Particle in cell simulation of combustion synthesis of TiC nanoparticles

Abstract

A coupled continuum-discrete numerical model is presented to study the synthesis of TiC nanosized aggregates during a self-propagating combustion synthesis (SHS) process. The overall model describes the transient of the basic mechanisms governing the SHS process in a two-dimensional micrometer size system. At each time step, the continuum (micrometer scale) model computes the current temperature field according to the prescribed boundary conditions. The continuum system is discretized with a desired number of uniform computational cells. Each cell contains a convenient number of computational particles which represent the actual particles mixture. The particle-in-cell (discrete) model maps the temperature field from the (continuum) cells to the particles. Depending on the temperature reached by the cell, the titanium particles may undergo a solid-liquid transformation. If the distance between the carbon particle and the liquid titanium particles is within a certain tolerance they react and a TiC particle is formed in the cell. Accordingly, the molecular dynamic method updates the location of all particles in the cell and the amount of transformation heat accounted by the cell is entered into the source term of the (continuum) heat conduction equation. The new temperature distribution progresses depending on the cells which undergo the chemical reaction. As a demonstration of the effectiveness of the overall model some examples are shown.