Shear induced grain boundary motion for lamellar phases in the weakly nonlinear regime

TL;DR

This study investigates how oscillatory shear influences grain boundary motion in lamellar phases of diblock copolymers, revealing that shear induces boundary movement through flow advection and order parameter diffusion, with velocity depending on shear parameters.

Contribution

It provides a detailed numerical and analytical analysis of shear-induced grain boundary motion in lamellar phases, highlighting the roles of flow advection, diffusion, and instabilities in boundary dynamics.

Findings

Boundary moves toward the transverse region under shear.

Net boundary velocity increases with shear frequency and amplitude.

Order parameter diffusion includes lamellae breakup, reconnection, and weak instabilities.

Abstract

We study the effect of an externally imposed oscillatory shear on the motion of a grain boundary that separates differently oriented domains of the lamellar phase of a diblock copolymer. A direct numerical solution of the Swift-Hohenberg equation in shear flow is used for the case of a transverse/parallel grain boundary in the limits of weak nonlinearity and low shear frequency. We focus on the region of parameters in which both transverse and parallel lamellae are linearly stable. Shearing leads to excess free energy in the transverse region relative to the parallel region, which is in turn dissipated by net motion of the boundary toward the transverse region. The observed boundary motion is a combination of rigid advection by the flow and order parameter diffusion. The latter includes break up and reconnection of lamellae, as well as a weak Eckhaus instability in the boundary region for sufficiently large strain amplitude that leads to slow wavenumber readjustment. The net average velocity is seen to increase with frequency and strain amplitude, and can be obtained by a multiple scale expansion of the governing equations.