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Publication Detail
Bubble growth in a two-dimensional viscoelastic foam
Abstract
The effects of viscoelasticity on the expansion of gas bubbles arranged ina hexagonal array in a polymeric fluid are investigated. The expansion isdriven by the diffusion of a soluble gas from the liquid phase, and therate of expansion is controlled by a combination of gas diffusion, fluidrheology and surface tension.In the diffusion limited case, the initial growth rate is slow due tosmall surface area, whereas at high diffusivity initial growth is rapidand resisted only by background solvent viscosity. In this high Deborahnumber limit, we see a two stage expansion in which there is an initialrapid expansion up to the size at which the elastic stresses balance thepressure difference. Beyond this time the bubble expansion is controlledby the relaxation of the polymer. We also illustrate how viscoelasticityaffects the shape of the bubble.In addition to a full finite element calculation of the two-dimensionalflow, two one-dimensional approximations valid in the limits of small andlarge gas area fractions are presented. We show that these approximationsgive accurate predictions of the evolution of the bubble area, but giveless accurate predictions of the bubble shape.
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Dept of Mathematics
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