Analytical solution of gas bubble dynamics between two-phase flow

• Main Authors: S.A. Mohammadein, G.A. Shalaby, A.F. Abu-Bakr, A.K. Abu-Nab
• Format: Article
• Language: English
• Published: Elsevier 2017-01-01
• Series: Results in Physics
• Online Access: http://www.sciencedirect.com/science/article/pii/S2211379717306745

The growth of a gas bubble between two-phase flow represents the current physical problem. The mathematical model is performed by mass, momentum and diffusion equations. The Problem is solved analytically by using the modified Plesset and Zwick method. The growth process is affected by shear stress, coefficient of consistency, surface tension and void fraction in order to derive the growth of a gas bubble between two-phase in non-Newtonian fluids. The growth of a gas bubble in non-Newtonian fluids flow performs lower values than that in case of Newtonian one. The initial time of bubble growth for the different values of superheating and flow index n in the thermal stage is obtained. Moreover, the effect of critical bubble radius Rcr is studied on the growth process. The results satisfy the growth model in Newtonian fluids given by Foster and Zuber (1954) [34] and Scriven theory (Scriven, 1959) [35] for limited values of physical parameters. Keywords: Gas growth bubbles, Shear stress, Extended Plesset and Zwick method, Initial time of bubble