Striped Patterns in Radially Driven Suspensions with Open Boundaries

TL;DR

This study investigates how radially driven suspensions in a Hele-Shaw cell develop stable striped patterns under oscillatory conditions, revealing relationships between pattern features and driving parameters.

Contribution

It introduces a new experimental setup and mechanism explaining pattern formation in suspensions driven by oscillatory shear with open boundaries.

Findings

Stripe spacing increases exponentially with amplitude and frequency.

Stripe width decreases as a power-law with frequency.

Pattern reaches steady state after a few minutes.

Abstract

We study the motion of radially driven fluid-immersed particles in a novel Hele-Shaw cell with open boundaries. The initially uniform suspension forms a striped pattern within a specific range of horizontal oscillation frequencies and for sufficiently large amplitudes. We observe that the initial coarsening dynamics of the stripes gradually slows down and the pattern reaches a steady state after a few minutes. The distance between the stripes in the steady state exhibits an exponentially saturating increase with increased oscillation amplitude or frequency. The width of the stripes decreases as a power-law with the frequency while its amplitude dependence follows a logistic function. We propose a mechanism -- based on the interplay between shear stress, hydrodynamic interactions, and frictional forces -- to link the structural characteristics of the stripes to the properties of the oscillatory external drive.