Method for Determining Particle Growth Dynamics in a Two-Component Alloy

Abstract

The paper deals with the issue of particle growth in a two-component alloy. The particle is formed from chemical reaction products that occur at the phase boundary. A generalized mathematical model of particle growth includes diffusion equations, mass transfer equations in the boundary layer, and equations characterizing a change in the growing particle radius. The paper proposes an approach that reduces issues to the system of PDEs and ODE that describes the state of growing particle. This approach provides a basis for developing a numerical method for calculating the growing particle radius as a function of time, based on the obtained equations. The computational scheme involves the finite-difference analogues of equations with an additional regularizing functional that ensure method stability with respect to accumulated computational error. In order to verify reliability of the proposed computational scheme and to obtain experimental error estimates of numerical solutions, computational experiments were carried out. In the experiments, the growing particle radius is determined with respect to the time via the proposed method. Also, comparative analysis of the calculated radius with test values was carried out and experimental estimates of deviations of the calculated radius from the test functions were obtained. The experiment results presented in the work indicate sufficient accuracy of the developed numerical method.