On the slow motion of two spheres in contact along their line of centres through a viscous fluid

An exact solution in terms of analytic functions is given for the Stokes stream function and forces acting on two spheres in contact when the spheres move uniformly with the same velocity along their line of centres. For the case of equal sized spheres, the values of the forces agree with the Faxén limit of the Stimson–Jeffery forces for separated spheres when the minimum clearance between the spheres tends to zero. Numerical values of the forces for arbitrary sized spheres are tabulated and compared with corresponding values when the spheres are separated over a range of values of the minimum clearance. Comparison of the theoretical results with those obtained experimentally for the case of equal sized spheres is also given.