Stokes Equation in a Semi-Infinite Region: Generalization of the Lamb Solution and Applications to Marangoni Flows
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Abstract
We consider the creeping flow of a Newtonian fluid in a hemispherical region. In a domain with spherical or nearly spherical geometry, the solution of the Stokes equation can be expressed as a series of spherical harmonics. However, the original Lamb solution is not complete when the flow is restricted to a semi-infinite space. The general solution in hemispherical geometry is then constructed explicitly. As an application, we discuss the solutions of Marangoni flows due to a local source at the liquid–air interface.Keywords
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This publication has 16 references indexed in Scilit:
- Azimuthal instability of the radial thermocapillary flow around a hot bead trapped at the water–air interfacePhysics of Fluids, 2020
- Symmetrization of Thin Freestanding Liquid Films via a Capillary-Driven FlowPhysical Review Letters, 2020
- Surfactant dynamics: hidden variables controlling fluid flowsJournal of Fluid Mechanics, 2020
- Hydrodynamic response of a surfactant-laden interface to a radial flowPhysical Review Fluids, 2019
- Effect of surface-active contaminants on radial thermocapillary flowsThe European Physical Journal E, 2019
- Liquid meniscus friction on a wet plate: Bubbles, lamellae, and foamsPhysics of Fluids, 2013
- The hydrodynamics of swimming microorganismsReports on Progress in Physics, 2009
- Influence of an adsorption layer on the structure and stability of surface tension driven flowsPhysics of Fluids, 2005
- Thermocapillary convection in a fluid filling a half-space: PMM vol. 31, no. 3, 1967, pp. 577–580Journal of Applied Mathematics and Mechanics, 1967
- The Marangoni EffectsNature, 1960