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

B.S. Gardiner; B.P. Boudreau; B.D. Johnson

doi:10.1016/S0307-904X(03)00086-6

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

Journal article

Peer reviewed

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

B.S. Gardiner, B.P. Boudreau and B.D. Johnson

Applied Mathematical Modelling, Vol.27(10), pp.817-829

2003

DOI: https://doi.org/10.1016/S0307-904X(03)00086-6

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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.

Details

Title: Slow growth of an isolated disk-shaped bubble of constant eccentricity in the presence of a distributed gas source
Authors/Creators: B.S. Gardiner (Author/Creator)
B.P. Boudreau (Author/Creator)
B.D. Johnson (Author/Creator)
Publication Details: Applied Mathematical Modelling, Vol.27(10), pp.817-829
Publisher: Elsevier BV
Identifiers: 991005541860307891
Murdoch Affiliation: Murdoch University
Language: English
Resource Type: Journal article

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Collaboration types: Domestic collaboration; International collaboration
Citation topics: 2 Chemistry; 2.89 Ionic, Molecular & Complex Liquids; 2.89.1121 Supercritical Carbon Dioxide
Web Of Science research areas: Engineering, Multidisciplinary; Mathematics, Interdisciplinary Applications; Mechanics
ESI research areas: Engineering