  Recent experimental studies of molten metal droplets wetting high temperature
reactive substrates have established that the majority of triple-line motion
occurs when inertial effects are dominant. In light of these studies, this
paper investigates wetting and spreading on reactive substrates when inertial
effects are dominant using a thermodynamically derived, diffuse interface model
of a binary, three-phase material. The liquid-vapor transition is modeled using
a van der Waals diffuse interface approach, while the solid-fluid transition is
modeled using a phase field approach. The results from the simulations
demonstrate an $O \left( t^{-\nicefrac{1}{2}} \right)$ spreading rate during
the inertial regime and oscillations in the triple-line position when the metal
droplet transitions from inertial to diffusive spreading. It is found that the
spreading extent is reduced by enhancing dissolution by manipulating the
initial liquid composition. The results from the model exhibit good qualitative
and quantitative agreement with a number of recent experimental studies of
high-temperature droplet spreading, particularly experiments of copper droplets
spreading on silicon substrates. Analysis of the numerical data from the model
suggests that the extent and rate of spreading is regulated by the spreading
coefficient calculated from a force balance based on a plausible definition of
the instantaneous interface energies. A number of contemporary publications
have discussed the likely dissipation mechanism in spreading droplets. Thus, we
examine the dissipation mechanism using the entropy-production field and
determine that dissipation primarily occurs in the locality of the triple-line
region during the inertial stage, but extends along the solid-liquid interface
region during the diffusive stage.
