A Coupled Stagnation Flow and Knudsen Layer Analysis for Laser Drilling

The application of lasers in industrial drilling processes is rapidly increasing. Consequently there is a great need to understand the fundamental physics of the laser drilling process. Recent experiments have shown that material removal occurs via the combined action of vaporization and melt expulsion due to the vaporization-induced recoil pressure. The authors (Batteh et al., 1998) developed a quasi-steady stagnation flow analysis to study the physical mechanisms of laser drilling by examining the heat transfer and fluid flow in the molten metal. This paper presents an extension of that analysis by including the effects of nonequilibrium vaporization. A Knudsen layer analysis is used to model the nonequilibrium evaporation at the liquid-vapor interface and the compressible flow outside the Knudsen layer. The analysis gives the pressure, temperature, and density jumps across the Knudsen layer. Numerical results for the combined stagnation flow and Knudsen layer analysis are shown for several different materials over a range of laser intensities commonly used in laser drilling. Drilling trends are shown as functions of the laser energy and beam radius. The results show that a significant portion of the material removed occurs through melt expulsion due to the vaporization-induced recoil pressure. The results from both the equilibrium and Knudsen layer models for vaporization are compared, and the validity of equilibrium vaporization models are discussed.