Models for Solidification and Splashing in Laser Percussion Drilling

This paper studies systems of partial differential equations modelling laser percussion drilling. The particular phenomenon considered in detail is the ejection of the thin layer of molten material. This thin layer is modelled as an inviscid flow between the fluid surface and fluid/solid interface, both of which are unknown moving boundaries. Through a regular asymptotic expansion, the governing equations are reduced to a combination of the shallow water equations and a two-phase Stefan problem; the key small parameter being the square of the aspect ratio. These leading-order problems exhibit shocks which represents a possible mechanism for the previously unexplained fluid clumping. Approximate formulas and a parameter gronping are derived to predict the rate of melt solidification during ejection. Finally, weak formulations of thp convection-diffusion equation for energy conservation are presented. These weak formulations are novel becanse the energy equation in the fluid contains convection terms. An appropriate extension to the enthalpy method is suggest{~d as a first stage towards numerical calculations.