  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
geometry system. At each time step, the continuum (micrometer scale) model
computes the current temperature field according to the prescribed boundary
conditions. The overall system domain is discretized with a desired number of
uniform computational cells. Each cell contains a convenient number of
computation particles which represent the actual particles mixture. The
particle-in-cell (discrete) model maps the temperature field from the
(continuum) cells to the respective internal 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 will react and
a TiC particle will be formed in the cell. Accordingly, the molecular dynamic
method will update the location of all particles in the cell and the amount of
transformation heat accounted by the cell will be entered into the source term
of the (continuum) heat conduction equation. The new temperature distribution
will progress depending on the cells which will time-by-time undergo the
chemical reaction. As a demonstration of the effectiveness of the overall model
some paradigmatic examples are shown.
