Search

Lotus-type porous metals, characterized by low densities, large surface areas, and directional properties, are contemporarily utilized as lightweight, catalytic, and energy-damping materials; heat sinks; etc. In this study, the effects of dimensionless working parameters on the morphology of lotus-type pores in metals during unidirectional solidification were extensively investigated via general algebraic expressions. The independent dimensionless parameters include metallurgical, transport, and geometrical parameters such as Sieverts' law constant, a partition coefficient, the solidification rate, a mass transfer coefficient, the imposed mole fraction of a solute gas, the total pressure at the top free surface, hydrostatic pressure, a solute transport parameter, inter-pore spacing, and initial contact angle. This model accounts for transient gas pressure in the pore, affected by the solute transfer, gas, capillary, and hydrostatic pressures, and Sieverts' laws at the bubble cap and top free surface. Solute transport across the cap accounts for solute convection at the cap and the amount of solute rejected by the solidification front into the pore. The shape of lotus-type pores can be described using a proposed fifth-degree polynomial approximation, which captures the major portions between the initial contact angle and the maximum radius at a contact angle of 90 degrees, obtained by conserving the total solute content in the system. The proposed polynomial approximation, along with its working parameters, offers profound insights into the formation and shape of lotus-type pores in metals. It systematically provides deep insights into mechanisms that may not be easily revealed with experimental studies. The prediction of a lotus-type pore shape is thus algebraically achieved in good agreement with the available experimental data and previous analytical results. [ABSTRACT FROM AUTHOR]

In this study, the velocity distribution functions of the ions and electrons in a collisional presheath and collisionless sheath of a plasma near a wall emitting and reflecting ions and electrons are systematically determined. The collisions in the presheath are modeled by a relaxation time approximation (namely, Bhatnagar--Gross--Krook model, or simply BGK model). To find the variation in electrostatic potential with position, the model and analysis from Emmert et al. are used. Distribution functions of the ions and electrons in a collisionless presheath and sheath on a wall partially reflecting ions and electrons, therefore, can be exactly obtained. The reflections of the ions and electrons by a wall play important roles in studying heat transfer from a plasma sheath to a workpiece surface, and sputter etching and deposition, ion implantation, and ion scattering spectroscopy. Irrespective of ion and electron reflectivities, velocities of the ions in the presheath and sheath are of highly non-Maxwell--Boltzmann distributions. The electrons in the presheath are close to Maxwell--Boltzmann distributions, whereas those in the sheath are non-Maxwell--Boltzmann distributions. Even though the wall partially reflects ions and electrons, the Bohm's criterion is marginally satisfied at the sheath edge. The computed distribution functions for a completely absorbing surface agree with theoretical results provided in the literature. Good comparison of the resulted transport variables with available analytical work is presented in the companion paper. Index Terms--Kinetic analysis of plasma, plasma materials processing, plasma-wall interactions, space charge.

Transport variables of the positive ions and electrons in the presheath and sheath of a plasma near a wall that partially reflects ions and electrons are determined from a kinetic analysis. Because velocity distributions of the ions and electrons near the wall are highly non-Maxwell--Boltzmann distributions, accurate predictions of transport variables, such as density, fluid velocity, mean pressure, fluid-like viscous stress, and conduction, require kinetic analysis. The results find that dimensionless transport variables of ions and electrons in the presheath and sheath can be exactly expressed in terms of transcendental functions determined by dimensionless independent parameters of ion and electron reflectivities of the wall, ion-to-electron mass ratio, charge number, and electron-to-ion temperature ratio at the presheath edge. The effects of the parameters on transport variables at the wall are also obtained. The computed transport variables in the presheath and sheath show agreement with available theoretical data for a completely absorbing wall. Index Terms--Plasma materials processing, plasma-wall interactions, space charge, transport processes of plasma.