Controlling the rotation of particles in a suspension

Levan Jibuti (LSP)Salima Rafaï (LSP - CNRS)Ashok Sangani (Syracuse Univ.) Andréas Acrivos (City College of NY)

Philippe PeylaLSP

Université de Grenoble

Eppur si muove ! Nancy, 2010

Why controlling rotation of particles in a suspension?

Clutches, dampers, brakes

Audi R8 Smart fluids:

Before applying a magnetic field

… After

Industry:

Nature:

.

chloroplast

Consequence on rheology,Flow focusing, …

Rotation in presence of an external torque (Smart fluids)

Controlling the rotation of particles in a suspension

Rotation of a particle in a shear

H

V0

=V0/H

z

Rotation of a particle in a shear

H

V0

=V0/H

z

0

0 0( ) x

y)(V0X

Voy)( =

0

0( ) x

y)(=0

0( ) x

y)(+

x

y

x

yy

x

Extension/compression Rotation z

Rotation of a particle in a shear

H

V0

=V0/H

zx

y

y

x

Rotation z

2nd Faxen Law:Torque exerted by the fluid on the particle:T=-8a3 (1/2 rot V0-)

Torque free particule:T=0, donc =1/2 rot V0=- /2 eza

Control of the particle rotation by an external field

Rheology of smart fluids

Torque-free particle External torque External torque

z z z

effeffeffxy eff

eff

Control of the particle rotation by an external field

Rheology of smart fluids

External torque

T

T=-8R3 [1/2 rot V0-]

2nd Faxen Law :Dilute regime

x

y

z

Control of the particle rotation by an external field

Rheology of smart fluids

External torque

T

T=-8R3 [1/2 rot V0-]

2nd Faxen Law :Dilute regime

Tz=8R3 [/2+z]

x

y

z

Control of the particle rotation by an external field

External torque

T

T=-8R3 [1/2 rot V0-]

2nd Faxen Law :

Dilute regime with N particles

Tz=8R3 [/2+z]

z

Rxy= N Tz/2V

xy=0xy+R

xy

x

y

z

Control of the particle rotation by an external field

External torque

T

T=-8R3 [1/2 rot V0-]

2nd Faxen Law :

Dilute regime with N particles

Tz=8R3 [/2+z]

z

Rxy= N Tz/2V

Reff=R

xy/=3/2 z

=N 4/3 R3/V

eff=0eff+R

eff=(0xy+R

xy)/=(1+5/2+ 3/2

x

y

z

xy=0xy+R

xy

Control of the particle rotation by an external field

External torque

T

Dilute regime with N particles

eff5/2+ 3/2

eff=0 =-5/31.67if

ef

f

x

y

z

xy=0xy+R

xy

Control of the particle rotation by an external field

External torque

T

eff= (eff-)/

More concentrated regimes(no dipole-dipole interactions)

ef

f

x

y

z

eff()=mmKrieger & Dougherty law:

xy=0xy+R

xy

Control of the particle rotation by an external field

External torque

T

xy

Feffeff=

More concentrated regimes

F

x

y

z

Control of the particle rotation by an external field

External torque

T

xy

<T>Veffrot V

More concentrated regimes

x

y

z

A Faxen law for more concentrated regimes:

<T>T 0R3rot V

z

Controlling the rotation of particles in a suspension

Torque-free particle

z

effxy

External torque

z

effeff

External torque

z

effeff

Rotation in presence of walls (Microfluidic conditions)

Controlling the rotation of particles in a suspension

Rotation of a very confined particle in a shear

z Increasesor decreases??

2H

V0

=V0/H

z

x

y

-V0

Rotation of a very confined particle in a shear

2H

V0

=V0/H

x

y

Naive argument :z V0/a V0/H =

2a

-V0

H/a

1

z/(/2)

2

1

Rotation of a very confined particle in a shear

2H

V0

=V0/H

x

y

2a

-V0

Our numerical simulations

z

Rotation of a very confined particle in a shear

2H

V0

=V0/H

x

y

2a

-V0

Our numerical simulationsAndReflection method (A. Sangani)

z

Rotation of a very confined particle in a shear

VT(r) VT(r) - V0(r)

x

y

z

y

x x

Rotation of a very confined particle in a shear

VT(r) VT(r) - V0(r)

Rotation/2

Pure shear flow =

Rotation /2 + ext./compr. flow

x

y

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)