Pathak Kedar, Mullenix Nathan, Povitsky Alex
Department of Mechanical Engineering, The University of Akron, Akron, OH 44325-3903, USA.
J Nanosci Nanotechnol. 2006 May;6(5):1271-80. doi: 10.1166/jnn.2006.143.
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.
碳纳米管的主要生产方法之一是激光烧蚀工艺。在这个过程中，一束强大的纳秒级激光束照射一个靶材。产生的爆炸会产生一股快速膨胀的气态碳羽流，其中嵌入了金属催化剂，纳米管就在这些催化剂的表面形成。单个激光脉冲的时间尺度约为纳秒，而羽流的发展和纳米管的生长则需要长达几毫秒的时间。合成过程在很大程度上取决于羽流的特性，即膨胀羽流的温度、压力和密度。反过来，羽流的传播又取决于烧蚀速度、压力和密度。在当前的研究中，提出、实施并测试了一个热动力学和气体动力学相结合的模型。所提出的模型基于固体靶材内部的传导传热、由平衡热力学描述的碳升华过程以及由连续气体动力学描述的羽流发展过程。碳升华模型基于克劳修斯 - 克拉佩龙方程和微分控制体积的能量守恒。注入羽流的参数由这个热模型定义。讨论了羽流动力学的粘性和无粘性模型的有效性。针对各种数值格式，比较了有限体积离散化捕捉羽流动力学及其卷起的能力。为了评估羽流动力学数值模拟的准确性，我们将基于松弛总变差递减（Relaxing TVD）格式的有限体积离散化与基于单元界面处采用 Roe 平均的迎风格式以及用于二阶通量公式的非线性本质非振荡（ENO）格式的有限体积离散化进行了比较。
