Structural rheological modelling of complex fluids developed in Part I of this series and
applied to shear thickening systems (Parts II & III), is now used to improve such a modelling
in the case of unsteady behaviour, that is, in the presence of thixotropy. The model is based
on an explicit viscosity-structure relationship, η(S), between the viscosity
and a structural variable S. Under unsteady conditions, characterized by a reduced shear,
Γ(t), shear-induced structural change obeys a kinetic equation (through shear-dependent
relaxation times). The general solution of this equation is a time-dependent function,
S(t) ≡ S[t, Γ(t)]. Thixotropy is automatically modelled by introducing
S[t, Γ(t)] into η(S) which leads directly to η(t) ≡ η[t, Γ(t)],
without the need for any additional assumptions in the model. Moreover, whilst observation of
linear elasticity requires small enough deformation i.e. no change in the structure,
larger deformations cause structural buildup/breakdown, i.e. the presence of thixotropy,
and hence leads to a special case of non-linear viscoelasticity that can be called “thixoelasticity”.
Predictions of a modified Maxwell equation, obtained by using the above-defined η(S) and
assuming G = G
S (where G
0 is the shear modulus in the resting state defined by
S = 1) are discussed in the case of start-up and relaxation tests. Similarly modified
Maxwell-Jeffreys and Burger equations are used to predict creep tests and hysteresis loops.
Discussion of model predictions Maynly concerns (i) effects of varying model variables
or/and applied shear rate conditions and (ii) comparison with some experimental data.