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Article

Stokes Equation in a Semi-Infinite Region: Generalization of the Lamb Solution and Applications to Marangoni Flows

Laboratoire Ondes et Matière d’Aquitaine (UMR 5798), CNRS, University of Bordeaux, F-33400 Talence, France
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Fluids 2020, 5(4), 249; https://doi.org/10.3390/fluids5040249
Received: 1 December 2020 / Revised: 12 December 2020 / Accepted: 15 December 2020 / Published: 18 December 2020
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics: Feature Papers)
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. View Full-Text
Keywords: Stokes flow; Lamb solution; spherical harmonics; hemispheric Legendre functions; Marangoni and thermocapillary flows Stokes flow; Lamb solution; spherical harmonics; hemispheric Legendre functions; Marangoni and thermocapillary flows
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MDPI and ACS Style

Koleski, G.; Bickel, T. Stokes Equation in a Semi-Infinite Region: Generalization of the Lamb Solution and Applications to Marangoni Flows. Fluids 2020, 5, 249. https://doi.org/10.3390/fluids5040249

AMA Style

Koleski G, Bickel T. Stokes Equation in a Semi-Infinite Region: Generalization of the Lamb Solution and Applications to Marangoni Flows. Fluids. 2020; 5(4):249. https://doi.org/10.3390/fluids5040249

Chicago/Turabian Style

Koleski, Goce, and Thomas Bickel. 2020. "Stokes Equation in a Semi-Infinite Region: Generalization of the Lamb Solution and Applications to Marangoni Flows" Fluids 5, no. 4: 249. https://doi.org/10.3390/fluids5040249

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