Early-time free-surface flow driven by a deforming boundary

Abstract

When a solid boundary deforms rapidly into a quiescent liquid layer, a flow is in- duced that can lead to jet formation. An asymptotic analytical solution is presented for this flow, driven by a solid boundary deforming with dimensionless vertical velocity Vb(x, t) = ε(1 + cos x)f(t), where the amplitude ε is small relative to the wavelength and the time dependence f(t) approaches 0 for large t. Initially, the flow is directed outward from the crest of the deformation and slows with the slowing of the boundary motion. A domain-perturbation method is used to reveal that when the boundary stops moving, nonlinear interactions with the free surface leave a remnant momentum directed back toward the crest, and this momentum can be a precursor to jet formation. This scenario arises in a laser-induced printing technique in which an expanding blister im- parts momentum into a liquid film to form a jet. The analysis provides insight into the physics underlying the interaction between the deforming boundary and free surface, in particular the dependence of the remnant flow on the thickness of the liquid layer and the deformation amplitude and wavelength. Numerical simulations are used to show the range of validity of the analytical results, and the domain-perturbation solution is ex- tended to an axisymmetric domain with a Gaussian boundary deformation to compare to previous numerical simulations of BA-LIFT.