Viscoplastic sessile drop coalescence

TL;DR

This paper investigates the coalescence dynamics of sessile yield-stress drops, revealing that the liquid bridge initially behaves like a viscous Newtonian fluid before arresting, with the final shape depending on yield stress and geometry.

Contribution

It provides experimental observations and a numerical model for the arrested shape of coalescing yield-stress drops, incorporating a new scaling argument for the bridge evolution.

Findings

Bridge height initially scales linearly with time.

Final arrested shape depends on yield stress and aspect ratio.

Scaling laws for bridge evolution are proposed.

Abstract

The evolution of the liquid bridge formed between two coalescing sessile yield-stress drops is studied experimentally. We find that the height of the bridge evolves similar to a viscous Newtonian fluid, $h_0\sim t$, before arresting at long time prior to minimizing its liquid/gas interfacial energy. We numerically solve for the final arrested profile shape and find it depends on the fluid's yield stress $\tau_y$ and coalescence angle $\alpha$, represented by the Bingham number $\tau_y h_{drop} / \sigma$ modified by the drop's height-width aspect ratio. We present a scaling argument for the bridge's temporal evolution using the length scale found from an analysis of the arrested shape as well as from the similarity solution derived for the bridge's evolution.