Rheologica Acta

, Volume 30, Issue 3, pp 274–283

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

  • A. Arefmanesh
  • S. G. Advani
Original Contributions

DOI: 10.1007/BF00366641

Cite this article as:
Arefmanesh, A. & Advani, S.G. Rheol Acta (1991) 30: 274. doi:10.1007/BF00366641


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 growthmass diffusionMaxwell fluidconcentration profile

Copyright information

© Steinkopff-Verlag 1991

Authors and Affiliations

  • A. Arefmanesh
    • 1
  • S. G. Advani
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of DelawareNewarkUSA
  2. 2.Dept. of Mechanical Engineering Spencer LaboratoryUniversity of DelawareNewarkUSA