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

TL;DR

This paper investigates how shear flow suppresses long-range concentration fluctuations in a liquid mixture, revealing crossover behaviors and providing experimental avenues for observation using light scattering.

Contribution

It demonstrates the shear-induced crossover from a known long-range correlation to a weaker divergence in concentration fluctuations within a liquid mixture.

Findings

Long-range correlations are suppressed at low wave numbers under shear.

A crossover wave number depends on shear rate and diffusivity.

Experimental observation of shear suppression is feasible with light scattering.

Abstract

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 $|\nabla c|^2/k^4$ long-range correlation at large wave numbers $k$ crosses over to a weaker divergent one for wave numbers satisfying $k<(\dot{\gamma}/D)^{1/2}$, while an asymptotic shear-controlled power-law dependence is confirmed at much smaller wave numbers given by $k\ll (\dot{\gamma}/\nu)^{1/2}$, where $c$, $\dot{\gamma}$, $D$ and $\nu$ are the mass concentration, the rate of the shear, the mass diffusivity and the kinematic viscosity of the mixture, respectively. The result will provide for the first time the possibility to observe the shear-induced suppression of a long-range correlation experimentally by using, for example, a low-angle light scattering technique.