Family-Vicsek scaling of detachment fronts in Granular Rayleigh Taylor Instabilities during sedimenting granular/fluid flows

TL;DR

This study investigates the scaling behavior of detachment fronts in granular sedimentation, revealing Family-Vicsek scaling and universal features across different fluids and particle sizes through experiments and models.

Contribution

It demonstrates that sedimentation fronts follow Family-Vicsek scaling and characterizes their dynamic and Hurst exponents, showing independence from fluid viscosity and compressibility.

Findings

Detachment fronts exhibit Family-Vicsek scaling.

Dynamic exponent z is approximately 1.

Hurst exponent ζ is approximately 0.75.

Abstract

When submillimetric particles are confined in a fluid such that a compact cluster of particles lie above the clear fluid, particles will detach from the lower boundary of the cluster and form an unstable separation front giving rise to growing fingers of falling particles. We study this problem using both experiments and hybrid granular/fluid mechanics models. In the case of particles from 50 to 500 microns in diameter falling in air, we study the horizontal density fluctuations at early times: the amplitude of the density difference between two points at a certain horizontal distance grows as a power law of time. This happens up to a saturation corresponding to a power law of the distance. The way in which the correlation length builds up to this saturation also follows a power law of time. We show that these decompaction fronts in sedimentation problems follow a Family-Vicsek scaling, characterize the dynamic and Hurst exponent of the lateral density fluctuations, respectively z \sim 1 and \zeta \sim 0.75, and show how the prefactors depend on the grain diameter. We also show from similar simulations with a more viscous and incompressible fluid, that this feature is independent of the fluid compressibility or viscosity, ranging from air to water/glycerol mixtures.