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: The dissolution of spherical particles in liquids is analyzed dynamically. Here, we consider the case the dissolution of solute yields a solute-free solid phase in the outer portion of a particle. As dissolution proceeds, the interface between the undissolved solid phase and the solute-free solid phase moves towards the center of the particle. We assume that there exist two resistances for the diffusion of solute molecules: the resistance due to the solute-free portion of the particle and that due to a surface layer near solid-liquid interface. In general, the equation governing the dynamic behavior of dissolution needs to be solved numerically. However, analytical expressions for the temporal variation of the size of the undissoved portion of a particle and the variation of dissolution time can be obtained in some special cases. The present analysis takes the effect of variable bulk solute concentration on dissolution into account.