Stripe formation in differentially forced binary systems

TL;DR

This paper investigates how stripe patterns form in binary systems with differential forcing, demonstrating analytically and numerically that stripes emerge above a critical forcing amplitude with a wavelength related to sound waves.

Contribution

The study introduces a continuum model showing spontaneous stripe formation in differentially forced binary systems, linking pattern wavelength to sound wavelength, supported by analytical and numerical evidence.

Findings

Stripes form spontaneously above a critical forcing amplitude.

Stripe wavelength is close to the sound wavelength at low viscosity.

Numerical simulations confirm analytical predictions.

Abstract

We consider pattern formation in periodically forced binary systems. In particular we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting of two isothermal ideal gases which interact via a frictional force we demonstrate analytically that stripes form spontaneously above a critical forcing amplitude. The wavelength of the stripes is found to be close to the wavelength of sound in the limit of small viscosity. The results are confirmed numerically. We suggest that the same mechanism may contribute to the formation of stripes in experiments on horizontally oscillated granular mixtures.