Free surface instability in a confined suspension jet

TL;DR

This paper investigates the instability of a confined suspension jet's free surface driven by gravity, combining numerical simulations and theoretical modeling to understand the underlying hydrodynamic interactions causing surface destabilization.

Contribution

It introduces a theoretical framework and numerical analysis for the free surface instability of a confined suspension jet in the Stokes regime, highlighting the role of long-range hydrodynamics.

Findings

The free surface becomes unstable with coarsening of modes to large structures.

Structural waves develop and propagate in the bulk of the suspension.

The analytical model predicts the instability driven by hydrodynamic interactions without surface tension.

Abstract

A jet of non-Brownian particles confined in a thin cell and driven by gravitational force is studied both numerically and theoretically. We present a theoretical scheme aimed to describe such a system in the Stokes regime. We focus on the dynamics of the interface between the suspension and the pure fluid. Numerical simulations solving Newton's equations for all particles show that the jet free surface becomes unstable: the fastest growing modes at small sizes coarsen up to the largest structures reaching the jet lateral scale. In the bulk, structural waves develop and travel at slightly slower speed than the jet average fall. An analytical model, based on hydrodynamic-like equations for the suspension, is derived and predicts the development of the interfacial instability. It captures in essence, the collective effects driving the interface destabilization i.e. the long range hydrodynamic interactions coupled with the abrupt interface, and no analogous to a surface tension is found.