Two-scale competition in phase separation with shear

TL;DR

This paper investigates phase separation under shear flow, revealing two-scale domain structures, oscillatory behaviors, and power-law growth of domain sizes through simulations and RG analysis.

Contribution

It introduces a combined numerical and RG approach to analyze two-scale domain formation and oscillations in shear-induced phase separation.

Findings

Existence of two characteristic domain scales.

Log-time periodic oscillations in domain structures.

Power-law growth of domain size with specific exponents.

Abstract

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group (RG) approach. Results show the simultaneous existence of domains of two characteristic scales. Stretching and cooperative ruptures of the network produce a rich interplay where the recurrent prevalence of thick and thin domains determines log-time periodic oscillations. A power law growth $ R(t) \sim t^{\alpha}$ of the average domain size, with $\alpha =4/3$ and $\alpha = 1/3$ in the flow and shear direction respectively, is shown to be obeyed.