Mathematical models of bubble evolution in a Hele-Shaw Cell

Dallaston, Michael C. (2013) Mathematical models of bubble evolution in a Hele-Shaw Cell. PhD by Publication, Queensland University of Technology.

Abstract

This thesis concerns the mathematical model of moving fluid interfaces in a Hele-Shaw cell: an experimental device in which fluid flow is studied by sandwiching the fluid between two closely separated plates. Analytic and numerical methods are developed to gain new insights into interfacial stability and bubble evolution, and the influence of different boundary effects is examined.

In particular, the properties of the velocity-dependent kinetic undercooling boundary condition are analysed, with regard to the selection of only discrete possible shapes of travelling fingers of fluid, the formation of corners on the interface, and the interaction of kinetic undercooling with the better known effect of surface tension. Explicit solutions to the problem of an expanding or contracting ring of fluid are also developed.

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Full-text downloads:

460 since deposited on 31 Oct 2013
82 in the past twelve months

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ID Code: 63701
Item Type: QUT Thesis (PhD by Publication)
Supervisor: McCue, Scott & Simpson, Matthew
Additional Information: Recipient of 2013 Outstanding Doctoral Thesis Award.
Keywords: Hele-Shaw, free boundary problem, Saffman-Taylor instability, kinetic undercooling, bubble extinction, ODTA
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Institution: Queensland University of Technology
Deposited On: 31 Oct 2013 02:17
Last Modified: 08 Sep 2015 23:49

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