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

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.

References in corpus (5)

• The hydrodynamics of swimming microorganisms
• Thermally driven Marangoni surfers
• Azimuthal instability of the radial thermocapillary flow around a hot bead trapped at the water-air interface
• Effect of surface-active contaminants on radial thermocapillary flows
• Hydrodynamic response of a surfactant-laden interface to a radial flow

Cited by in corpus (1)

• Blockage of thermocapillary flows by surface-active impurities