On the growth of a non‐ideal gas bubble in a solvent‐polymer solution

Abstract

A model for the growth of an ideal and a non-ideal spherical gas bubble in a quiescent viscous liquid is presented. The growth of the bubble is assumed to be controlled by both mass transfer and viscous forces. Using the integral method, the differential momentum and binary mass balances were transformed into ordinary differential equations, which were numerically solved. Some analytical solutions for simple cases are also presented. The relevance of this work to the process of polymer melt devolatilization is discussed.

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

“…In view of the above restrictions, the equation of motion, integral mass (gas) balance over the bubble and differential mass (dissolved gas) balance in the surroundings mother phase take the following forms [14]. Equation of motion is given by Equation (3):…”

“…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.…”

Numerical simulation of bubble growth in a limited amount of liquid

“…Furthermore, he predicted the cell size distribution. Among the numerical methods, the finite difference method and integral method have been widely used in many studies on bubble growth, and the finite element method was introduced to simulate the bubble growth process gradually in recent years 11, 12, 14–19…”

Dynamics of Spherical Bubble Growth

“…A large number of mathematical models for spherical bubble growth in a quiescent liquid have been presented in the literature. In the devolatilization process and in the related area of foamed plastics, it is common to assume an isothermal bubble growth, that is, a growth controlled by momentum and mass transfer [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Heat transfer has been usually neglected; however, when it was taken into account, its contribution came through the dependence of the physical properties (such as viscosity and diffusion coefficient) on the temperature, or by assuming a temperature profile within the liquid [22][23][24].…”