Mathematical model for laser ablation to generate nanoscale and submicrometer-size particles

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Abstract
Nanosize particles have several interesting features for synthesizing new materials with improved properties compared to the coarser-grained conventional materials, but the rate of production of such particles in various processes is usually very low. However, laser ablation is expected to give a higher yield. In this paper, a gas-dynamical model is developed for analyzing the plasma formation, and the velocity and particle-size distributions in the plasma during laser ablation. The melting and evaporation rates are determined by using the heat-conduction equation and the Stefan condition. To account for the discontinuity of various state variables across the Knudsen layer, jump conditions are used; the gas-dynamics equations are solved to study the convective flow of the metal particles in the region above the Knudsen layer. The plasma physics is used to model the formation of plasma and to compute the laser-beam attenuation coefficient and ion concentration in the plasma. The particle-size distribution in the plasma is determined by using a droplet-growth theory. Nanosize particles are found to exist near the vaporization front, and the particle size increases as one moves towards the plasma boundary. Similarly, the velocity of the particles is found to be higher at the plasma boundary than that inside the plasma.

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