Abstract: The electrical interaction between two axisymmetric
spheroidal particles in an electrolyte solution is examined numerically.
A Galerkin finite element method combined with a Newton-Raphson
iteration scheme is proposed to evaluate the spatial variation in the
electrical potential, and the result obtained used to estimate the
interaction energy between two particles. We show that if the surface
charge density is fixed, the potential gradient is larger at a point, which
has a larger curvature, and if surface potential is fixed, surface charge
density is proportional to the curvature. Also, if the total interaction
energy against closest surface-to-surface curve exhibits a primary
maximum, the maximum follows the order (oblate-oblate) >
(sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve
has a secondary minimum, the absolute value of the minimum follows
the same order.
Abstract: A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional
axisymmetric region is developed. The boundary of the region
is defined by an arbitrary analytic function. The method uses a
coordinate transformation and an expansion in eigenfunctions. The
effectiveness is checked and confirmed by applying the method to a
particular example, which is a prolate spheroid.