Combined Thermal and Gas Dynamics Numerical Model for Laser Ablation of Carbon

Abstract

One of the major methods of production of carbon nanotubes is the laser ablation process. In this process, a powerful nanosecond-scale laser beam illuminates a target. The resulting explosion produces a plume of rapidly expanding gaseous carbon with embedded metallic catalysts, on whose surfaces the nanotubes are formed. The time-scale of a single laser pulse is of the order of nanoseconds whereas the plume development and growth of nanotubes take up to several milliseconds. The synthesis process largely depends on the plume properties, i.e., on the temperature, pressure, and density of the expanding plume. In turn, the plume propagation depends on the ablation speed, pressure, and density. In the current study, a combined thermal and gas dynamics model is proposed, implemented and tested. The proposed model is based on combined conduction heat transfer within the solid target, carbon sublimation process described by equilibrium thermodynamics, and process of plume development described by continuous gas dynamics. The carbon sublimation model is based on Clausius-Clapeyron equation and conservation of energy for differential control volume. The parameters of the injected plume are defined by this thermal model. The validity of viscous and inviscid models of plume dynamics is discussed. The ability of finite-volume discretizations to capture the plume dynamics and its roll-up is compared for various numerical schemes. To evaluate the accuracy of numerical modeling of plume dynamics, we compare finite-volume discretization based on Relaxing TVD scheme with that based on the upwind scheme with Roe averaging at the cell interface and non-linear ENO scheme for second-order flux formulas.