About the Transport Equations
There are a number of different formulations available for modeling mass transport, ranging from a simple reaction, convection, diffusion equation to the Maxwell–Stefan (sometimes called Stefan-Maxwell) equations. The Maxwell–Stefan equations are the only formulation that conserves the total mass in the system and also satisfies a number of auxiliary constraints. The main drawback of the Maxwell–Stefan equations is the amount of computational resources needed to solve them. In many situations, simplified forms of the Maxwell Stefan equations can be applied, which do not rigorously satisfy the laws of multicomponent diffusion but are much easier to implement and consume less computational resources.
Neutral and excited species in a plasma require a suitable transport equation. Typically the concentration of excited species is very low and they can be considered dilute. This is true with atomic gases, where the concentration of ions and electronically excited species is much lower than the concentration of the ground state atoms. Molecular gases can dissociate into stable neutral fragments via electron impact dissociation. These fragments can have a long lifetime and accumulate inside a reactor. In this case, the dilute approximation is no longer valid and a more rigorous description of the mass transport is necessary. Conservation of mass dictates that the sum of the mass fractions of all the species must equal one. The most accurate technique is to solve the Maxwell–Stefan equations which correctly take into account diffusive transport due to mole fraction, pressure and temperature gradients. The Maxwell–Stefan equations quickly become computationally very expensive when the number of species becomes large (>6). In a plasma, there might be 20+ neutral and excited species, so solving the full Maxwell–Stefan equations is not practical.
The Heavy Species Transport interface provides two different Diffusion models to choose from, Mixture averaged and Fick’s law. The Mixture averaged option fulfills all the criteria for mass conservation. It is much less computationally expensive to solve than the full Maxwell–Stefan equations, which are not available in the Heavy Species Transport interface. The Fick’s law option uses an even simpler diffusion model, which is less accurate than the Mixture averaged model, but is computationally less expensive.