A model is developed to describe the dynamic forces acting between two deformable drops, or between one drop and a solid surface, when they are in relative axisymmetric motion at separations of Շ100 nm in a Newtonian liquid. Forces arise from hydrodynamic pressure in the draining liquid film that separates the interfaces and from disjoining pressure due to repulsive or attractive surface forces. Predictions of the model are successfully compared with recent experimental measurements of the force between two micrometer-scale surfactant stabilized decane drops in water in an atomic force microscope ͓S. and with subnanometer resolution measurements of time-dependent deformations of a millimeter-scale mercury drop approaching a flat mica surface in a modified surface force apparatus ͓J. N. Connor and R. G. Horn, Faraday Discuss. 123, 193 ͑2003͒; R. G. Horn, M. Asadullah, and J. N. Connor, Langmuir 22, 2610 ͑2006͔͒. Special limits of the model applicable to small and moderate deformation regimes are also studied to elucidate the key physical ingredients that contribute to the characteristic behavior of dynamic collisions involving fluid interfaces.

A model developed previously to analyze force measurements between two deformable droplets in the atomic force microscope [Langmuir 2005, 21, 2912-2922] is used to model the drainage of an aqueous film between a mica plate and a deformable mercury drop for both repulsive and attractive electrical double-layer interactions between the mica and the mercury. The predictions of the model are compared with previously published data [Faraday Discuss. 2003, 123, 193-206] on the evolution of the aqueous film whose thickness has been measured with subnanometer precision. Excellent agreement is found between theoretical results and experimental data. This supports the assumptions made in the model which include no-slip boundary conditions at both interfaces. Furthermore, the successful fit attests to the utility of the model as a tool to explore details of the drainage mechanisms of nanometer-thick films in which fluid flow, surface deformations, and colloidal forces are all involved. One interesting result is that the model can predict the time at which the aqueous film collapses when attractive mica-mercury forces are present without the need to invoke capillary waves or other local instabilities of the mercury/electrolyte interface.