Abstract
In this paper we use a combination of analytical and numerical techniques to analyse the onset of steady Marangoni convection in a spherical shell of fluid with an outer free surface surrounding a rigid sphere. In so doing we correct the formulation of the problem and the results presented by Cloot & Lebon (Microgravity sci. technol. 3 (1) 1990: 44–46). We find that if the free surface of the layer is non-deformable then the layer is always stable when heated from the outside and is unstable when heated from the inside if the magnitude of the (positive) non-dimensional Marangoni number is sufficiently large. If the free surface of the layer is deformable then the layer is always unstable when heated from the inside. It is stable when heated from the outside if C r < r 2/4, but if C r > r 2/4 then it is unstable if the magnitude of the (negative) Marangoni number is sufficiently large, where C r is the non-dimensional Crispation number and r 2 the non-dimensionalradius of the undisturbed outer free surface of the fluid.
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Wilson, S.K. The onset of steady Marangoni convection in a spherical geometry. J Eng Math 28, 427–445 (1994). https://doi.org/10.1007/BF00058913
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DOI: https://doi.org/10.1007/BF00058913