Traveling spatially periodic forcing of phase separation

TL;DR

This paper analyzes how a traveling, spatially periodic forcing influences phase separation, revealing three regimes of behavior and stability conditions through analytical and numerical methods.

Contribution

It introduces a generalized 2d-Cahn-Hilliard model to study the effects of traveling periodic forcing on phase separation, identifying regimes and stability conditions.

Findings

Spatially periodic phase separation occurs at high forcing amplitudes.

Locked solutions are stable only within specific parameter ranges.

Unstable solutions exhibit coarsening dynamics similar to unforced cases.

Abstract

We present a theoretical analysis of phase separation in the presence of a spatially periodic forcing of wavenumber q traveling with a velocity v. By an analytical and numerical study of a suitably generalized 2d-Cahn-Hilliard model we find as a function of the forcing amplitude and the velocity three different regimes of phase separation. For a sufficiently large forcing amplitude a spatially periodic phase separation of the forcing wavenumber takes place, which is dragged by the forcing with some phase delay. These locked solutions are only stable in a subrange of their existence and beyond their existence range the solutions are dragged irregularly during the initial transient period and otherwise rather regular. In the range of unstable locked solutions a coarsening dynamics similar to the unforced case takes place. For small and large values of the forcing wavenumber analytical approximations of the nonlinear solutions as well as for the range of existence and stability have been derived.