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Solutocapillary instability in slipping falling films

Sanghasri Mukhopadhyay1,*, Séverine Millet2, Bastien Di Pierro2, and Asim Mukhopadhyay3

  • *Contact author: sanghasri.m@iiitb.ac.in
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Phys. Rev. Fluids 11, 084004 – Published 14 August, 2026

DOI: https://doi.org/10.1103/5xrv-cjwg

Abstract

We present a comprehensive framework for gravity-driven, surfactant-laden thin films flowing over slippery substrates, elucidating how wall slip modifies the coupled hydrodynamics and interfacial transport. A long-wave model is formulated with a conservative bulk-surface mass balance and a Navier slip condition. The Orr-Sommerfeld eigenvalue problem governs the linear regime, while a weighted-residual model captures the nonlinear evolution over a range of equilibrium surfactant coverages, Marangoni strengths, and adsorption kinetics. The analysis predicts a nonmonotonic variation of the critical Reynolds number with equilibrium coverage, exhibiting a maximum at intermediate Γe, revealing the dual role of soluble surfactants: Increasing Γe stabilizes the flow up to an optimal coverage, whereas further enrichment weakens this stabilizing effect and promotes destabilization. Nonlinear simulations show that wall slip and Marangoni stresses modify the amplitude, phase, and capillary-ripple structure of localized traveling pulses. Under fast adsorption kinetics, the bulk-surface exchange rapidly reequilibrates the surfactant field, preserving the mean film shape and flux while strongly flattening the bulk inventory χ+hϕ and only weakly modifying the surface concentration Γ. A spurious interfacial mass growth reported by Pascal et al. [Phys. Rev. Fluids 4, 054004 (2019)] and D'Alessio et al. [J. Fluid Mech. 887, A20 (2020)] is resolved through a revised surface balance ensuring strict conservation. Wall slip thus emerges as a key control parameter, reducing viscous resistance and mitigating Marangoni back-stress. The slip parameter β therefore provides a useful control parameter for surfactant-laden films, linking substrate slip to wave amplitude, ripple damping, and the bulk-surface surfactant balance.

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Phys. Rev. Fluids 11, 084004– Published 14 August, 2026
  • Received 6 February 2026
  • Accepted 21 July 2026
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