Eur. Phys. J. AP
Volume 5, Number 2, February 1999
|Page(s)||191 - 207|
|Published online||15 February 1999|
Rheological modelling of complex fluids: IV: Thixotropic and “thixoelastic” behaviour. Start-up and stress relaxation, creep tests and hysteresis cycles
Laboratoire de Biorhéologie et d'Hydrodynamique Physico-chimique (CNRS ESA 7057),
Université Denis Diderot Paris VII, LBHP, case 7056, Université Paris VII,
2 place Jussieu, 75251 Paris Cedex 05, France
Revised: 9 November 1998
Accepted: 26 November 1998
Published online: 15 February 1999
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 = G0S (where G0 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.
PACS: 83.20.Bg – Macroscopic (phenomenological) theories / 83.50.By – Transient deformation and flow; time-dependent properties: start-up, stress relaxation, creep, recovery, etc. / 83.50.Gd – Nonlinear viscoelasticity
© EDP Sciences, 1999
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