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We propose a boundary integral method to study the shape of a bubble rising under gravity in a dilute polymer solution. Constitutive properties are modelled using a FENE model [M.D. Chilcott, J.M. Rallison, J. Non-Newtonian Fluid Mech. 29 (1988) 38 1] with a pure surface tension interface. We employ a birefringent strand representation [O.G. Harlen, J.M. Rallison, M.D. Chilcott, High-Deborah-number flows of dilute polymer, J. Non-Newtonian Fluid Mech.34 (1990) 319-349] of the wake to simulate the shape and the time-dependent motion of the bubble. Steady and non-steady solutions reproduce qualitatively the bubble deformation seen in experiment with a small region of very high curvature near the rear stagnation point of the bubble. We find a limit point for steady axisymmetric solutions if the polymer concentration is increased or the surface tension is decreased. Rise speed jump discontinuities were not found. (c) 2006 Elsevier B.V. All rights reserved. |
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