Ordering of the lamellar phase under a shear flow

TL;DR

This paper investigates the behavior of lamellar phases under shear flow using a large-N limit approach, revealing anisotropic growth and scaling properties in different dimensions.

Contribution

It provides a theoretical analysis of lamellar ordering dynamics under shear flow, highlighting anisotropic growth laws and the dimensional dependence of scaling.

Findings

Lamellae tend to align with the vorticity direction.

Growth laws differ between flow and shear directions, with specific power laws.

Scaling behavior is dimension-dependent, holding in 2D but not in 3D.

Abstract

The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free-energy and the evolution follows a convection-diffusion equation. Lamellae order preferentially with the normal along the vorticity direction. Typical lengths grow as $\gamma t^{5/4}$ (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3.