Self-similar growth of a gas bubble induced by localized heating: the effect of temperature-dependent transport properties

Abstract

A gas bubble growing in a saturated liquid under the action of an internal heat source is studied theoretically as a model problem for the growth of a bubble around a miniature spherical heater submerged in the liquid. In general, this problem does not admit a self-similar solution but it is shown that for a heat source with strength increasing in proportion to the square root of time, a self-similar solution exists even under temperature-dependent transport properties. In that case the bubble radius is also proportional to the square root of time with a proportionality constant which can be found from the solution of a boundary value problem. The effect of temperature dependence of gas-in-liquid diffusivity and liquid and gas thermal conductivities on bubble growth is examined in detail. Finally, approximating explicit procedures are proposed for the computation of bubble growth rate without resorting to the solution of the boundary value problem. (C) 2004 Elsevier Ltd. All rights reserved.