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Interactions of coherent structures in a film flow: Simulations of a highly nonlinear evolution equation

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Abstract

Numerical simulations of the evolution equation [14] for thickness of a film flowing down a vertical fiber are presented. Solutions with periodic boundary conditions on extended axial intervals develop trains of pulse-like structures. Typically, a group of several interacting pulses (or a solitary pulse) is bracketed by spans of nearly uniform thinned film and is virtually isolated: The evolution of such a “section” is modeled as a solution with periodic boundary conditions on the corresponding, comparatively short, interval. Single-pulse sections are steady-shape traveling waveforms (“cells” of shorter-period solutions). The collision of two pulses can be either a particle-like “elastic” rebound, or—and only if a control parameter S (proportional to the average thickness) exceeds a certain critical value, S c ≈ 1—a “deeply inelastic” coalescence. A pulse which grows by a cascade of coalescences is associated with large drops observed in experiments by Quéré [39] and our S c is in excellent agreement with its laboratory value.

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama, 35487-0350, Tuscaloosa, AL, U.S.A.

    V. I. Kerchman & A. L. Frenkel

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  1. V. I. Kerchman
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  2. A. L. Frenkel
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Additional information

Communicated by D.D. Joseph

This research was supported in part by U.S. DOE under Grant DE-FG05-90ER14100.

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Kerchman, V.I., Frenkel, A.L. Interactions of coherent structures in a film flow: Simulations of a highly nonlinear evolution equation. Theoret. Comput. Fluid Dynamics 6, 235–254 (1994). https://doi.org/10.1007/BF00417922

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  • DOI: https://doi.org/10.1007/BF00417922

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