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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References
Chomaz, J.M.: The dynamics of a viscous soap film with soluble surfactant. J. Fluid Mech. 442, 387–409 (2001)
Couder, Y., Chomaz, J.M., Rabaud, M.: On the hydrodynamics of soap films. Physica D 37(1–3), 384–405 (1989)
Craster, R.V., Matar, O.K.: Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81(3), 1131–1198 (2009)
Oron, A., Davis, S.H., Bankoff, S.G.: Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69(3), 931–980 (1997)
Rutgers, M.A., Wu, X.L., Bhagavatula, R., Petersen, A.A., Goldburg, W.I.: Two-dimensional velocity profiles and laminar boundary layers in flowing soap films. Phys. Fluids 8, 2847–2854 (1996)
Rutgers, M.A., Wu, X.L., Daniel, W.B.: Conducting fluid dynamics experiments with vertically falling soap films. Rev. Sci. Instrum. 72, 3025–3037 (2001)
Schlichting, H., Gersten, K., Gersten, K.: Boundary-Layer Theory. Springer, Berlin (2000)
Taylor, G.I.: The dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc. R. Soc. Lond. A 253(1274), 296–312 (1959)
Tran, T., Chakraborty, P., Gioia, G., Steers, S., Goldburg, W.: Marangoni shocks in unobstructed soap-film flows. Phys. Rev. Lett. 103(10), 104501 (2009)
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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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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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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