Bubble growth in a viscous Newtonian liquid

Transport analysis of diffusion‐induced bubble growth and collapse in viscous liquids

“…Amon and Denson (1984) appear to be the first to have used this approach to describe the growth of a bubble surrounded by a finite shell of a Newtonian liquid. Arefmanesh et al (1992) developed a similar model and made comparisons of predicted bubble growth to those from the TBL approximation model of Rosner and Epstein (1972) and Patel (1980). The results of such a comparison are somewhat inconclusive since the bubble radius at all but early stages of the growth process predicted by the finite shell model can be strongly influenced by the approach of the bubble radius to its terminal value.…”

“…34 can be eliminated using a simple change of variable. [The following change of variable suggested by Patel (1980) can be used to resolve the singularities in Eqs. 34 and 41: 6 = pg R 3 -( 1 + 2Nc).l The change of variable required to resolve the singularity in Eq.…”

“…The dissolution of a gas bubble in a Newtonian liquid and in a viscoelastic liquid (Oldroyd B fluid) was modeled by Zana and Leal (1975) who also used the IDS approximation. A model for bubble growth in a Newtonian liquid was developed by Patel (1980) based on a TBL approximation used by Rosner and Epstein (1972), which also used the IDS approximation. The TBL approximation used by Rosner and Epstein (1972), who developed a model for bubble growth in which viscous and inertial effects were neglected, can be classified as a special type of weighted residuals method where the species continuity equation is satisfied only in an average sense.…”

Theoretical and experimental study of foaming process with chain extended recycled PET

“…Therefore, researchers have attempted to optimize the foaming processes in order to produce high quality final products. One of the most used methods for the optimization of the manufacturing process, as well as final product quality is numerical modeling: a large number of mathematical models for bubble growth were presented in the literature [11][12][13][14][15][16][17][18][19][20][21]. Some models have been written for bubble growth assumed to be governed by mass transfer alone, while others assumed momentum transfer alone.…”

“…The goal of this work is twofold: -starting from preliminary results obtained in a previous work [7], the first goal of this work is to improve the process of extrusion foaming by chemical blowing agent (CBA) in order to produce high density foams from PET industrial scraps with a very low viscosity; -the second goal of this work is to develop a simple and useful tool which can help the companies in choosing foaming conditions without performing complicated laboratory tests. With this aim, according to literature indications [11,14,16], the growth of a spherical bubble in a polymeric liquid has been theoretically studied by taking into account both mass transfer phenomenon and viscous forces effect. Moreover, with the aim of predicting the morphology of the final foam, a non isothermal model was developed.…”