A Solution of the Spherical Diffusion Equation and Its Application to Nucleating Particle Lifetimes.
NAVAL WEAPONS CENTER CHINA LAKE CALIF
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The dissolution of a spherical particle in a spherical water drop is governed by the radial diffusion equation provided the predominate transport process is diffusion. The boundary conditions are no flow through the water-drop surface and a saturated solution of the particle material at the particle-water interface. The initial condition is an arbitrary radial distribution of concentration. Since the particle radius is shrinking, the inner boundary condition is time dependent. However, instead of attempting the solution with a moving boundary, the concept of a fixed, effective particle radius is introduced. With these boundary and initial conditions, an infinite series solution to the diffusion equation is found by the Laplace transform technique. The particle lifetime is found by using this solution of the diffusion equation to determine the time at which the particle has just completely dissolved. Curves of lifetimes as functions of solubility and particle and drop radii are given. Author
- Physical Chemistry