The effect of shear-flow on critical correlations in colloidal systems: Microstructure, turbidity, and dichroism

Abstract

On the basis of the Smoluchowski equation, ‘‘the Liouville equation for colloidal systems,’’ shear flow distortion effects on the structure factor for temperatures and densities close to the spinodal, c.q. the critical point, are considered. The results are valid in the classical region where the equilibrium structure factor attains the Ornstein–Zernike form. From the structure factor distortion we derive scaling relations for the shear-rate dependent turbidity and flow dichroism for various flow geometries. The dimensionless group which expresses the effect of the shear flow is essentially λ=Pe0(γ̇)/(ξRV)4, with Pe0(γ̇)=γ̇R2V/2D0 (γ̇ is the shear rate, RV the range of the pair-interaction potential, ξ−1 the correlation length, D0 is the Stokes–Einstein diffusion coefficient). As a consequence, very small shear rates (small values of Pe0) have very large effects close to the spinodal, c.q. the critical point, since then ξRV is a small number. Flow dichroism can be many decades larger than for systems far into the stable region of the phase diagram. Relaxation of turbidity and flow dichroism as a shear flow is turned off is also considered. The temperature, density, shear rate, and time dependence of the relaxation is described by scaling functions depending on the two dimensionless groups λ and γ̇t (t is the time lapse after switching off the shear flow).