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Inspired by geological structures formed by magmatic intrusions that deform the Earth's crust, we investigate the elastohydrodynamic growth of a viscoplastic blister under an elastic sheet resting on a prewetted substrate. By combining experiments, scaling analysis and numerical simulations, we reveal new regimes for the elastoviscoplastic growth dynamics of the blister. The blister height and its apparent radius grow as $h(0,t) \sim t^{5/9}$ and $R(t) \sim t^{2/9}$ if the fluid pressure is set by bending of the sheet, and as $h(0,t) \sim t^{5/13}$ and $R(t) \sim t^{4/13}$ if the fluid pressure is set by stretching of the sheet. A plug-like flow inside the blister dictates its dynamics, whereas the blister takes a self-similar shape given by a balance of the fluid's yield stress and the pressure gradient induced by the deformation of the elastic sheet.

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, h0 ∼ 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 τy and coalescence angle α, represented by the Bingham number τyh drop /σ 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.

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