Numerical Investigation of Grain Coarsening and Coalescence Model

A kinetic nonlinear model of mass transfer, grain coarsening and coalescence with potential applications in sintering processes is studied. The model involves nonlinear differential equations that determine the transport of mass between grains. The rate of mass transfer is controlled by the activation energy (an Arrhenius factor) leading to a nonlinear model of mass transfer and grain coarsening. The resulting dynamical system of coupled nonlinear differential equations with random initial conditions (i.e., initial grain mass configuration) is solved by means of the Runge-Kutta method. An analysis of the fixed points of the two-grain system is carried out, and the solution of the multi-grain system is studied. We incorporate coalescence of smaller grains with larger neighbors using a cellular automaton step in the evolution of the system.