Viscoplastic sessile drop coalescence

Abstract

The evolution of the liquid bridge formed between two coalescing sessile yield-stress drops is studied experimentally. Surprisingly, we find that the height of the bridge evolves similar to a Newtonian fluid as h0(t)∼t, before arresting at long time due the fluid's yield stress. From viscoplastic lubrication theory we find a model for the arrested interface shape based on the balance between capillary pressure and yield stress. We then solve numerically for this final arrested profile shape and find it to depend on the fluid's yield stress τy, the surface tension coefficient σ and the coalescence angle α, represented by a modified Bingham number. We also present a scaling argument for the bridge's temporal evolution using the length scale found from this arrested shape analysis and present a similarity solution for the spatial evolution of the liquid bridge.