Movement of Small Gas Bubbles in Smoothly Decelerating Liquid

The time-dependent motion of small gas bubbles in a decelerating liquid is studied. Expressions for the distance traveled by the bubble and for the bubble slip are derived as functions of liquid gas bubble densities, initial velocities, and in terms of a parameter denoting the ratio of the pressure and viscous interaction forces. Results indicate that in cases where the initial velocity of the bubble is lower than the liquid velocity less the limiting slip, the bubble accelerates relative to the liquid. In cases where the bubble initial velocity is equal to or greater than that of the liquid, the bubble decelerates much faster than the liquid until a limiting slip between the gas bubble and liquid is reached. At the equilibrium conditions, in all cases the gas bubble velocity is found to be smaller than that of the corresponding liquid velocity.