Characteristics of velocity, bubble's radius, and pressure in liquid and gas bubble mixture

Abstract

The study focuses on the formation of gas bubbles, a crucial phenomenon that significantly impacts the hydrodynamics in liquid–gas reactors. This phenomenon has been observed in industrial engineering, leading to the development of model equations that describe the velocity of a liquid–gas mixture, pressure, and deviation in the gas bubble's initial radius. Kudryashov–Sinelshchikov (KS) established coupled equations (CEs) to describe the dynamics of the liquid–gas mixture. Here, the study aims to investigate the behavior of velocity, deviation in the bubble radius, and pressures by deriving exact solutions of the KSCEs and representing them graphically. The findings show that the velocity can take negative or positive values, representing interfacial velocity or superficial velocity for both liquid and gas, respectively. The pressure may also be negative or positive, corresponding to the shrinking or stretchering of the liquid surface, respectively. The dynamics of the velocity and the deviation in the bubble radius exhibit similar qualitative behavior, while the pressure shows a variant behavior. The dominant parameters are found to be the gas bubble's initial radius and the polytropic exponent. The stability of the steady-state solution is also analyzed. This study contributes to the existing literature by examining the CEs, which have not been studied until now.