Potential theory in the problems of interfraction at small gap widths. Sphere and flat interface

An asymptotic model is proposed for the flow pattern inside a droplet when a thin liquid layer is formed at its advancing nose; at small gap widths, so far as the substantial part of the flow inside the droplet is concerned, the interface may be regarded as a flat interface. Calculations are made using the classical potential theory. The problem of hydrodynamic interaction is brought to the investigation of an integral equation for the radial velocity a the flat interface. The equation is asymptotically solved for low and high viscosities in the droplet. For these cases, results are also reported about drag force.