An exact solution for the axisymmetric incompressible potential flow over two touching spheres is presented. A tangent-sphere coordinate system is used to simplify the boundary conditions. The Laplace equation is solved by means of separation of variables and the expression for the added mass obtained.
Small RD, Weihs DD. Axisymmetric Potential Flow Over Two Spheres in Contact. ASME. J. Appl. Mech. 1975;42(4):763-765. doi:10.1115/1.3423701.