Thinning of a liquid film as a small drop or bubble approaches a solid plane

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Abstract
When a small drop or bubble approaches a solid surface, a thin liquid film forms between them, drains, until an instability forms and coalescence occurs. A hydrodynamic theory is developed for the first portion of this coalescence process: the drainage of the thin liquid film while it is still sufficiently thick that the effects of London‐van der Waals forces and electrostatic forces can be ignored. This theory describes the time rate of change of the film profile, given only the drop radius and the required physical properties. Predictions are compared with profiles measured by Platikanov (1964) for gas bubbles. It is concluded that, even with only a trace of surfactant present, the liquid‐gas interface may be nearly immobile (tangential components of velocity are zero) and the surface viscosities will have little effect upon the drainage rate.