Abstract
A theoretical prediction of the lubrication force resisting the close approach of two spherical drops of arbitrary radii and viscosities separated by a thin viscous fluid layer is presented. The hydrodynamic resistance is predicted to be weaker than that for two colliding rigid spheres in near contact due to the mobility of the drop interfaces. Solutions are also presented for the limiting cases of (a) a drop or bubble approaching a rigid sphere or flat plate, (b) a drop approaching a bubble or a flat free surface and (c) a rigid sphere approaching a flat free surface. When one of the interfaces is completely mobile, as for a bubble or a free surface, the ratio of the lubrication force to that for two rigid spheres with the same relative velocity and reduced radius is predicted to be less than one-fourth; when one interface is completely rigid or immobile, this ratio is predicted to be greater than one-fourth. The results are shown to be in good agreement with previous solutions based on the method of bispherical coordinates when the gap is much smaller than the radius of the smallest drop.
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