Coalescence of Two Viscous Cylinders by Capillarity: Part I, Theory

The creeping plane flow of two viscous cylinders coalescing under the influence of surface tension is described theoretically in a series of three articles. Part I is a theoretical overview. The physical assumptions affecting applicability of the theory are discussed. The shape as a function of time and of the initial diameter ratio D ≥ 1 is given in parametric form. For D = 1 and D ∞, the shape sequences are known exactly; for finite D > 1, a first‐order differential equation is solved numerically. The time requires a quadrature. This is accurate, and easier than solving the fluid‐dynamical field equations. The theory encompasses time‐dependent liquid properties.