Controlling the rotation of particles in a suspension

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Presentation transcript:

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

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

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

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

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

Rotation of a particle in a shear V0 2nd Faxen Law: Torque exerted by the fluid on the particle: T=-8pa3 h (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

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

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

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

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

Control of the particle rotation by an external field Dilute regime with N particles sxy=s0xy+sRxy g g 2nd Faxen Law : 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)

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 (heff-h)/h=0 if Q=-5/31.67

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:

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)

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)

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

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

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

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

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

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

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

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

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

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)

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)