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

Published online by Cambridge University Press:  24 February 2015

C. Frederik Brasz*
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Craig B. Arnold
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Howard A. Stone
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
John R. Lister
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Email address for correspondence:


When a solid boundary deforms rapidly into a quiescent liquid layer, a flow is induced 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 $V_{b}(x,t)={\it\epsilon}(1+\cos x)\,f(t)$, where the amplitude ${\it\epsilon}$ is small relative to the wavelength and the time dependence $f(t)$ approaches 0 for large $t$. Initially, the flow is directed outwards 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 towards 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 imparts 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 extended to an axisymmetric domain with a Gaussian boundary deformation to compare with previous numerical simulations of blister-actuated laser-induced forward transfer.

© 2015 Cambridge University Press 

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Brasz et al. supplementary movie

Time evolution of the liquid layer and velocity field from an axisymmetric numerical simulation with ε=0.4 and β=0.4.

Download Brasz et al. supplementary movie(Video)
Video 4 MB

Brasz et al. supplementary movie

Time evolution of the liquid layer and velocity field from an axisymmetric numerical simulation with ε=0.4 and β=0.4.

Download Brasz et al. supplementary movie(Video)
Video 2 MB