A Thermodynamic Description of Coupled Flow and Diffusion in a Viscoelastic Binary Mixture

Abstract

We use an irreversible thermodynamics approach to derive hydrodynamic equations which govern the flow-induced concentration changes produced by inhomogeneous stresses in a viscoelastic binary mixture. The most relevant effects arising from these inhomogeneous flows are manifested in the migration of the dispersed phase and as flow-induced concentration fluctuations. Coupled constitutive equations for the mass flux and the stress tensor are derived self-consistently from our formalism. We show that our approach is consistent with different existing isothermal formalisms which predict the growth of concentration fluctuations and shear-induced diffusion of mass. Finally, we also comment on the possibility of extending our approach to incorporate nonisothermal effects and on the limitations and advantages of our description.