The prediction of bubble terminal velocities from wave theory

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Abstract
The terminal velocity of bubbles in low viscosity liquids of infinite extent is known to undergo a marked transition in behavior at an equivalent radius in the order of 0.07 cm. This transition is apparently due to a change from viscous to inviscid flow. It is also known that the inviscid flow regime can be further subdivided into surface tension‐ (Weber number) and buoyancy‐ (Froude number) dominated regimes. This behavior of rising bubbles is strikingly similar to the behavior of surface waves propagated over deep water. The analogy is found to be in quantitative agreement when the wavelength is suitably interpreted in terms of bubble dimensions. The inference of this analogy is that bubbles may be thought of as interfacial disturbances whose rate of propagation is governed by the well‐known laws of wave motion.

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