Concentration Slip and Its Impact on Heterogeneous Combustion in a Micro Scale Chemical Reactor

The rarefied gas effect on concentration slip and on heterogeneous combustion in microscale chemical reactors was investigated. First, a concentration slip model to describe the rarefied gas effect on the species transport in microscale chemical reactors was derived from the approximate solution of the Boltzmann equation. Second, the model was verified using the direct Monte-Carlo method for the pure diffusion problems at different Knudsen numbers. The comparison showed that the present analytical model for the concentration slip boundary condition reasonably predicted the rarefied gas effect in the slip regime. Finally, the impact of the concentration slip on the coupling between the surface catalytic reactions and the homogeneous gas phase reactions in a microscale chemical reactor was examined using the one-step overall surface reaction model with a wide range of Knudsen and Damköhler numbers. It was shown that the rarefied gas effect significantly reduced the reaction rate of the surface catalytic oxidization for large Knudsen numbers. Furthermore, it was shown that the impact of slip effects on catalytic reactions strongly depends on the competition between the reaction rate and diffusion transport. It was found that the concentration slip causes a nonlinear reaction rate distribution at large Damköhler numbers. The results also showed that an accurate prediction of the rarefied gas effect on catalytic reactions in microscale reactors has to consider both the temperature slip and the concentration slip. Chemical engineering science 2005 3 3 NOMENCLATURE a Thermal accommodation coefficient A Constant in Eq. 19 Bc Density-weighted collision rate p c Specific heat at constant pressure D Diffusion coefficient Da Damköhler number Eg, Es Activation energy of gas and surface reactions f , f Molecular velocity distribution function H Channel height hk Enthalpy of the kth species K Equilibrium constant Kn Knudsen number k Collision frequency m Molecular mass NS Total species number n Molar concentration or number density P Pressure Pe Peclet number R, R Gas or universal gas constant T Temperature U, V Flow velocity in x and y directions vx, y, z Molecular thermal velocity υ Molecular mean thermal velocity W Molecular weight x, y, z Coordinates Y Mass fraction of species ψ Molecular transport flux γ Ratio of the specific heats λ Molecular mean free path κ Thermal conductivity μ, μ’ Fluid dynamic viscosity b Momentum accommodation coefficient σ Stoichiometric mass ratio ν’, ν’’ Molar concentration coefficient ρ Density ω& Reaction rate Subscripts f Fuel g Gas phase in Inlet boundary i Coordinates x ,y, z k Species o Oxygen s Outer edge of the Knudsen layer or surface w Wall ~ Nondimensional parameters * Nondimensional coordinate Chemical engineering science 2005