Asymptotic expansions and estimates for the capillary problem
Abstract
The asymptotic properties for the small Bond number B of the equilibrium capillary interface interior to a circular cylindrical tube vertically dipped in an infinite reservoir of liquid are discussed. (The Bond number B is a dimensionless parameter which is the ratio of gravitational to capillary forces.) The formal expansion in powers of B of the solution to the differential equation describing the equilibrium surface (as can be obtained by standard perturbation methods) is proved to be truly asymptotic  to all orders and uniformly in the variable and parameter gamma, the contact angle. Sequences of general estimates, in closed form, from above and from below, are also given for the solution and related functions. The Mth term in these sequences are asymptotically exact to order m. An idiosyncrasy of the problem, crucial in obtaining these estimates, is the absolute monotonicity of the structural function of the system in integral form.
 Publication:

2d International Colloquium on Drops and Bubbles
 Pub Date:
 March 1982
 Bibcode:
 1982drbu.coll..344B
 Keywords:

 Asymptotic Methods;
 Capillary Flow;
 Capillary Tubes;
 Estimates;
 Expansion;
 Fluid Boundaries;
 Menisci;
 Boundary Value Problems;
 Differential Equations;
 Gravitation;
 Interfacial Tension;
 Reservoirs;
 Fluid Mechanics and Heat Transfer