On the Thermodynamic Consistency of a Two Micro-Structured Thixotropic Constitutive Model

Abstract

The time-dependent rheological behavior of the thixotropic fluids is presented in various industrial fields (cosmetics, food, oil, etc.). Usually, a couple of equations define constitutive model for thixotropic substances: a constitutive equation based on linear viscoelastic models and a rate equation (an equation related to the micro-structural evolution of the substance). Many constitutive models do not take into account the micro-structural dependence of the shear modulus and viscosity in the dynamic principles from which are developed. The modified Jeffreys model (con-sidering only one single micro-structure type) does not show this incoherence in its formulation. In this chapter, a constitutive model for thixotropic fluids, based on modified Jeffreys model, is presented with the addition of one more micro-structure type, besides of comments on some possible generalizations. The rheological coherence of this constitutive model and thermodynamic consistency are analyzed too. This model takes into account a simple isothermal laminar shear flows, and the micro-structures dynamics are relate to Brownian motion and de Gennes Reptation model via the Smoluchowski ™ s coagulation theory.