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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. [ABSTRACT FROM AUTHOR]

Adhesive contact between a thin elastic sheet and a substrate arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow, long-wavelength elastic deformations and microscopic adhesion, we analyse a sixth-order thin-film equation for the short-time dynamics of the onset of adhesion and the long-time dynamics of a steadily propagating adhesion front. Numerical solutions corroborate scaling laws and asymptotic analyses for the characteristic waiting time for adhesive contact and for the speed of the adhesion front. A similarity analysis of the governing partial differential equation further allows us to determine the shape of a fluid-filled blister ahead of the adhesion front. Finally, our analysis reveals a near-singular behaviour at the moving elastohydrodynamic contact line with an effective boundary condition that might be useful in other related problems. [ABSTRACT FROM AUTHOR]

We consider the dynamics of an elastic sheet as it starts to adhere to a wall, a process that is limited by the viscous squeeze flow of the intervening liquid. Elastohydrodynamic lubrication theory allows us to derive a partial differential equation coupling the elastic deformation of the sheet, the microscopic van der Waals adhesion, and viscous thin film flow. We use a combination of numerical simulations of the governing equation and a scaling analysis to describe the self-similar touchdown of the sheet as it approaches the wall. An analysis of the equation in terms of similarity variables in the vicinity of the touchdown event shows that only the fundamental similarity solution is observed in the time-dependent numerical simulations, consistent with the fact that it alone is stable. Our analysis generalizes similar approaches for rupture in capillary thin film hydrodynamics and suggests experimentally verifiable predictions for a new class of singular flows linking elasticity, hydrodynamics, and adhesion. [ABSTRACT FROM AUTHOR]

Adhesion in the context of mechanical attachment, signaling, and movement in cellular dynamics is mediated by the kinetic interactions between membraneembedded proteins in an aqueous environment. Here, we present a minimal theoretical framework for the dynamics of membrane adhesion that accounts for the kinetics of protein binding, the elastic deformation of the membrane, and the hydrodynamics of squeeze flow in the membrane gap. We analyze the resulting equations using scaling estimates to characterize the spatiotemporal features of the adhesive patterning and corroborate them using numerical simulations. In addition to characterizing aspects of cellular dynamics, our results might also be applicable to a range of phenomena in physical chemistry and materials science where flow, deformation, and kinetics are coupled to each other in slender geometries. [ABSTRACT FROM AUTHOR]