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<p>The stability and rupture dynamics of a gravity-driven thin liquid film coating a vertical cylinder are analyzed, incorporating van der Waals forces, thermocapillary stresses, and wall slip. A nonlinear evolution equation is derived under the assumption of small film thickness relative to cylinder radius. Linear stability analysis shows that van der Waals attraction destabilizes the film, with wall slip amplifying disturbance growth and shifting the most unstable wavenumber. Weakly nonlinear analysis reveals both supercritical and subcritical regimes, underscoring the interplay among slip length, thermocapillarity, and intermolecular forces. Numerical simulations validate these predictions, demonstrating rupture dynamics governed by the disturbance spectrum. Spatiotemporal analysis identifies conditions for absolute instability driven by van der Waals forces, with thresholds that depend on the slip length. Finally, using self-similar scaling, a power law is proposed between minimum film thickness and time during film thinning close to rupture. These findings provide a unified framework for thin-film instabilities on curved substrates, with relevance to coating flows and microfluidic applications.</p>

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Stability and rupture of thin film on a vertical cylinder with slip and thermocapillarity

  • 期刊论文

  • 发表日期：

    2026年7月18日

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  • Souradip Chattopadhyay,
  • Sonam,
  • Naveen Tiwari

摘要

The stability and rupture dynamics of a gravity-driven thin liquid film coating a vertical cylinder are analyzed, incorporating van der Waals forces, thermocapillary stresses, and wall slip. A nonlinear evolution equation is derived under the assumption of small film thickness relative to cylinder radius. Linear stability analysis shows that van der Waals attraction destabilizes the film, with wall slip amplifying disturbance growth and shifting the most unstable wavenumber. Weakly nonlinear analysis reveals both supercritical and subcritical regimes, underscoring the interplay among slip length, thermocapillarity, and intermolecular forces. Numerical simulations validate these predictions, demonstrating rupture dynamics governed by the disturbance spectrum. Spatiotemporal analysis identifies conditions for absolute instability driven by van der Waals forces, with thresholds that depend on the slip length. Finally, using self-similar scaling, a power law is proposed between minimum film thickness and time during film thinning close to rupture. These findings provide a unified framework for thin-film instabilities on curved substrates, with relevance to coating flows and microfluidic applications.