Numerical solutions for shape evolution of a particle growing in axisymmetric flows of supersaturated solution

Abstract

Numerical studies are performed to investigate the growth behaviors of a precipitate particle in the well-defined flows of supersaturated solution with consideration of the isotropic and the anisotropic interfacial free energies. For the well-defined flows, three types of axisymmetric flows are considered: uniform streaming flow, uniaxial straining flow, and biaxial straining flow. The numerical solutions are obtained on the numerically generated orthogonal curvilinear coordinate system, which is automatically adjusted to fit the boundary shape at any time. The initial value problem of particle growth is solved using a fully implicit first-order backward time differencing in order to ensure the numerical stability. The numerical solutions show that the convection effect results in higher local growth rate near the surface where the flow is incoming and lower local growth rate near the surface where the flow is outgoing. Due to the difference in local growth rate, an initially spherical particle evolves into a peach-like shape in the uniform streaming flow, an oblate spheroidal shape in the uniaxial straining flow, and a prolate barrel-like shape in the biaxial straining flow. (C) 1998 Elsevier Science B.V. All rights reserved.