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Controlling the rotation of particles in a suspension

Controlling the rotation of particles in a suspension. Philippe Peyla LSP Université de Grenoble. Levan Jibuti (LSP) Salima Rafaï (LSP - CNRS) Ashok Sangani (Syracuse Univ.) Andréas Acrivos (City College of NY). Eppur si muove !. Nancy, 2010.

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Controlling the rotation of particles in a suspension

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  1. Controlling the rotation of particles in a suspension Philippe Peyla LSP Université de Grenoble Levan Jibuti (LSP) Salima Rafaï (LSP - CNRS) Ashok Sangani (Syracuse Univ.) Andréas Acrivos (City College of NY) Eppur si muove ! Nancy, 2010

  2. Why controlling rotation of particles in a suspension? Smart fluids: Audi R8 Industry: Clutches, dampers, brakes … After Before applying a magnetic field Nature: chloroplast . Consequence on rheology, Flow focusing, …

  3. Controlling the rotation of particles in a suspension Rotation in presence of an external torque (Smart fluids)

  4. Rotation of a particle in a shear V0 H wz=-g/2 g=V0/H

  5. Rotation of a particle in a shear V0 ( ) ( ) ( ) V0X g x 0 = Voy y 0 0 H ) ( ) ) ( ) ( ( x x g/2 g/2 0 0 + = y y g/2 y 0 -g/2 0 y y wz=-g/2 x g=V0/H x x Rotation wz=-g/2 Extension/compression

  6. Rotation of a particle in a shear V0 2nd Faxen Law: Torque exerted by the fluid on the particle: T=-8pa3h (1/2 rot V0-w) Torque free particule: T=0, donc w=1/2 rot V0=- g/2 ez H a y y wz=-g/2 x g=V0/H x Rotation wz=-g/2

  7. Control of the particle rotation by an external field Rheology of smart fluids External torque Torque-free particle External torque wz=-g/2 wz>-g/2 wz<-g/2 heff>h0eff heff=sxy/g heff<h0eff

  8. Control of the particle rotation by an external field Rheology of smart fluids Dilute regime 2nd Faxen Law : g y T=-8phR3 [1/2 rot V0-w] x z T External torque

  9. Control of the particle rotation by an external field Rheology of smart fluids Dilute regime 2nd Faxen Law : g y T=-8phR3 [1/2 rot V0-w] w x Tz=8phR3 [g/2+wz] z T External torque

  10. Control of the particle rotation by an external field Dilute regime with N particles sxy=s0xy+sRxy 2nd Faxen Law : g g y T=-8phR3 [1/2 rot V0-w] wz x Tz=8phR3 [g/2+wz] z sRxy= N Tz/2V T External torque

  11. Control of the particle rotation by an external field Dilute regime with N particles sxy=s0xy+sRxy 2nd Faxen Law : g g y T=-8phR3 [1/2 rot V0-w] wz x Tz=8phR3 [g/2+wz] z sRxy= N Tz/2V T Q=(wz+g/2)/(g/2) hReff=sRxy/g=3/2 h f Q External torque f=N 4/3 p R3/V heff=h0eff+hReff=(s0xy+sRxy)/g=h(1+5/2 f + 3/2 f Q)

  12. Control of the particle rotation by an external field Dilute regime with N particles (heff-h)/h=5/2 f + 3/2 f Q sxy=s0xy+sRxy g g y w x (heff-h)/h z T External torque Q if Q=-5/31.67 (heff-h)/h=0

  13. Control of the particle rotation by an external field More concentrated regimes (no dipole-dipole interactions) (heff-h)/h= (h0eff-h)/h (1+3/5Q) sxy=s0xy+sRxy g g y w x (heff-h)/h z T External torque Q h0eff(f)=h (1-f/fm)-5/2fm Krieger & Dougherty law:

  14. Control of the particle rotation by an external field More concentrated regimes g g y sxy w x F(Q,f) z T External torque Q F(Q,f)=(heff-h)/(h0eff-h)= (1+3/5Q)

  15. Control of the particle rotation by an external field More concentrated regimes g g A Faxen law for more concentrated regimes: y sxy <T>=-(12V/5N) (h0eff-h) (1/2 rot V-w) w x z T wz External torque f f <T>Tf 0=-8pR3h (1/2 rot V-w)

  16. Controlling the rotation of particles in a suspension External torque External torque Torque-free particle wz=-g/2 wz>-g/2 wz<-g/2 heff>h0eff heff<h0eff heff=sxy/g

  17. Controlling the rotation of particles in a suspension Rotation in presence of walls (Microfluidic conditions)

  18. Rotation of a very confined particle in a shear V0 wz Increases or decreases?? wz 2H y x -V0 g=V0/H

  19. Rotation of a very confined particle in a shear V0 Naive argument : wz V0/a V0/H = g 2H 2a wz/(g/2) y 2 x -V0 1 g=V0/H H/a 1

  20. Rotation of a very confined particle in a shear V0 2H 2a wz/(g/2) y x -V0 Our numerical simulations g=V0/H

  21. Rotation of a very confined particle in a shear V0 2H 2a wz/(g/2) y x -V0 Our numerical simulations And Reflection method (A. Sangani) g=V0/H

  22. Rotation of a very confined particle in a shear VT(r) VT(r) - V0(r) y y x z x x

  23. Rotation of a very confined particle in a shear Pure shear flow = Rotation g/2 + ext./compr. flow VT(r) VT(r) - V0(r) Rotation g/2 y x z

  24. Rotation of a very confined particle in a shear VT(r) VT(r)-V0(r)

  25. Rotation of a very confined particle in a shear VT(r) VT(r)-V0(r) Also obtained by B. Kaoui et al, on circular vesicles (To be published)

  26. Control of the particle rotation Rotation is modified both by - confinement - external field Dipole-dipole interaction should be added (changes the rheology at small shear rate)

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