The chapter discusses the stability of gas bubbles in liquid-gas solutions, focusing on the rates of bubble dissolution and growth. The authors, P. S. Epstein and M. S. Plesset, from the California Institute of Technology, present approximate solutions for the rate of solution by diffusion and the rate of growth of a bubble in an undersaturated or oversaturated liquid-gas solution, respectively. They neglect the translational motion of the bubble to simplify the analysis, noting that this approximation is valid due to the small concentration of dissolved gas compared to the gas density in the bubble. The diffusion equation is solved using spherical symmetry, and the concentration gradient at the bubble boundary is derived. The mass flow into the bubble is then calculated, leading to differential equations for the radius of the bubble over time. These equations are solved for both undersaturated and oversaturated solutions, with and without the effect of surface tension. For undersaturated solutions, the time required for complete dissolution is proportional to the square of the initial bubble radius. For oversaturated solutions, the radius of the bubble grows linearly with time when the time is large. The inclusion of surface tension effects is also considered, showing that it slightly reduces the dissolution rate and increases the growth rate of the bubble. The chapter includes graphical representations and numerical tables to illustrate the solutions and their dependencies on various parameters, such as the ratio of dissolved gas concentrations and the surface tension constant.The chapter discusses the stability of gas bubbles in liquid-gas solutions, focusing on the rates of bubble dissolution and growth. The authors, P. S. Epstein and M. S. Plesset, from the California Institute of Technology, present approximate solutions for the rate of solution by diffusion and the rate of growth of a bubble in an undersaturated or oversaturated liquid-gas solution, respectively. They neglect the translational motion of the bubble to simplify the analysis, noting that this approximation is valid due to the small concentration of dissolved gas compared to the gas density in the bubble. The diffusion equation is solved using spherical symmetry, and the concentration gradient at the bubble boundary is derived. The mass flow into the bubble is then calculated, leading to differential equations for the radius of the bubble over time. These equations are solved for both undersaturated and oversaturated solutions, with and without the effect of surface tension. For undersaturated solutions, the time required for complete dissolution is proportional to the square of the initial bubble radius. For oversaturated solutions, the radius of the bubble grows linearly with time when the time is large. The inclusion of surface tension effects is also considered, showing that it slightly reduces the dissolution rate and increases the growth rate of the bubble. The chapter includes graphical representations and numerical tables to illustrate the solutions and their dependencies on various parameters, such as the ratio of dissolved gas concentrations and the surface tension constant.