ThixotropyThixotropy-- a reviewa reviewby Howard A. Barnesby Howard A. Barnes

Giorgia BettinHatsopoulos Microfluids Laboratory

Department of Mechanical EngineeringMassachusetts Institute of Technology

http://web.mit.edu/nnf

Introduction Introduction Introduction

• Thixotropy is seen in many fluids:PaintsResinsClaysPersonal products Chemical productsHome cleaning supplies: detergents

History of ThixotropyHistory of ThixotropyHistory of Thixotropy

• The term Thixotropy was first used by Peterfi in 1927 from the Greek work thixis (stirring or shaking) and trepo (turning or changing)

• Thixotropy was originally referred to reversible changes from fluid to solid-like elastic gel.

• ‘explanation of thixotropy as being due to the secondary minimum so that particles can form a loose association which is easily destroyed by shaking but re-established itself on standing’

• Shear-thinning (‘structural viscosity’) vs. Thixotropy: ‘structural viscosity is seen as a material with nearly zero time of recovery’

Thixotropy: Description of the phenomenaThixotropy: Description of the phenomenaThixotropy: Description of the phenomena

‘All liquids with microstructure can show thixotropy’

Competition between:

Break-down v.s Build updue to flow stresses due to in-flow collisions and Brownian motion

The magnitude of the viscosity of thixotropic fluids is dependent on the microstructure, in particular:

• Size of the floc (for suspension)• Mean alignment of fibers• Favorable spatial distribution of particles• Entanglement density • Molecular association (in polymer solution)

Thixotropic BehaviorThixotropic Thixotropic BehaviorBehavior

• The ‘transient’ viscosity of the fluid depends on its shearing history

Initial rate 0.1 s-1 Final rate 0.25 s-1

Dullaert K, Mewis J, JoR 49(6) 1213-1230 (2005)

( )( )/, , ,0( ) 1

rte e e e τη η η η −∞ ∞= + − −

Stretched exponential model

Structure break-down Structure build-up

Step ExperimentsStep ExperimentsStep Experiments

Extreme Shear Thinning & Antithixotropy Extreme Shear Thinning &Extreme Shear Thinning & Antithixotropy Antithixotropy

Double shear-thinning effect:• Shear thinning of floc• Reduction in floc size with

shear rates

Antithixotropy • Give the right particles attraction,

shearing can promote aggregation • Certain flocs can became looser

and more open under shear

Viscoelasticity & ThixotropyViscoelasticity Viscoelasticity & Thixotropy& Thixotropy

• Linear viscoelasticity: the microstructure responds to flow but it remains unchanged

• Thixotropy: the microstructure responds to flow & it is broken down by deformation.

Shear Thinning mechanism:• Alignment of rod-like particles in flow

direction • Loss of junctions in polymer solutions • Rearrangement of microstructure in

suspension and emulsion • Breakdown of flocs

Thixotropy is always expected from shear-thinning mechanism

BUTbecomes significant only if time-scale is longer than instrument response time

Thixotropy Loops & Start-up experimentsThixotropy Loops & StartThixotropy Loops & Start--up experimentsup experiments

Hysteresis loops are repeated again and again until a constant loop behavior is seen

Hysteresis loops:• Often carried out too quickly• Both shear rate & time changes

simultaneously• On startup the behavior is elastic but as

strains increase it becomes non-linear elastic response

Hysteresis loops Start-up experiments

Artifacts:• Instrument inertia causes delayed

instruments response often mistaken for thixotropy

• Slip at wall (wall depletion)

Mathematical theoriesMathematical theoriesMathematical theories

• Viscous theoriesIndirect microstructural theoriesDirect structure theoriesSimple viscosity theories

Scalar measure of structure λ

1, build structure0, broken-up structure

λλ==

( )( , ) 1 b dd g a cdtλ γ λ λ λγ= = − −

Build-up term

Breakdown term

( )( )

, 0,system is building up

, 0,system is breaking down

g

g

γ λ

γ λ

>

<

Relate λ to stress and viscosity

( ) ( )( )

12

20

, , 11

t KKη ηη σ η λ

ηλ∞ ∞

= = = − −

12

1 / Kηλη∞

= −

Direct Structure theoriesDirect Structure theoriesDirect Structure theories

• Viscous theoriesIndirect microstructural theories Direct structure theoriesSimple viscosity theories

( ) ( ) ( )1 2n md unbroken

k unbroken k brokendt

− = − Assume viscosity is proportional to unbroken structure

Example: Cross Model

( )2 0 1mdN k P k k N

dtγ= − +

N number of link per chaink2 rate constant associated with Brownian collisionsk0 k1 rate constants for brownian and shear contribution to breakupP particles per unit volume

2

10

0

1e

m

k PNkkkγ

= +

10

0

1

1e

mkk

η ηη η γ

∞

∞

−=

− +

Simple viscosity theoriesSimple viscosity theoriesSimple viscosity theories

• Viscous theoriesIndirect microstructural theories Direct structure theoriesSimple viscosity theories

[ ]21 2 0

d k kdt

γ ∞Θ Θ −Θ = − Θ−Θ Θ

1η

Θ =

( )( )ns

d Kdtη η γ η= −

Examples:

( ) ( ) ( )1 101 1m mm ktη η η η− −

∞ ∞ − = − + −

Viscoelastic TheoriesViscoelastic TheoriesViscoelastic Theories

• Generalized Maxwell model can be modified to account for thixotropy

iiσ σ=∑ i i

i ii i

dG dt Gσ σθ θ γ

+ =

0i i iG G λ= 0i i iθ θ λ=

Introduce thixotropy by letting G and θ be a function of λ, the structure parameter

121i i i i

i i i

d a Edt Gλ λ λ

θ θ −

= −

Break-up and Build-up of flocsBreakBreak--up and Buildup and Build--up of up of flocsflocs

• Two mechanism: floc erosion and Brownian collision

• Rate translational diffusion

• Rotational diffusion

• Rebuild starts relatively fast but then floc grow in size and the process gets slower and slower

1tranD

a∝

3

1rotD

a∝

In Shear Flow

Size of the floc

Surface shear stress experience by the floc

gfd Cγ=

fd dτ ηγ=

ConclusionConclusionConclusion

• Thixotropy happens because of the finite time required for flow-induced changes in the microstructure.

• When flow stops Brownian motion slowly allows microstructure to return to initial configuration

• The process is completely reversible