visosi daa ieased as he shea ae deeased idiaig ha he visosi was moe iflueed b hemoheologial paamees suh as hemaoi ad ield sess a low shea aes ha a high shea aes Daa Reduio wih Heshel-Bulkle H-B Model The deailed mahemaial poedue fo uve-fiig usig a Heshel- Bulkle H-B model was povided i Chape 4. As i he ase of he Casso model, he H-B model a also hadle he ield sess of blood. Howeve, i he daa

155 40 eduio wih he H-B model, hee ae fou ukow values o be deemied hough he uve-fiig ehique, wheeas he Casso model has ol hee ukows. The fou ukow values, i.e., m,, hs, ad h, ae o be deemied hough a leas-squae mehod usig he same sofwae pakage Exel-Solve, Miosof; see Appedix E ha uses he fomula of Newo s mehod. I he poess of uve fiig, Eq was used fo heoeial values. I he ase of he H-B model, he expeimeal daa of bovie blood wih 7.5% EDTA wee used o validae he mehod of daa eduio. Figue 6-a shows mea-veloi values a a ise ube whih wee obaied boh expeimeall ad heoeiall. I he ase of heoeial values, he iiial guesses fo he fou ukows, whih ae show i Table 6-3, wee used. I Fig. 6-b, he uve-fiig esuls afe he ieaios o deemie he fou ukows ae show. The iiial guesses ad fial values of m,, h hs, ad fo bovie blood wih 7.5% EDTA usig he H-B model ae show i Table 6-3. Figue 6- shows he visosi of he bovie blood wih 7.5% EDTA a 5, whih was measued wih he SCTR. Thee oseuive ess wee pefomed wih bovie blood. As expeed, he H-B model also podued ve auae ad epeaable esuls. The fial values of fou ukows fo eah es ae epoed i Table 6-4. The effes of osiuive models o he visosi ad ield sess measueme of blood will be fuhe disussed i he ex seio.

156 4 CCD-LED aas Rise ube Rise ube Tes Fluid Sopok Capilla ube Fig Piue of a SCTR wih plasi ise ubes.

157 4 Rheomee Ssem Heaig Pad Fig Heaig pad fo a es wih uaduleaed huma blood.