Abstraet--A numerical study is presented of the drainage and rupture of the liquid film between two drops whose centres approach each other at constant velocity. The considerations are restricted to the partially-mobile case (in which the drop viscosity is rate-determining) and to small approach velocities. The latter restriction permits a transformation of the governing equations to a single universal form, which is solved with the help of boundary integral theory. As in the constant force case, the numerical results show the formation of a dimple but the final drainage behaviour differs considerably. Finally, the influence of van der Waals forces is investigated and the results are shown to correspond well with a simple model proposed earlier for the effective critical film-rupture thickness.

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In the present analysis the classical film model (or film theory) is reviewed and extended. First, on the basis of a thorough analysis, the governing equations of diffusion, energy and momentum of a stagnant film are derived and solved. Subsequently, the well-known correction factors for the effect of suction/injection on mass, heat and momentum transfer are derived. Next, employing global balances of mass, energy and momentum, the film model is applied to channel flow. This application yields a new expression for the pressure drop and hence it is compared extensively with experimental and theoretical results of previous investigators, yielding good agreement. The onset of fog formation in a binary mixture, both in the transferring film and/or in the bulk, is explained graphically with the help of the relation between temperature and vapour mass fraction and the saturation line of the vapour.