Modelling drop-drop interactions in an atomic force microscope

Recent experimental developments enabled dynamical measurement of the force between two moving oil drops in solution using an Atomic Force Microscope. The drop sizes (about 40 microns) and velocities (up to 15 microns/s) of the experiments produce a regime where surface forces, hydrodynamics and drop deformation are all significant. A detailed model of the experiments developed by Carnie, Chan, Dagastine, Lewis and Manica (2004) produces calculated force curves with attractive forces due mainly to hydrodynamic lubrication forces, in agreement with experiment. Details of the evolution of the drop surface deformations and surface velocity profiles are included in movies accompanying this paper. A feature of the model is the use of a new boundary condition, obtained by matched asymptotic expansions, to incorporate the weak deformation at the drop scale into the thin film scale. This boundary condition is necessary to obtain results independent of the computational domain size. It also requires modeling assumptions about the three-phase contact line where the drops meet the solid surfaces of the Atomic Force Microscope. We determine the sensitivity of calculated force curves to two simple models for the three-phase contact line motion, and to the assumed values for the drop/solid contact angle