CONDUCTION IN THE SMALL-GAP BETWEEN 2 SPHERES

A solution to the conduction equation has been developed for two equal size, nonconducting spheres with the line between centers perpendicul ar to the applied field. The solution, valid when the gap between the spheres is small compared to their radius, is based on a matched asymp totic expansion. For the case when the conductivity is uniform everywh ere (i.e., Laplace's equation), the solution agrees well with numerica l results obtained from an infinite series solution in bispherical coo rdinates. An example with a nonuniform conductivity in the gap is pres ented to demonstrate how the method can be extended to more general co nduction problems. (C) 1997 American Institute of Physics.