The effect of the variation of surface tension with temperature on the motion of bubbles and drops

Abstract

The boundary conditions at the surface of a small bubble rising in a liquid are examined theoretically, and it is shown by order-of-magnitude arguments, which are confirmed by detailed calculation in a special case, that although surfacetension gradients must always exist around the bubble, they are too small to affect the motion appreciably unless surface-active substances are present. This is because gradients of surface tension imply gradients of temperature in a pure liquid, and these turn out to be always small near the bubble if they tend to zero at large distances from it. The same is true for drops of one fluid in another.