Shear induced displacement of the spinodal, and spinodal demixing kinetics under shear

An equation of motion for the macroscopic density of a sheared suspension is derived from the Smoluchowski equation, with an appropriate closure for the pair-correlation function. This equation of motion is used to (i) predict the shear induced shift of the spinodal (both of its off-critical part and the critical point itself), and (ii) to analyse the anisotropic initial spinodal decomposition kinetics under shear flow. The off-critical part of the spinodal is predicted to be shifted linearly with the shear rate gamma over dot, for not too large shear rates, while the critical temperature is shifted like gamma over dot(0.81). The location of the cloud-point curve is argued to be much more sensitive to shear flow than the location of the spinodal. The cloud-point cuurve of a sheared suspension no longer coincides with the spinodal, but is located far below the spinodal, in the unstable part of the phase diagram. The predicted characteristics of ansotropic spinodal decomposition kinetics are found to be in accord with experiments on polymer systems and binary fluids. No experiments on colloidal systems exist as yet to quantitatively test the theoretical predictions developed in this paper.