A hyperbolic model for two-layer thin film flow with a perfectly soluble anti-surfactant Article Swipe

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YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2502.17205

We consider the motion of a two-phase thin film that consists of two immiscible viscous fluids and is endowed with an anti-surfactant solute. The presence of such solute particles induces variations of the surface tension and interfacial stress and can drive a Marangoni-type flow. We first analyze a lubrication limit and derive one-dimensional evolution equations of film heights and solute concentrations. Then, under the assumption that the capillarity and diffusion effects are negligible and the solute is perfectly soluble, we obtain a conservative first-order system in terms of film heights and concentration gradients. This reduced system is found to be strictly hyperbolic for a certain set of states and to admit an entire class of entropy/entropy-flux pairs. We also provide a strictly convex entropy for the hyperbolic system. Thus, the well-posedness for the Cauchy problem is given. Moreover, the system is almost a Temple-class system which allows to provide explicit solutions of the Riemann problem. The paper concludes with some numerical experiments using a Godunov-type finite volume method which relies on the exact Riemann solver.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2502.17205
PDF: https://arxiv.org/pdf/2502.17205
OA Status: green
OpenAlex ID: https://openalex.org/W4414849213

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DOI: https://doi.org/10.48550/arxiv.2502.17205

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Title: A hyperbolic model for two-layer thin film flow with a perfectly soluble anti-surfactant

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-02-24

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Authors: Rahul Barthwal, Christian Rohde

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Landing page: https://arxiv.org/abs/2502.17205

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PDF URL: https://arxiv.org/pdf/2502.17205

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Open access: Yes

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OA status: green

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OA URL: https://arxiv.org/pdf/2502.17205

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Cited by: 0

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