Binary fluids under steady shear in three dimensions

TL;DR

This study uses lattice Boltzmann simulations to analyze steady shear flow in three-dimensional binary fluids, revealing finite correlation lengths and potential different behaviors at low Reynolds numbers, extending previous 2D findings.

Contribution

First comprehensive 3D simulation of binary fluids under shear with hydrodynamics, showing steady states and scaling behaviors, and highlighting the need for larger resources at low Reynolds numbers.

Findings

Steady states with finite correlation lengths in all directions.

Scaling exponents similar to 2D at moderate Reynolds numbers.

Possible crossover to different behavior at low Reynolds numbers.

Abstract

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture with full hydrodynamics in three dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite correlation lengths in all three spatial directions. Using large simulations we obtain at moderately high Reynolds numbers apparent scaling expon ents comparable to those found by us previously in 2D. However, in 3D there may be a crossover to different behavior at low Reynolds number: accessing this regime requires even larger computational resource than used here.