Numerical modeling of dissolution process of spherical precipitates in alloys by differential quadrature method (DQM)

Prediction of the dissolution kinetics of precipitates is important in various metallurgical processes such as welding, homogenization, and preheating of the age hardenable alloys. The problem of spherical particle dissolution is a moving boundary problem, which has no exact solution yet. In the present study, a numerical model based on the differential quadrature method is presented to solve the problem of precipitate dissolution with spherical geometry in a matrix with finite dimensions. In the proposed model, the dissolution kinetics is expressed as a function of the volume fraction of the precipitate, the concentration of the alloying element in the matrix, and precipitate, equilibrium concentration at the precipitate /matrix interface, and the annealing temperature. The convergence of the presented numerical model in solving the dissolution problem is evaluated by examining the effect of time step size and number of grid points on the numerical solution results. The accuracy of the proposed model is also evaluated by comparing the model results with the results of an approximate analytical model as well as experimental data. The results show that the proposed model converges even with a low number of grid points and is in good agreement