Flux Matching
Flux matching must be performed for each species in order for the total molar mass in the system to be conserved. If a model also contains a physics interface to compute the fluid velocity and pressure (the Laminar Flow interface for example) and the gas temperature (the Heat Transfer in Fluids interface for example) then those physics interfaces require appropriate flux matching boundary conditions. The Heavy Species Transport interface automatically computes flux matching variables for the total mass flux and heat source of reaction on surfaces.
Flux Matching for Each Species
The inward mass flux for species k on a reacting surface is given y
(5-21)
This is the natural boundary condition for Equation 5-4 and results in either an inward or outward mass flux for species k, depending on the surface chemical mechanism stoichiometry. If the species is an ion, then there is an additional flux contribution due to migration. In this case, Equation 5-21 becomes
This additional flux contribution ensures that when the normal electric field is directed to the wall, there is an outflux of ions due to migration.
Flux Matching for the Total Mass Flux
Heterogeneous reactions on fluid–solid surfaces can affect the mass, momentum, and energy balances at the interface separating the fluid and the solid. Under these conditions, the resulting mass-averaged velocity, commonly referred to as the Stefan velocity, must be incorporated into the fluid transport equations. The Stefan velocity is calculated as follows:
where Mf is the inward mass flux which is defined, from the surface chemistry as:
Flux Matching for the Total Heat Flux and surface heating by the plasma
If a model contains the Heat Transfer in Fluids interface, an expression for the total heat source of reactions is available. The Plasma and Plasma, Time Periodic interfaces create an appropriate variable for the total heat source of reactions, which can be accepted as a feature input in the Boundary Heat Source boundary condition of the Heat Transfer in Fluids interface. The heat source related with surface reactions (SI unit: W/m2) is given as:
Depending on the surface chemical mechanism stoichiometry, this can either cause heating (exothermic) or cooling (endothermic). The option in the Boundary Heat Source feature is called Total surface heat source of reaction when computed in the Plasma interface or Total surface heat source of reaction, period averaged when computed in the Plasma, Time Periodic interface. For the heat source computed in the Plasma, Time Periodic interface some quantities exist along the period and are period averaged before being used in a Heat Transfer in Fluids interface. For the Plasma, Time Periodic another option exists called Total surface heat source, period averaged. In this option, a rough estimate of the energy flux from electrons and ions arriving at the surface is added to the total heat source of reactions
where the first term on the right-hand-side is the period-averaged normal electron current density arriving at the surface times the period-averaged electron temperature, and the second term is the period-averaged normal ion current density arriving at a surface times an estimate of the voltage drop seen by the ions when traveling toward the surface. This estimate is computed as the difference of the maximum value of the period-averaged potential in the plasma and the period-averaged potential at the surface. Hence, this is an estimate for the maximum ion energy at the surface.