Bubble growth in viscous Newtonian and non-Newtonian liquids

A model for the dynamics of hydrodynamically controlled spherical bubble growth in quiescent viscous newtonian and non-newtonian liquids is presented. Two constitutive equations were used to describe the behavior of the liquid medium: (1) a simple power law relation and (2) a truncated power law. Application of the truncated power law resulted in four different cases: (a) at all times the liquid acts as a newtonian liquid; (b) at all times the liquid behaves as a simple power law liquid; (c) at all times the liquid close to the growing bubble obeys a power law relation and the liquid far away from the bubble behaves as a newtonian liquid; (d) all the liquid initially behaves as a newtonian liquid and at some time transforms to a two-region liquid. Analytical expressions were derived for bubble growth as a function of dimensionless system parameters. The relevance of this work to the process of polymer devolatilization is discussed.