An asymptotic and numerical study of slow, steady ascent in a Newtonian fluid with temperature-dependent viscosity

Abstract

In this paper, we revisit, both asymptotically and numerically, the problem of a hot buoyant spherical body with a zero-traction surface ascending through a Newtonian fluid that has temperature-dependent viscosity. Significant analytical progress is possible for four asymptotic regimes in terms of two dimensionless parameters: the Péclet number, Pe, and a viscosity variation parameter, ϵ. Even for mild viscosity variations, the classical isoviscous result due to Levich is found to hold at leading order. More severe viscosity variations lead to an involved asymptotic structure that was never previously adequately reconciled numerically; we achieve this successfully with the help of a finite-element method.