Dynamics of three-dimensional thin film rupture. (English) Zbl 0992.76013
Summary: We consider the problem of thin film rupture driven by van der Waals forces. A fourth-order nonlinear PDE governs the low-Reynolds number lubrication model for a viscous liquid on a solid substrate. Finite-time singularities in this model equation lead to formation of dry spots in the film. Our study addresses the problem of rupture in the full three-dimensional geometry. We focus on stability and selection of the dynamics determined by initial conditions on small finite domains with planar and axisymmetric geometries. We also address the final stages of the dynamics – self-similar dynamics for point, line, and ring rupture. We demonstrate that line and ring rupture are unstable and generically destabilize the axisymmetric rupture at isolated points.
MSC:
| 76A20 | Thin fluid films |
| 76D08 | Lubrication theory |
| 76E17 | Interfacial stability and instability in hydrodynamic stability |
Keywords:
finite-time singularities; thin film rupture; van der Waals forces; low-Reynolds number lubrication model; viscous liquid; solid substrate; dry spots; stability; self-similar dynamicsReferences:
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