Shear-induced quench of long-range correlations in a liquid mixture

A static correlation function of concentration fluctuations in a (dilute) binary liquid mixture subjected to both a concentration gradient and uniform shear flow is investigated within the framework of fluctuating hydrodynamics. It is shown that a well-known |∇c|²/k⁴ long-range correlation at large wave numbers k crosses over to a weaker divergent one at wave numbers satisfying k<(γ̇/D)^1/2, while an asymptotic shear-controlled power-law dependence is found at much smaller wave numbers given by k≪(γ̇/ν)^1/2, where c, γ̇, D, and ν are the mass concentration, the rate of the shear, the mass diffusivity, and the kinematic viscosity of the mixture, respectively. The result will provide the possibility to observe the shear-induced suppression of a long-range correlation experimentally by using, for example, a low-angle light scattering technique.