Stokes flow of a cylinder and half-space driven by capillarity

The coalescence of a cylinder with half-space by creeping viscous flow driven solely by surface tension is analysed using methods developed previously. The evolution of the shape with time is described, exactly, in terms of a time-dependent mapping function z = ω(ζ, t ) of the upper half-plane, conformal on Im ζ [Gt ] 0. The results are in closed analytic form except for the time, which requires a quadrature. The height of the figure decays as t −1 as t → ∞, which is consistent with Kuiken's analysis of an isolated disturbance. (Previously, the author reported an erroneous solution which behaved otherwise.) The results are compared with the coalescence of equal cylinders obtained previously. For a modest degree of coalescence, the shapes are rather alike. In the limit as t → 0. the time dependence of the minimum widths (necks) are the same. At the times when the minimum widths disappear, the heights of the two shapes are equal. Appended is a note providing a counter-example to earlier conjecture. A simply connected region undergoing this type of flow need not remain so.