8. Powder mixing and blending; Fluid flow through particle beds

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1 Fig Powder mixing and blending; Fluid flow through article beds 8. Product tailoring by article mixing, 8.1 Microrocesses and mixing efficiency of articles Model of stochastic homogeneity 8.1. Mixing kinetics 8. Rotating vessels, kneaders and agitators 8.3 Pneumatic mixing Permeation of article beds 8.3. Fluidized bed mixer Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.1

2 Fig. 8. Processes or unit oerations of mechanical rocess engineering according to RUMPF without change of article size with change of article size searation mechanical searation (filters, searators, screens, sifters) size reduction (crushing and grinding) combination owder mixing and blending size enlargement (agglomeration) transort and storage of bulk materials article size analysis Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.

3 Fig. 8.3 Characterisation of article mixtures 1. characterisation of mixing states of a granular material or article system a) comletely searated b) ideal mixture (regular distribution) c) c) random mixture Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.3

4 Fig Characterisation of the comosition of a mixture and its uality of mixing a) exected value µ m /m of a comosition of a mixture is known ~ s 1 n n ( µ,j µ ) j 1 ~ s standard deviation, ~ s estimated variance of the exected value n number of samles µ,j mass fraction of the comonent in the j th samle a) exected value of a comosition of a mixture is not known and has to be estimated µ ~ s 1 n n j 1 µ 1 n 1, j n ( µ,j µ ) j 1 mean value (estimated exectation of µ ) 3. Variance σ Z of stochastic homogeneity or an ideal random mixture, consisting of two comonents according to STANGE σ Z µ µ m S [ µ m ( 1+ v ) + µ m ( 1+ v )] µ, µ mass fractions of the comonents (P) and (Q) m S mass of a single samle m, m mean article mass of the comonents (P) and (Q) Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.4

5 v σ m, v σ m Fig. 8.5 variation coefficients of the article mass (size) distributions of the comonents (P) and (Q) 4. Secial cases: a) narrow size distributions of both comonents v 0, v 0, average article number in one samle N m S / m σ Z µ µ / N b) nearly euivalent size distributions m m, v v σ Z µ m µ S m ( 1+ v ) c) large mass fraction of comonent (P) µ > 0.9 and m m σ Z µ m µ S m ( 1+ v ) d) comonent (P) is very coarse m >> m σ Z µ m µ S m ( 1+ v ) 5. Mixing efficiency ME 1 SE segregation index: σ s~ σ... σ 0... ME σ ( ) 1 1 σz / s~ ( µ ) µ max µ 1 µ ME 3 / max Z / max Z 1 s~ σ ( s~... )/ σmax σz σmax Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.5

6 Process rinciles for inut of mechanical energy into articulate systems Process rincile schematic sketch examle Fig. 8.6 rotating rocess chambers or vessels drum mixer drum mill drum dryer agitated systems mechanical silo discharging forced mixing imact mill flow of fluids through granular beds vibrations neumatic silo discharging neumatic homogenisation fluidised beds vibration systems for charging and discharging screen machine vibration mill Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.6

7 Fig. 8.7 Mixing - of granular materials 1. drum mixer a) cylindrical mixing drum d) cubic mixer b) double cone mixer e) tetrahedral mixer c) double cone mixer with a tumbling f ) V - mixer Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.7

8 Fig. 8.8 Motion rocesses in a drum mixer a) small number of revolutions b) higher number of revolutions c) number of revolutions near n crit. cataract zone cascade zone cascade zone cascade zone Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.8

9 Fig. 8.9 Mixing rocesses in a drum mixer a) before mixing b) after mixing c) comosition of samles taken from different heights of the mixing bulk materials, before mixing (t 0), while mixing, and after mixing (t > t M ) Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.9

10 Fig s f (t) for different mixing rocesses a) without segregation rocesses b) with segregation rocesses in the beginning, comonents of higher density are above those of lower density c) with segregation rocesses in the beginning, comonents of higher density are under those of lower density Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.10

11 Fig Mixing - of granular materials. kneader, an mixer a) double-shaft kneader or an mixer b) fast running addle mixer 1 rotating mixing tool A feed reel share, loughshare M mixed roduct Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.11

12 Fig. 8.1 Mixing - of granular materials 3. Pneumatic mixer a) fluidised bed mixer b) air jet mixer LE air inlet LA air outlet A feed material for mixing S1 S4 searate aeration segments Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.1

13 Fig Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.13

14 Fig Flow of fluids through granular beds - imortant mechanical micro rocesses 1. schematic flow of fluids through a granular bed entrance streaming rofile of fluid fluid exit streaming rofile of P - P 1 u u ε ε A I ressure dro across the bed average velocity of flow of the fluid average velocity of flow of the fluid in the ores orosity of the bed total cross sectional area of the bed thickness of the bed Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.14

15 Fig different states of granular beds while fluid ermeation bulk material begin of homogeneous inhomogeneous unsteady fluidisation fluidised bed fluidised bed fluidised bed gas or liuid gas or liuid liuid gas gas gas or liuid low velocity of flow high velocity of flow of the fluid of the fluid Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.15

16 Fig ressure dro in the granular bed deendent on the fluid flow rate Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.16

17 a) Fixed article bed No Author 1 Darcy Carman, Kozeny 3 Gute 4 Molerus, Pahl, Rumf Euation h B k u K ( 1 ε) Fig Fluid Flow through Particle Beds Permeation Models η u, K Darcy constant Valid for Laminar flow-around Re < 0.5 transition Re Turbulent flow-around Re > 1000 Porosity ε Model of Pore system Random acking monodiserse sheres Particle shae Remarks Homogeneous ore system arallel A 3 S,V η u KCK, K h B ε CK Carman Kozeny constant, K CK 5 for sheres bended, cylindrical ores of eual size with small deviation d K Dimension 5.5 ρf u h B Re ε analysis d K Basing on 4 ( 1 ε) ρf u h B Re ε results of Gute Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.17

18 5 Pärnt η u ( 1 ε) Fig Exeriments ξ Re h Re 3, Re h B ψ F ψ R d ST ε h 1 ε with fine Re h hydraulic Reynolds number diserse article beds ψ F shae factor, ψ R roundness factor ξ fluid drag coefficient 6 Burke, d K 1 ε Exeriments Plummer ρf u h B ε 7 Ergun d K ( 1 ε) 1 ε Exeriments λ 3, λ ρf u h B ε Re 8 Molerus 4 d 1 d (u / ε) d ρ f Eu B Re < 10 4 Re η Re a a 0.95 Surface d d searation Re a 0.95 a 0.95 Re ratio 3 d 1 ε 3 Euler number of fixed bed: a ε 4 d ε Eu B d 3ρ u h 1 ε d f B d+a a d+a Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.18

19 Fig b) Fluidized bed No Author 9 Beranek, Rose, Winterstein 10 Molerus Euation ( 1 εl ) ( ρs ρf ) g hb ε L Porosity at oint of bed exansion 4 d 1 Eu W Re a d Re a Euler number of fluidized bed: Eu 4 ρ ρ d g d a limeu d a Re c s f W W with W 3 ρf (u / ε) ε 1 Valid for Laminar flow-around Re < 0.5 Transition Re Turbulent flow-around Re > 1000 Porosity ε Model of Pore system Random acking monodiserse sheres Particle shae Remarks const. for comlete range of fluidized bed Re < (u / ε) d ρ Re η Surface searation ratio d a d d+a a f 1 ε ε d d+a Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.19

20 Fig. 8.0 Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.0

21 Fig. 8.1 Survey of constitutive functions, rocessing and handling roblems of cohesive owders. Proerty, roblems Large adhesion otential 1) Large intensification of adhesion ) Poor Physical rincile F N F N F H0 H0 F H (F N ) F G F H (F N ) σ 1 σ flowablity ) c σ1 ff c σc Large comressibility ) Small ermeability 3,4) h h W u σ 1 h b F F G ρ ρ Physical assessment of roduct uality Physical law Assessment Value characteristic range CH,sls Adhesion (100 µm) πg a 0 ρs d Weight d κ Contact consolidation κ κ A κ coefficient κ by flattening > 0.77 b b,0 σ 1+ σ u k f h h M,st Poor fluidisation 5,6) f ( u(d )) P 0 W b n Flow function ff c < 1 Comressibility index n Permeability k f in m/s < Evaluation slightly adhesive adhesive very adhesive soft very soft extreme soft cohesive very cohesive non-flowing comressible very comressible non-ermeable very low low Channelling Grou C, non-fluidising Particle size d in µm < 10 < 1 < 0.1 < 100 < 10 < 0.1 < 100 < 10 < < 10 1) Rumf, H.: Die Wissenschaft des Agglomerierens. Chem.-Ing.-Technik, 46 (1974) ) Tomas, J.: Product Design of Cohesive Powders - Mechanical Proerties, Comression and Flow Behavior. Chem. Engng. & Techn., 7 (004) ) Förster, W.: Bodenmechanik - Mechanische Eigenschaften der Lockergesteine, 4. Lehrbrief, Bergakademie Freiberg ) Terzaghi, K., Peck, R. B., Mesri, G.: Soil mechanics in engineering ractice, Wiley, New York ) Geldart, D.: Tyes of Gas Fluidization, Powder Techn. 7 (1973) ) Molerus, O.: Fluid-Feststoff-Strömungen, Sringer, Heidelberg 198. Fig_MPE_8 Dr. W. Hintz + Prof. Dr. Tomas Mechanical Process Engineering - Particle Technology Powder mixing and blending Figure 8.1