Binary interactions of solitary pulses in falling liquid films

Pradas, Marc; Kalliadasis, Serafim and Tseluiko, Dmitri (2012). Binary interactions of solitary pulses in falling liquid films. IMA Journal of Applied Mathematics, 77(3) pp. 408–419.

DOI: https://doi.org/10.1093/imamat/hxs028

Abstract

We examine binary interaction of two-dimensional solitary pulses in falling liquid films. We make use of a two-field system of equations for the local flow rate and interface position that includes (second-order) viscous dispersion effects. By applying a coherent-structure theory, we obtain a dynamical system for the separation length between the pulses. The system is re-formulated in terms of a potential function which not only allows us to predict bound-state formation but also to interpret physically this formation. Numerical results of the fully non-linear second-order model are in very good agreement with the theoretically predicted distances. In addition, we numerically show that there are different types of dynamics associated with each bound state, including an overdamped, underdamped and undamped oscillating state depending on both the initial separation length and the Reynolds number.

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