Slow growth of an isolated disk-shaped bubble of constant eccentricity in the presence of a distributed gas source

Gardiner, B.S., Boudreau, B.P. and Johnson, B.D. (2003) Slow growth of an isolated disk-shaped bubble of constant eccentricity in the presence of a distributed gas source. Applied Mathematical Modelling, 27 (10), 817-829. (doi:10.1016/S0307-904X(03)00086-6).

Abstract

In this paper we consider the diffusion-controlled (small Péclet number) growth of an isolated, oblate-spheroidal (disk-shaped) bubble of constant eccentricity (aspect ratio) in a medium that actively produces the volatile substance via a distributed source, but does not itself offer significant resistance to growth. Oblate spheroidal bubbles are predicted to grow faster than spherical ones, due to the higher surface area to volume ratio; yet, bubbles of all eccentricities grow proportionally to the square root of time, as expected for a diffusive process. In the presence of a distributed source, however, the growth time becomes dependent on the square-root of the source strength, in the limit as the boundary forcing, i.e., the degree of super-saturation, becomes negligible. Furthermore, we demonstrate that the previously known spherical solution is contained within the more general spheroidal solution. In addition, we produced new expression to describe the growth of a disk in terms of the evolution of the radius of a volume-equivalent sphere and another simple expression relating the growth time of a disk to that of a sphere.

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