Coalescence time for a small drop or bubble at a fluid-fluid interface



When a small drop or bubble is driven through a liquid phase to a fluid-fluid interface, a thin liquid film which forms between them drains, until an instability forms and coalescence occurs. Lin and Slattery (1982b) developed a hydrodynamic theory for the first portion of this coalescence process: the drainage of the thin liquid film which occurs while it is sufficiently thick that the effects of London-van der Waals forces and electrostatic forces can be ignored. Here we extend their theory to include the effects of the London-van der Waals forces. To simplify the analysis, we follow the suggestion of Buevich and Lipkina (1975, 1978) in developing an expression for the rate of thinning at the rim or barrier ring of the draining film. A linear stability analysis permits us to determie the coalescence time or the elapsed time between the formation of a dimpled film and its rupture at the rim.

For comparison, this same linear stability analysis is applied to the thinning equations developed by MacKay and Mason (1963) for the plane parallel disc model and by Hodgson and Woods (1969) for the cylindrical drop model.

For all three models, our linear stability estimate for the coalescence time tc is in better agreement with the available experimental data than is the elapsed time t between the formation of a dimpled film and its drainage to zero thickness at the rim in the absence of instabilities.