Original Contributions

Rheologica Acta

, Volume 30, Issue 3, pp 274-283

First online:

Diffusion-induced growth of a gas bubble in a viscoelastic fluid

  • A. ArefmaneshAffiliated withDepartment of Mechanical Engineering, University of Delaware
  • , S. G. AdvaniAffiliated withDepartment of Mechanical Engineering, University of Delaware

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The diffusion-induced growth of a spherical gas bubble surrounded by a thin shell of viscoelastic fluid containing a limited amount of dissolved gas is analyzed. This is representative of a situation when a large number of bubbles grows in close proximity in a viscoelastic medium. The upper-convected Maxwell model is employed to describe the rheology of the fluid. Limited quantities of the dissolved gas available in the liquid shell mandates solution of the convection-diffusion equation, as opposed to using similarity solutions or polynomial profiles to describe the mass transport across the interface. Utilizing the properties of a potential field and a Lagrangian transformation, a new approach is introduced to solve the coupled system of integro-differential equations governing the bubble growth. The results indicate that, at the early stages of the growth, bubbles in a viscoelastic fluid grow faster than in a Newtonian fluid. However, eventually they attain the same steady-state configuration.

Key words

Bubble growth mass diffusion Maxwell fluid concentration profile