Thermodynamic approach to rheology of complex fluids: flow-concentration coupling

In this work, the generalized Bautista-Manero-Puig (BMP) model derived from extended irreversible thermodynamics (EIT) is used to analyze the coupling of stress with concentration in complex fluids. It is shown that this model is consistent with previous analyses that predict mechanical and thermodynamic instabilities in the shear-banding regime. In particular, for simple shear flows, the model presented here predicts the structure factor in the plane of shear and the onset of instabilities in the gradient-vorticity plane. Furthermore, the model predicts distinctive features of the models of Brochard-de Gennes and Schmitt as particular cases. For finite stress relaxation time, the generalized BMP model allows the prediction of transient structures normal to the vorticity axis. Instabilities are predicted in the regions of high viscosity, which suggest that the induction of a more viscous phase in a shear-thickening solution can lead the system to instability, in this case, the layering is predicted perpendicular to the vorticity direction. These transient structural patterns within the shear-thickening region correspond to spinodal phase separation. When the mechanical and thermodynamic instabilities are uncoupled, the model predictions agree with experiments and with the transient-gel model of Brochard and de Gennes.