chemical engineering

1. Thixotropy
Thesis Presentation
Naji Navas Pachayi | Chemical Engineering | NIT Calicut
A short presentation on the paper “ Thixotropy - a review”
by Howard A. Barnes

2. • In response to a stress and strain imposed, a materials deform either linearly without undergoing any change in
microstructure or in the non linear region where the microstructure changes. This time dependent nature of
microstructure is what make things thixotropic.
• Thixotropic process is reversible, because the structure breaks down progressively on shearing and slowly rebuild at rest.
The time scale of breaking and rebuilding are different.
Time for rebuilding > Time for breaking
• First observed when Iron Oxide gels were liquified simply just by shaking. The liquified gel was hardly distinguishable from
original sol. When let undisturbed for a period of time they solidified back again. This change of state process could be
repeated a number of times without any visible change in the system.
• Previously, these kind of behaviors were exhibited by materials only upon change in temperature.
• With the present understanding, it is believed that all materials that are shear thinning are thixotropic, but is
differentiated by the finite amount of time to bring about the rearrangements needed in the microstructural elements that
result in shear thinning.
Scott-Blair has concluded that “ If this recovery is very rapid, the phenomenon is observed as structural viscosity
(shear thinning) and if slow, it is observed as thixotropy “.
Introduction

3. • The material as a whole undergoes significant change in
viscosity. Upon deformation there is a decrease in viscosity
and an increase in viscosity is observed in a state of rest.
• Thixotropy is often associated with a change in viscosity,
which is induced by the structural change. So as a result it is
occasionally confused with shear thinning.
Thixotropic
Behavior of Paint

4. What drives the structural change ?
• The opposite action of breaking down and building up the structure has led to the establishment of a dynamic equilibrium in
the material. The driving force for microstructural change in flow is the result of the competition between break-down due
to flow stresses, build-up due to in-flow collisions and Brownian motion.
• Brownian motion causes a random thermal agitation of atoms and molecules where the elements of microstructure are
randomly are constantly bombarded. This causes the elements to proceed to a much more favorable position and attach
themselves where there are sufficient attractive forces.
• Anti-thixotropy: In materials situation arises, when the existing weakly attached microstructural elements that were earlier
brought together by collision during shear, are now slowly torn apart by the constant action of the random Brownian
motion.

5. • The diffusion rates of an isolated floc decreases as their size grows. This is the reason why a factor of (1- λ) appears along
side the driving force for build up expressions, because rebuilding starts at a given floc size that grows and then the
diffusion coefficient decreases. This means that collisions become less frequent, and as rebuilding progresses it gets slower
and slower, but theoretically never stops.
• Meanwhile in case of a floc breakdown, it is observed that the breakdown in a given shear field is fastest for the largest sized
flocs, i.e., at the shortest times, also it is proportional to the shear rate raised to a power. That’s why a product of λ and
shear rate appears in the break down rate.
Let’s look onto an isolated floc !

6. • In the next case after an equilibrium is achieved, the shear rate is instantaneously decreased to a lower value, the
measured shear stress drops instantly, but thereafter it will slowly increase towards a new equilibrium.
• Now instead of applying a given shear rate if a particular shear stress is applied, then the inverse of the previous case
happens, the shear rate would increase as the structure breaks down and then change to another lower shear stress will
result in a sudden decrease in shear rate followed by a further drop.
Typical Behavior

7. • If a thixotropic sample material into a viscometer and a constant shear rate is applied, the measured viscosity will
decrease with time, but it will eventually steady out to a constant value.
• But what is peculiar in the current scenario is the resting time.
Stretched Exponential Model
• In a flocculated system, an equilibrium is achieved by the counter active nature of hydrodynamic shear stresses pulling
structures apart by erosion and a combination of Brownian and shear forces building the structure up by collision and
accretion of particles which agglomerate into flocs.
• Due to the increasing size of flocs over the course of rebuilding, it takes longer time for the flocs to arrange into a most
favorable structure. Hence rebuilding is very long.

8. • ηe,0 -> Viscosity at the starting of shearing.
• ηe,α -> Viscosity after shearing for an infinite time.
• r is a dimension less constant, it varies with the condition (shear rate) of test.
• Viscoelastic in the linear region show time dependence.
• At short times it gives elastic response.
• If given time, the system adjust continuously and displays viscous effects.
• Meanwhile in the non-linear region, the microstructure not only takes time to respond.
• But the microstructure also changes with flow over finite interval of time.
The essential difference between linear viscoelasticity and thixotropy is that while both are time effects, the former is
in the linear region, where the structure responds but remains unchanged and the latter takes place in the non-linear region
where the structure is broken down by deformation as well as responding to it.
Viscoelasticity and Thixotropy

9. • Hysteresis Test: In this stress (or sometimes shear rate) is linearly increased from zero to a maximum value and then
decreased at the same rate back to zero. This test is repeated again and again. Upon plotting a loop is
obtained. The area between the loop gives an estimate of thixotropy.
Since the loop test is carried out quickly care must be taken to consider the inertial effects.
• Start-up Experiments: During any kind of start-up experiments thixotropic response will be seen either as an overshoot in
the stress in strain-controlled experiments or an increase in the slope of the strain-time curve in
creep tests.
Challenges with Thixotropic materials:-
1. The deformation prehistory of the material needs to be known. Which is unfortunately not known to us in most of
the instances.
2. The mechanical inertia of the rotating members in rheometers is mistaken for thixotropy.
Thixotropic Experiments

10. It is very crucial to understand the change of microstructure, while modelling the thixotropic behavior. This is
because all the fundamental parameters of a material is strong function of its microstructure.
Viscous Theories:
1. The description of the microstructure with the help of a scalar parameter and then use the rate of change of this scalar
parameter as a working parameter.
2. The temporal change of microstructure explained with the help of some direct description like the number of bonds, or
an attempt at describing real floc architecture using fractal analysis etc..
3. The time data involving viscosity and fluidity can be used.
Mathematical Theories

11. • Here a numerical scalar measure λ is used to define the structure. The model is built upon the idea that λ assumes a value
between 0 and 1. Hence a completely built structure is represented by λ = 1 and a completely broken-down structure as
λ = 0. In the simplest case of a typical, inelastic, non-Newtonian liquid with upper and lower Newtonian viscosity plateaus,
λ = 1 corresponds to ηo and λ = 0 corresponds to ηα.
• The rate of change of λ is expressed as of function of current level of structure (λ) and shear rate.
• The rate of breakdown due to shearing is given by the product of the current level of structure and the shear rate
raised to some power.
• The driving force for buildup is determined by how far the structure is away from its maximum value.
• If g > 0, then the system is building up towards equilibrium.
• If g < 0, then the system is breaking down towards equilibrium.
• At equilibrium,
𝐝λ
𝐝𝐭
= 0.
1. Indirect microstructural theories

12. • Now after obtaining the structural parameter λ, this has to be related various parameters in the model equation of the
material.
• Or else the structural parameter λ can be expressed in terms of current value of viscosity.
• The equilibrium value of λ and shear stress can be related by,
• From any state of equilibrium in the material, an increase and decrease in stress were made and the following set of
correlation were obtained.

13. • Here the reaction kinetics of the distribution of broken and unbroken bonds were used to study about the structure. Later
this estimated number of bonds were linked to viscosity.
• The forward rate constant k1 signified the breakdown kinetics
• The reverse rate constant k2 signified the buildup kinetics
After solving, the viscosity is estimated by assuming it is linearly proportional to the amount of unbroken structure,
with a maximum value of ηo when completely structured and a minimum value of ηα when completely destructured .
• In this model, the constant k2 is assumed to be independent of shear rate, rather it is a sole function of Brownian collisions
only, while the rate of breakdown constant k1 is related to shear rate by a power-law expression.
Cross Model
N is the average number of links per chain.
P is the number of single particles per unit volume.
2. Direct structure theories

14. So in the cross model, m is a constant less than 1.
k2 was a rate constant describing Brownian collision for build up.
k0 and k1 were rate constants for the Brownian and shear contributions to break-down
At equilibrium,
Then this number of bonds is used to determine the viscosity by the equation,
3. Simple viscosity theories
Fluidity is defined as the inverse of viscosity.

15. • Thixotropy can be deduced from a viscoelastic theory, by assuming a purely viscous behavior in the viscoelastic domain.
To best demonstrate it, a model based on a series of Maxwell elements was considered.
G denotes the modulus.
Θ denotes the relaxation time.
The rate of change of structural parameter λ for every ith element is given by,
Ei is the instantaneous elastic energy in the ith element.
Viscoelastic Theories

16. Thank You