Stability Analysis of a Multicomponent Vapor-Gas Bubble in Contact with a Liquid-Gas Solution

Stability of vapor-gas bubbles, homogeneously nucleated within a liquid-gas solution, depends on the temperature and pressure of the liquid phase, along with the concentration of dissolved gaseous components. While extensive theoretical and experimental investigations have been conducted on bubble nucleation within single-component systems, research on multicomponent systems has mainly focused on binary liquid-gas solutions comprising a solvent and one dissolved gas. Moreover, existing studies on the stability of vapor-gas bubbles have predominantly examined the stability with respect to bubble size, leaving other critical factors relatively unexplored. Here, we present a methodology to determine potential equilibrium states for a single vapor-gas bubble homogeneously nucleated within a large multicomponent liquid-gas solution, encompassing a subcritical solvent and n - 1 gaseous components, with temperature and liquid phase pressure held constant. Additionally, we assess equilibrium state stability by analyzing the free energy change of the system with respect to both bubble size and the composition of the vapor-gas phase within the bubble, using rigorous phase equilibrium equations to account for nonideal behavior in both liquid-gas and vapor-gas phases. We then apply this to investigate the number and nature of equilibrium states in a ternary system of water-oxygen-nitrogen across various scenarios of oxygen and nitrogen saturation levels in the liquid phase, while also meticulously examining the effects of liquid phase temperature and pressure on the stability of the system. The proposed model can be used to optimize the design of micro-nano bubble technologies for diverse engineering applications, ranging from agriculture to water treatment and biomedicine.