We propose a classification scheme for the instabilities that might arise in sheared complex fluids. A central role is played by the coupling between the flow and the solute concentration, which is a combination of the parameters describing (a) the tendency of solute molecules to migrate to regions of small or high shear rates and (b) the variation of the viscosity with concentration. Using a mean field approach, we show that the nature and the geometry of the instability can be predicted from the knowledge of the coupling parameter, the diffuson coefficient, and the derivative of the stress with respect to the shear rate. We also successfully compare a description of the variation of the stress at and just beyond the instability threshold, with experimental results from a wormlike surfactant solution of ${\mathrm{CPClO}}_3$.

• Received 1 February 1995

DOI:https://doi.org/10.1103/PhysRevE.52.4009