Stokes equation in a semi-infinite region: generalization of Lamb solution and applications to Marangoni flows

G. Koleski; T. Bickel

doi:10.3390/fluids5040249

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arXiv · 2109.04773

Stokes equation in a semi-infinite region: generalization of Lamb solution and applications to Marangoni flows

G. Koleski·T. Bickel

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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 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.

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G. Koleski, T. Bickel. 2021-09-10. Stokes equation in a semi-infinite region: generalization of Lamb solution and applications to Marangoni flows. https://doi.org/10.3390/fluids5040249

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