SURFACE TENSION OF LIQUID MARBLES, AN EXPERIMENTAL APPROACH

SURFACE TENSION OF LIQUID MARBLES, AN EXPERIMENTAL APPROACH Tina Abatan, Wei Shen 1 1 Austalian Pulp and Pape Institute, Depatment of Chemical Engineeing, Monash Univesity, Clayton, 3800, Austalia, Wei.shen@monash.edu ABSTRACT The capillay ise technique has been used to expeimentally study the suface tension of liquid mables fomed by encapsulating wate doplets with polytetafluooethylene (PTFE) powde of 1, 35, and 100 µm paticle size. In a typical expeiment, a glass capillay tube was inseted into a wate mable to measue the capillay ise of the wate. The Laplace pessue exeted by the wate mable was diectly measued by compaing the capillay ise data fom the mable and fom a flat wate suface in a beake. An equation to calculate the wate mable suface tension based on the Muma s model is then poposed. It is also justified how the capillay ise measuements the liquid mable suface tension does not equie the wate contact angle with any solid suface to be consideed; which theefoe makes a simple but efficient method fo detemining liquid mable suface tension. A discussion on the natue and the ealistic magnitude of liquid mable suface tension is offeed. Intoduction Liquid mable is an inteesting intefacial phenomenon fist epoted by Aussilous and Quéé a decade ago. (Aussillous and Quee, 2001) This phenomenon involves liquid doplets being enwapped by hydophobic powde paticles that adhee to the liquid doplet, foming a powde-coated liquid sphee which can oll like a mable on a solid suface. Because of the hydophobic coating on the liquid mable suface, a liquid mable does not wet the suppoting suface, solid o liquid. Eve since the discovey, liquid mables have dawn much attention towads thei undelying science (Aussillous and Quéé, 2006, Mahadevan, 2001, McEleney et al., 2009, Bomashenko et al., 2008), popeties (Eshtiaghi et al., 2009, Nguyen et al., 2010b, Newton and et al., 2007, McHale et al., 2008, McHale et al., 2006) and applications (Xue et al., 2010, Tian et al., 2010, Bomashenko et al., 2010b, Gao and McCathy, 2007, Bhosale et al., 2008, Zhao et al., 2010, Bomashenko and Bomashenko, 2011). Recently, futhe new applications have been epoted on using liquid mables to build mico-pumps (Bomashenko et al., 2010a) and miniatue eactos (Xue et al., 2010). These epots spak a enewed inteest in the undestanding of the intefacial popeties of liquid mable, such as its suface tension o effective suface tension (Bomashenko et al., 2009a, Bomashenko et al., 2009b, Aussillous and Quéé, 2006), which can geatly influence phenomena such as the fomation of liquid mables using low suface tension liquids (Xue et al., 2010), and using liquid mables as micopumps. The effective suface tension of the liquid mable is a tem descibing the suface tension of the liquid doplet, unde the influence of coated powde paticles. A simplistic explanation on the oigin of liquid suface tension is that the molecules at the liquid-ai inteface expeience unbalanced attactive intemolecula foces esulting in a net pulling

foce towad the bulk of the liquid. In case of a liquid mable, howeve, a significant faction of the liquid/ai inteface is coveed by the powde paticles and becomes a liquid/solid inteface. (Nguyen et al., 2010b) Also, although showing no influence in macoscopic scale, the powde paticles on liquid suface may significantly change the cuvatue of the liquid dop suface at the micoscopic scale, since the paticles ae not wettable by the liquid and ae theefoe floating on the liquid suface, making mico indents on the liquid suface. Also, the inteactions between hydophobic powde paticles foced by the hydophilicity of the liquid coe may affect the net balance of foces on the shell of a liquid mable (Nguyen et al., 2010a). These foces may alte the suface tension of the liquid and causes the mable to have an effective suface tension that may o may not be the same as the suface tension of the coesponding coe liquid. (Aussillous and Quéé, 2006) Thee have been few epots in the liteatue on the measuement of the effective suface tension of liquid mables. (Aussillous and Quéé, 2006, Bomashenko et al., 2009a, Bomashenko et al., 2009b) Methods employed in those studies geneally include the mathematical cuve fitting of the mable shape, the chaacteization of the esponse of liquid mable to vibation, and the measuement of liquid mable puddle height. (Bomashenko et al., 2009b) The fact that the Young Equation was used in those appoaches equies the assumption that the liquid mable has an imaginay liquid/solid inteface with the suppoting substate, although thee is no contact between the encapsulated liquid inside the mable and the substate due to the pesence of the hydophobic powde on the mable shell. Hence, it is necessay to exploe novel methods that do not ely on the exploitation of the imaginay liquid/solid contact line o contact angle. Theoetical consideations The undelying theoy behind this epot is based on the fact that liquid mables can be egaded as a nea-spheical shell holding a finite esevoi of liquid, and the nea-spheical wate/powde inteface of the mable shell exets a Laplace pessue that can be measued. Theefoe, when a capillay tube of an intenal adius is inseted vetically into a flat wate suface in a beake, a capillay ise (h) of wate can be obtained in the tube: 2γ cosθ ρgh = 0 Inteestingly, accoding to Muma (Mamu, 1988), if this capillay is inseted into a spheical wate dop of adius R, assuming that R does not change as wate goes fom the doplet into the tube, the wate capillay ise in the tube is highe than that fom the flat wate suface. This additional capillay ise ( h) is caused by the cuved suface of the wate doplet. Muma poposed the following equation to descibe the capillay ise of the above mentionedsystem: 2γ 2γ cosθ + ρg( h + h ) = 0 R e Whee γ is the liquid suface tension, θ is the liquid/capillay wall contact angle, ρ and g ae the liquid density and the gavitational constant, Re and h ae the equilibium values of the adius of the spheical liquid dop and the height of capillay ise, espectively. In eal situation when the adius of the dop is geate than the capillay length of the liquid, (1) (2)

defomation of the liquid dop will occu due to gavity. Equation 2 must be evised to include the defomation: γ( 1 + 1 2γ cosθ ) + ρg(h + h) = 0 1 2 Whee 1 and 2 ae the pincipal adii of the cuvatue of the dop suface. Whilst 1 and 2 can be measued by mathematical techniques, a simple expeimental appoach of using the hydaulic adius, defined by Eq. 4, can be employed to descibe the cuvatue of the dop suface. 1 m = ( 1 1 + 1 2 ) Substituting Eq.4 into Eq.3 gives Eq.5. Equation 5 can then be used to expeimentally measue the m value of a doplet, by using a liquid of known suface tension and a capillay of known popeties. γ( 1 m ) + 2γ cosθ ρg(h + h) = 0 Muma s equation (Eq.2) applies to a doplet of liquid, but it can be easily adapted to measue the effective suface tension of liquid mable by consideing the expeimental convenience offeed by Eq. 5. In this study the capillay ise method was used to detemine the effective suface tension of wate mables encapsulated by PTFE powdes. The esults obtained using the capillay ise methods also evealed the natue of wate mable effective suface tension made using inet hydophobic powde paticles. Discussion on the effects of powde paticle size on the mable suface tension is offeed. Expeimental Section Mateials. PTFE powdes of 100 µm, 35 µm, and 1 µm nominal paticle sizes wee obtained fom Sigma-Aldich. Millipoe wate was used in all the expeiments. Capillay tubes of intenal adius of 0.45 mm and wall thickness of 0.1 mm wee used in all the expeiments. Mable fomation. A PTFE powde bed was pepaed in a Peti dish. Doplets of wate of the contolled sizes wee deposited on the powde bed with a mico-pipette to fom mables by allowing the doplets to oll. The Peti dish was then placed on a moving stage fo the capillay ise measuement (Figue 1). The mable sizes used in this study wee 30, 50, 100, 200, and 300 micolites. Wate doplets of the same volumes wee also used in this study fo capillay ise measuements. The wate doplets wee gently place on the powde bed without shaking. Since PTFE powde does not spontaneously spead ove wate suface (Nguyen et al., 2010a), aound 70% of the wate doplet suface was fee of powde. Since the aea aound the maximum latitude cicle of the doplet is fee of powde, the capillay ise data obtained fom the powde fee wate doplet was used to expeimentally calculate the hydaulic adius of the doplet (Eqs. 4 and 5). (3) (4) (5)

Fig. 1: Schematic illustation of the capillay ise set-up. Capillay ise measuement. Figue 1 shows the schematic expeimental set-up fo the capillay ise measuement. The capillay tube was fixed vetically using Scotch tape on a ule, was clamped to a lab stand. A wate mable o wate doplet caied by the moving stage was used to inset the capillay into the mable o doplet fo measuement. The height of capillay ise was measued by taking eading on the ule. Befoe being mounted, the capillay tubes wee immesed in a solution of laboatoy detegent (RBS 35) and wee sonicated fo 15 minutes. This was followed by thee cycles of insing with Millipoe wate and 15-minutes of sonication in Millipoe wate. The cleaned capillaies wee stoed immesed in Millipoe wate befoe use. In capillay ise measuements of the wate doplets and wate mable, capillay ise fom the flat wate suface in a beake (h, Eq.1) was fist measued. The same capillay tube was used to measue the additional capillay ise of wate doplet ( h, Eq.5) and then by the wate mable ( hm, Eq.7 below) Since a significant length of wate still emained in the capillay afte it was emoved fom the beake, when the same capillay was inseted into the wate doplet o the liquid mable, the amount of wate diven by the wate doplet o the mable into the capillay was small. This minimized the excessive loss of wate fom the doplet and fom the mable; the amount of wate that enteed the capillay was consideed in the final calculation of the doplet and mable suface tension. Capillay ise data obtained fom the above thee situations wee used fo the final calculation of the wate mable effective suface tension. Results and discussion Wate mable effective suface tension measuement by the capillay ise method. Table 1 pesents the capillay ise esults by inseting the capillay tube into a flat wate suface in a beake and the additional capillay ise caused by wate doplets of diffeent volumes.

Tab. 1: Summay of the capillay ise data measued fo the flat wate suface, wate doplets and wate mables, as well as the coesponding calculations. Liquid Volume (mico lite) 30 50 100 200 300 dh w (mm) 6.5 5.0 3.5 3.0 1.8 dh 1 (mm) 6.5 5.0 3.2 2.0 1.8 dh 35 (mm) 6.0 4.5 3.4 1.6 1.5 dh 100 (mm) 5.5 3.5 2.9 2.0 1.5 Theoetical dop dh 16.1 13.6 10.8 8.6 7.5 1/m 903 694 486 417 243 STW (mn.m -1 ) 70.6 ST1 (mn.m -1 ) 70.6 70.6 70.0 68.5 70.6 ST35 (mn.m -1 ) 69.6 69.6 70.4 67.7 70.0 ST100 (mn.m -1 ) 68.7 67.7 69.4 68.5 70.0 The collection of each datum was epeated 3 times and aveage values ae pesented. The eo associated with the capillay ise height eading is assumed to be the same of the liquid meniscus height eading fom a buette in acid-base titation, which is 0.2 mm. If wate doplets ae assumed to be spheical, a theoetical capillay ise can be calculated using Eq. (2) to be 16.1 mm fo the 30 ml wate doplet. Howeve, in ou expeiment the wate doplet of the same volume sitting on the PTFE powde bed only causes a capillay ise of 6.5 mm, and the additional capillay ise data fo lage doplets ae lowe than 6.5 mm (Table 1). This diffeence between the theoetical and expeimental h is caused by the doplet defomation unde the influence of gavity; it is theefoe necessay to use the hydaulic adius (1/m) to take into account the gavity influence expeimentally (Eq. (3) and (4)). The hydaulic adii (1/m) of doplets of diffeent volumes can be calculated using equation (5). The additional capillay ise ( hm) data caused by the PTFE wate mables of diffeent wate volumes ae also shown in Table 1. Fo calculating the effective suface tension of wate mables, we assume that wate mable and the wate doplet of the same volume have the same (1/m) value. This assumption fits wate mables made of smalle powde paticles quite well. Although thee is a degee of uncetainty as the paticles size inceases to 100 mm, this assumption will lead to only < 5% of eo in the mable suface tension calculation. Futhe discussion ove this point will be given in a late section. Ou assumption is suppoted by the following obsevations: Fist, attention should be paid to the simila magnitudes of the additional capillay values of the wate doplets ( h) and the wate mables ( hm) of the same volume. The simila magnitudes of h and hm suggest that PTFE paticles deposited on wate suface do not affect wate suface tension significantly. Fo mables of same volume, capillay ise shows elatively small diffeence fom one paticle size to anothe. Calculation below (Eq. 8) shows that 1 mm diffeence in hm coesponds to a diffeence in mable effective suface tension of < 2 mn/m. This calculation suggests that ou assumption is easonable. It should also be emphasized that pecise measuement of the mable cuvatue is difficult because of ough image bode. Theefoe mathematical cuve fitting of a liquid mable image is likely to have an uncetain level of eo. (Nguyen et al., 2010b) An image of a mable suface does not epesent the

actual powde/wate inteface which is the inteface esponsible fo the mable effective suface tension. Fig. 2: A wate doplet patially coveed by PTFE powde on the left, and a liquid mable on the ight. Second, the suface of a wate doplet that is patially coveed by PTFE (Figue 2) powde does not show any visually detectable changes in cuvatue acoss the bode of powdecoveed and powde-fee sufaces. Such continuity of cuvatue acoss the powde-coveed and powde-fee suface suggests that the cuvatue of powde-fee wate suface can pedict that of the powde-coveed wate suface. Thid, the addition of tiny amount PTFE powde, so it just coves a small faction of wate suface aea, does not change the wate suface tension; this point was confimed by the Wilhelmy plate measuement of the wate suface tension in the pesence o absence of a small amount of powde. This eliminates diffeence in wate suface tension fo the doplet and fo the mable as a possible facto affecting thei hydaulic adii. The assumption of mable and doplet having the same (1/m) value simplify the calculation of the effective suface tension of wate mables. Equation (5) needs to be futhe modified in ode to adapt the Muma model to calculate the effective suface tension of wate mables. When the capillay is inseted into a wate mable, the total capillay ise is diven by two cuved sufaces the wate meniscus inside the capillay tube and the mable shell outside the capillay. Adapting these diffeences into Eq. (5), Eq. (6) is obtained. γ m ( 1 m ) + 2γ w cosθ ρg(h w + h m ) = 0 (6) γ Whee m γ is the effective suface tension of the wate mable, w is the suface tension of wate, ρ is the density of the wate, g is the gavitational foce, hw is that capillay ise of wate measued fom the flat wate suface in the beake, hm is the additional capillay ise caused by the wate mable, and (1/m) is the hydaulic adius of the mable which is assumed to be the same as that of the wate doplet of the same volume. Futhe eaangement of Eq.(7) yields the equation (8): γ m m + 2γ w cosθ = ρgh w + ρg h m (7)

Since ρgh w 2γ w cosθ = 0 (Equation 1), we then conclude: ρg hm γ m = = ρg hm m (8) 1 ( ) m Calculation of the effective suface tension of the wate mables of diffeent sizes can be made using Eq.(8) and the data of (1/m) and hm of wate mables. The capillay ise values measued fom wate doplets ae also pesented in Table 1. The hydaulic adii of the wate doplets (1/m) wee calculated using the wate suface tension value detemined by the capillay ise method (Eq. (1)) and the additional capillay ise values of the doplets ( h) measued against flat wate suface by Eq. (5). Fig. 3: Schematic illustation of the Pincipal adii of a doplet unde the effect of gavity. Table 1 shows the additional capillay ise data of wate doplets ( h) decease as the doplet volume inceases. This tend is in ageement with the Laplace pinciple. Although the doplet unde the influence of gavity is not spheical, it can be seen that as the volume of the doplet inceases, the pinciple adii of cuvatues will also incease. Figue 3 pesents a diagam that schematically descibes the elationship of doplet volume and the pinciple adii of cuvatues at the lagest latitudinal cicumfeence and of a longitudinal cuve the doplet. The incease of the pinciple adii of cuvatue of the doplet will educe the Laplace pessue exeted by the doplet and this tend is also eflected by changes in hydaulic adii (1/m) of wate doplets calculated fom the h by Eq. (5). The additional capillay ise data fo the wate mables ( hm) of diffeent volumes measued against flat wate suface, as well as the wate mable effective suface tension values calculated fom the hm data using Eq. (8) ae listed in Table 1. The hm data fo wate mables of diffeent volumes show simila tends as the wate doplets, i.e., the hm values decease as the volume of the mables incease. This tend can also be intepeted by the decease in Laplace pessue as the volume of the wate mable coe incease. The effective suface tension values of wate mables ae calculated using the assumption that the hydaulic adius of wate mable is the same as the wate doplet of the same volume Data in Table 1 show an inteesting and consistent tend: All additional capillay ise data of wate mables ae slightly lowe than those of wate doplets of the same volume. It suggests that the Laplace pessue exeted by the wate mable shell is lowe than that exeted by the wate doplet. A possible explanation fo this obsevation is that PTFE

paticles occupy a faction of wate suface, changing it into solid/liquid inteface. The fee enegy equied to incease a unit aea of powde-coveed wate suface is theefoe smalle than that equied to incease a unit aea of powde-fee wate suface. The hydophobic PTFE paticles on wate suface also expeience a cohesive inte-paticle foce that acts to pull the hydophobic paticles togethe. This attactive foce may be explained by the hydophobic effect. The natue of the hydophobic effect is that wate has the natual tendency to minimize its contact with hydophobic sufaces and to estoe the hydogen netwok between wate molecules. Wate is able to inteact though the dispesion component of its suface fee enegy (21.8 mj/m2) (Shaw, 1992) with PTFE to educe the wate/ptfe intefacial enegy. Howeve, the high hydogen-bonding component of wate (51.0 mj/m2) (Shaw, 1992) is unable to be educed though the inteaction with PTFE, since PTFE is not capable of foming hydogen bonding. The cohesive behavio of PTFE powde on wate suface can theefoe be undestood as a manifestation of wate estoing its hydogen-bonding netwok via minimizing its contact with PTFE powde, theefoe pushing PTFE paticles togethe. Since the diving foce comes fom the hydogen-bonding component of the wate suface fee enegy, the cohesive foce between PTFE powde paticles on a powde/wate inteface is unlikely to be geate than the hydogen-bonding component of wate suface tension. It may theefoe be concluded that the effective suface tension of wate mables fomed with inet hydophobic paticles should be lowe than the suface tension of wate. The values of effective suface tension fo mables fomed with the powde of smalle paticles appea to be slightly highe than those fomed with lage paticles, although the magnitude of this tend is only aound 1 mn/m. This tend may be elated to the stuctue of the mable shells fomed with powdes of diffeent sizes. We obseved that mables made with 1 µm PTFE powde wee much moe unstable than those made of othe two powdes. The instability of mables made with 1-µm powdes can be explained as that thee ae elatively lage aeas on the mable shell that ae not completely coveed by powde paticles. It is also noticed that paticles of the 1-µm powdes have a stong tendency to fom lage aggegates. The tendency fo the 1-µm powde paticles to aggegate pevents the unifom distibution of powde paticles on the mable suface. This makes the wate coe of the mable susceptible to making diect contact with the suppot solid suface such as glass, causing the mable to collapse. Cicumstantially, the non-unifom distibution of powde paticles on mables made of 1-µm PTFE powde has led a geate faction of the mable suface to be powde-fee. A mable suface that has a lage faction of powde-fee wate suface is expected to have an effective suface tension close to wate suface tension. A futhe inteesting obsevation also lends suppot to ou easoning. When a wate mable made of 100-µm PTFE powde meges with anothe wate mable of the same volume but made of 1µm PTFE powde, the newly fomed mable has its suface coated with 100- and 1-µm paticles. Howeve, 100-µm paticles push fowad as the mables mege and occupied ~75% of the suface of the newly fomed mable, wheeas the 1-µm paticles only occupied ~25% of new mable suface at equilibium. The compession of the aea coveed by 1 µm paticles afte meging suggests that powde suface coveage of the 1µm mable befoe meging was lowe than that fo the 100µm mable. This suppots ou intepetation that the geate faction of powde-fee mable suface of mable made of 1µm powde as compaed to the mable made of 100µm mable allows the fome to have an effective suface tension close to the wate suface tension than the latte. The expansion of a lowe effective suface tension mable shell and the shinking of the highe effective suface tension show an inteesting analogy to the expansion of low suface

tension film on wate suface, although it must be said that the diving foces in these two systems ae completely diffeent. The diving foce of the fome is the film pessue (o the suface tension diffeence between wate and the film) and that of the latte is the diffeence in powde-fee suface aea. Conclusion This wok exploed an expeimental method fo measuing the effective suface tension of liquid mable. The method does not ely on the assumption of an imaginay inteface o contact angle between a liquid mable and the suppoting suface. Instead, they ely on data diectly obtained fom the Laplace pessue. The capillay ise method captues the Laplace pessue exeted by the liquid mable shell; this method equies the measuements of only the capillay-ise diffeences between the liquid mable and the flat liquid suface and only basic tools ae equied to pefom the measuements. We poposed that the effective suface tension of powde-coveed liquid is the same as that of the liquid mable, povided that the powde paticles ae inet to the liquid. This poposal will hopefully povide a fesh angle fo studying the liquid mable suface popeties, in applications such as liquid mable based- mico eactos and so foth. Acknowledgments Funding eceived fom the Austalian Reseach Council though the gant ARC LP0989823 is acknowledged. Refeences AUSSILLOUS, P. & QUERE, D. 2001. Liquid mables. Natue, 411, 924-927. AUSSILLOUS, P. & QUÉRÉ, D. 2006. Popeties of liquid mables. Poceedings of the Royal Society A: Mathematical, Physical and Engineeing Science, 462, 973-999. BHOSALE, P. S., PANCHAGNULA, M. V. & STRETZ, H. A. 2008. Mechanically obust nanopaticle stabilized tanspaent liquid mables. Applied Physics Lettes, 93, 034109-034109-3. BORMASHENKO, E., BALTER, R. & AURBACH, D. 2010a. Micopump based on liquid mables. Applied Physics Lettes, 97, 091908. BORMASHENKO, E. & BORMASHENKO, Y. 2011. Non-Stick Doplet Sugey with a Supehydophobic Scalpel. Langmui, 27, 3266-3270. BORMASHENKO, E., BORMASHENKO, Y., POGREB, R. & GENDELMAN, O. 2010b. Janus Doplets: Liquid Mables Coated with Dielectic/Semiconducto Paticles. Langmui, 27, 7-10. BORMASHENKO, E., POGREB, R., BORMASHENKO, Y., MUSIN, A. & STEIN, T. 2008. New Investigations on Feofluidics: Feofluidic Mables and Magnetic- Field-Diven Dops on Supehydophobic Sufaces. Langmui, 24, 12119-12122. BORMASHENKO, E., POGREB, R., WHYMAN, G. & MUSIN, A. 2009a. Suface tension of liquid mables. Colloids and Sufaces A: Physicochemical and Engineeing Aspects, 351, 78-82. BORMASHENKO, E., POGREB, R., WHYMAN, G., MUSIN, A., BORMASHENKO, Y. & BARKAY, Z. 2009b. Shape, Vibations, and Effective Suface Tension of Wate Mables. Langmui, 25, 1893-1896. ESHTIAGHI, N., LIU, J. S., SHEN, W. & HAPGOOD, K. P. 2009. Liquid mable fomation: Speading coefficients o kinetic enegy? Powde Technology, 196, 126-132.

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