Abstract
We derive the leading-order equations that govern the dynamics of the flow in a falling, free-standing soap film. Starting with the incompressible Navier–Stokes equations, we carry out an asymptotic analysis using parameters that correspond to a common experimental setup. We account for the effects of inertia, surface elasticity, pressure, viscous stresses, gravity, and air drag. We find that the dynamics of the flow is dominated by the effects of inertia, surface elasticity, gravity, and air drag. We solve the leading-order equations to compute the steady-state profiles of velocity, thickness, and pressure in an experiment in which the film is in the Marangoni elasticity regime. The computational results, which include a Marangoni shock, are in good accord with the experimental measurements.
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We dedicate this paper to the memory of Prof. Don Carlson, a gentleman and a scholar, a storied teacher and a sorely missed friend.
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Chakraborty, P., Tran, T. & Gioia, G. Leading-Order Dynamics of Gravity-Driven Flows in Free-Standing Soap Films. J Elast 104, 105–114 (2011). https://doi.org/10.1007/s10659-011-9317-6
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DOI: https://doi.org/10.1007/s10659-011-9317-6