Two touching spherical drops in uniaxial extensional flow: analytic solution to the creeping flow problem

We solve the problem of the creeping motion of a uniaxial extensional flow past two touching spherical drops when the line of centers is parallel to the axis of symmetry of the flow, using tangent sphere coordinates. We apply this solution to the case of two equal size drops. It provides an exact result for the equal and opposite force acting on each drop along the line of centers. We also use it to determine the magnitude of the internal recirculating flow in the vicinity of the rear stagnation point, which can be used to evaluate the importance of this flow on the film drainage process for two (nearly) touching drops in a coalescence process for the limiting case, Ca < 1.