Rheological modelling of complex fluids: IV: Thixotropic and "thixoelastic" behaviour. Start-up and stress relaxation, creep tests and hysteresis cycles

Structural rheological modelling of complex fluids developed in Part I of t his 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 i s, in the presence of thixotropy. The model is based on an explicit viscosi ty-structure relationship, eta(S), between the viscosity and a structural v ariable S. Under unsteady conditions, characterized by a reduced shear, Gam ma(t), shear-induced structural change obeys a kinetic equation (through sh ear-dependent relaxation times). The general solution of this equation is a time-dependent function, S(t) = S[t, Gamma(t)]. Thixotropy is automaticall y modelled by introducing S[t, Gamma(t)] into eta(S) which leads directly t o eta(t) = eta[t, Gamma(t)], without the need for any additional assumption s in the model. Moreover, whilst observation of linear elasticity requires small enough deformation i.e. no change in the structure, larger deformatio ns cause structural buildup/breakdown, i.e. the presence of thixotropy, and hence leads to a special case of non-linear viscoelasticity that can be ca lled "thixoelasticity". Predictions of a modified Maxwell equation, obtaine d by using the above-defined eta(S) and assuming G = G(0)S (where G(0) is t he shear modulus in the resting state defined by S = 1) are discussed in th e case of start-up and relaxation tests. Similarly modified Maxwell-Jeffrey s and Burger equations are used to predict creep tests and hysteresis loops . Discussion of model predictions mainly concerns (i) effects of varying mo del variables or/and applied shear rate conditions and (ii) comparison with some experimental data.