Viscoplastic sessile drop coalescence

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.