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Laser powder-bed fusion additive manufacturing of metals; physics, computational, and materials challenges
Published in Adedeji B. Badiru, Vhance V. Valencia, David Liu, Additive Manufacturing Handbook, 2017
Wayne E. King, Andrew T. Anderson, R. M. Ferencz, N. E. Hodge, C. Kamath, Saad A. Khairallah, Alexander M. Rubenchik
The theory of rapid vaporization is well established in the literature.55–57 Adjacent to the surface, there develops a thin layer where the vapor velocity distribution is dominated by the evaporating material, and so is not in translational equilibrium. Within a few mean-free paths, collisions between the vapor molecules establish equilibrium conditions. The gas dynamics model of this thin Knudsen layer employs jump conditions that conserve mass, momentum, and energy.
Introduction
Published in Mohamed Gad-el-Hak, MEMS, 2005
The nondimensionalized centerline and wall velocities for 0.01⩽Kn⩽30 flows are shown in Figure 6.8. The figure includes the data for the slip velocity and centerline velocity from 20 different DSMC runs, of which 15 are for nitrogen (diatomic molecules) and 5 for helium (monatomic molecules). The differences between the nitrogen and helium simulations are negligible; thus, this velocity scaling is independent of the gas type. The linearized Boltzmann solutions [Ohwada et al., 1989] for a monatomic gas are also indicated by triangles in Figure 6.8. The Boltzmann solutions closely match the DSMC predictions. Maxwell's first-order boundary condition b=0 (shown by solid lines) predicts, erroneously, a uniform nondimensional velocity profile for large Knudsen numbers. The breakdown of the slip flow theory based on the first-order slip-boundary conditions is realized around Kn=0.1 and Kn=0.4 for wall and centerline velocities respectively. This finding is consistent with the commonly accepted limits of the slip flow regime [Schaaf and Chambre, 1961]. The prediction using b=-1 is shown by small dashed lines. The corresponding centerline velocity closely follows the DSMC results, while the slip velocity of the model with b=-1 deviates from DSMC in the intermediate range for 0.1<Kn<5. One possible reason for this is the effect of the Knudsen layer. For small Kn flows, the Knudsen layer is thin and does not affect the overall velocity distribution too much. For very large Kn flows, the Knudsen layer covers the channel entirely. For intermediate Kn values, however, both the fully developed viscous flow and the Knudsen layer coexist in the channel. At this intermediate range, approximating the velocity profile as parabolic ignores the Knudsen layers. For this reason, the model with b=-1 results in 10% error in the slip velocity
Thermophoresis of a particle in a concentric cavity with thermal stress slip
Published in Aerosol Science and Technology, 2018
When a tangential temperature gradient exists in a rarified gas adjacent to a solid surface, a thin Knudsen layer of the fluid at the surface will flow along with the gradient (i.e., from cold to hot). This thermal creep phenomenon (Maxwell 1879) provides a mechanism in the slip-flow regime for the thermophoresis of aerosol particles and thermoosmosis of bounded gases with the Knudsen number of the order 0.1, where is the linear dimension of the particles or boundaries and is the mean free path of the gas molecules. Thermophoresis (viz., the Soret effect), which is the particle motion caused by a bulk-gas temperature gradient against its direction (i.e., from hot to cold), plays an important role in many practical applications such as aerosol sampling, air cleaning, microelectronic manufacturing, scale formation on heat exchanger surfaces, nuclear reactor safety, modified chemical vapor deposition, and catalysis-driven plasmonic nanomotors (Balsara and Subramanian 1987; Williams and Loyalka 1991; Chang and Keh 2010a,b; Hsieh and Keh 2012; Sagot 2013; Guha and Samanta 2014; Wu et al. 2015; Bhusnoor et al. 2017; Qin et al. 2017).