Calculation and application of combined diffusion coefficients in thermal plasmas

Abstract

The combined diffusion coefficient method is widely used to treat the mixing and demixing of different plasma gases and vapours in thermal plasmas, such as welding arcs and plasma jets. It greatly simplifies the treatment of diffusion for many gas mixtures without sacrificing accuracy. Here, three subjects that are important in the implementation of the combined diffusion coefficient method are considered. First, it is shown that different expressions for the combined diffusion coefficients, arising from different definitions for the stoichiometric coefficients that assign the electrons to the two gases, are equivalent. Second, an approach is presented for calculating certain partial differential terms in the combined temperature and pressure diffusion coefficients that can cause difficulties. Finally, a method for applying the combined diffusion coefficients in computational models, which typically require diffusion to be expressed in terms of mass fraction gradients, is given.

Thermocapillarity in Microfluidics—A Review

“…The effect of relative surface tension on coalescence of droplets of immiscible liquids has been studied by Blanchette [ 161 ]. Yi and coworkers also studied the effect of droplets temperature on the probability of coalescence on superhydrophobic surfaces experimentally [ 162 ]. The superhydrophobic surface was fabricated by silver-assisted etching of the silicon substrate and silanization with fluorosilane.…”

“… Head-on collision of binary droplets with increased temperature of the incoming droplet at releasing height of 13 mm ( T stationary = T room = 25 °C, Δ T = T incoming − T stationary ). Reprinted by permission from Macmillan Publishers Ltd: Scientific Reports [ 162 ], Copyright 2014. …”

Effects of copper vapour on thermophysical properties of CO2-N2 plasma

“…To completely model the diffusion in a mixture composed of q species, a total of q(q − 1)/2 ordinary diffusion coefficients D ij , q − 1 thermal diffusion coefficients D T i ,a n d q mass conservation equationsh a v et ob ec a l c u l a t e da n d solved [18]. To simplify this treatment, Murphy [24][25][26][27] proposed the combined diffusion coefficients, namely the combined ordinary diffusion coefficient D x AB , combined electric field diffusion coefficient D E AB , combined temperature diffusion coefficient D T AB , and combined pressure diffusion coefficient D P AB , which describe the diffusion due to composition gradients, applied electric fields, temperature gradients, and pressure gradients respectively. The calculation of combined diffusion coefficients are based on the collision integrals presented in Section 3.1, and was detailed comprehensively in our previous publication [18].…”

“…To our knowledge, no corresponding works have been reported. What's more, the combined diffusion coefficients which were proposed by Murphy [24][25][26][27] and greatly simplify the treatment of diffusion, are indispensable input data in developing model of metal vapour transfer both in arc welding [28] and circuit breakers [29]. Another aim of the present work is therefore to provide these four kinds of combined diffusion coefficients due to composition gradients, applied electric fields, temperature gradients, and pressure gradients respectively [18], which have not been reported either.…”

A collisional-radiative model of iron vapour in a thermal arc plasma

“…The influence of droplets on the plasma is neglected. An additional equation covers the conservation of metal vapour mass [25] employing the combined diffusion coefficient approach [26]. According to this approach, the plasma is generated in the gas mixture containing species attributed to the shielding gas (argon atoms and ions) and to the metal vapour (iron atoms and ions).…”