Kang, I. S. and Leal, L. G. (1989) Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number. II. Deformation of a bubble in a biaxial straining flow. Physics of Fluids A, 1 (4). pp. 644-660. ISSN 0899-8213. http://resolver.caltech.edu/CaltechAUTHORS:KANpofa89
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Numerical solutions of the full Navier–Stokes equations are used to investigate the steady and unsteady deformation of a bubble in a biaxial straining flow for Reynolds numbers in the range 0≤R≤400, and Weber numbers up to O(10). The steady-state bubble shape and the frequency of small amplitude oscillations of shape are both identical for biaxial and uniaxial straining flows in the potential flow limit. However, for a large, but finite Reynolds number, the bubble shape in the biaxial straining flow is found to be fundamentally different from the shape in uniaxial flows. This is shown to be a consequence of vorticity enhancement via vortex line stretching in the biaxial flow, which does not occur in the uniaxial flow. At the highest Reynolds number considered here, R=400, the steady-state bubble behavior for low W is qualitatively similar to the potential flow case, with a limit point for existence of the low W branch of steady solutions occurring at W~6. However, in this case a second branch of steady solutions is found for larger W≥7, which exhibits oblate bubble shapes for large W, and has no counterpart in the potential flow limit. In unsteady flows, the behavior of bubble deformation is fundamentally different in the uniaxial and biaxial flows for both high Reynolds numbers and the potential flow limit. This suggests that breakup will occur in far different ways in the two cases.
|Additional Information:||© 1989 American Institute of Physics. Received 11 August 1988; accepted 28 November 1988. This work was supported by grants from the Fluid Mechanics Program and the Office of Advanced Scientific Computing at the National Science Foundation.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||01 Apr 2008|
|Last Modified:||26 Dec 2012 09:55|
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