NEW LOOK AT WAVE ANALOGY FOR PREDICTION OF BUBBLE TERMINAL VELOCITIES

The analogy between waves on the surface of an infinite fluid and bubb les rising in low-viscosity fluids of infinite extent, originally prop osed by Mendelson for 3-D bubbles, has been used to predict the termin al velocity of plane bubbles. In terms of its terminal velocity a plan e bubble rising in a rectangular duct of small aspect (spacing-to-widt h) ratio behaves as if it were a 3-D bubble rising in an infinite medi um as long as the end walls (the walls in the widthwise direction) are sufficiently far apart. As the end walls are moved toward each other, a wall effect is found to exist. A general expression for the termina l velocity of a bubble of any size rising in a rectangular duct includ ing this wall effect is also developed based on the wave analogy and s hown to compare well with existing data.