A thermodynamic approach to rheology of complex fluids: The generalized BMP model

Abstract

In this paper, a set of constitutive relationships arising from the coupling of stress with concentration, are derived using the extended irreversible thermodynamics formalism. In complex fluids that present flow-induced changes in their internal structure, the stress constitutive equation is coupled to an evolution equation of a scalar representing the flow-induced modifications in the internal structure of the fluid, and to the constitutive equation for the mass flux. In particular, the generalization of a simple model, the Bautista–Manero–Puig (BMP) model, which has been used to reproduce the nonlinear viscoelastic behavior of polymer-like micellar solutions and other complex fluids, is derived. This model predicts rather well steady and unsteady nonlinear features of semi-dilute solutions that exhibit shear-banding flow and the shear-thickening transition observed in dilute surfactant solutions.