Transfer Calculations and Accommodation Coefficients

In nonequilibrium systems one can postulate the separation between stochastic and mean values, although it may be very difficult to arrive at explicit descriptions. The situation is simplified somewhat by the introduction of several restrictions. In the discussion which follows, it is assumed that the Brownian-particle approximation holds. Also the additional restriction of quasistationarity is introduced for the transfer processes. A single spherical particle in this regime is characterized by the four parameters, Kn, Ma -, Sc., and Br. In addition, other parameters arise such as the accommodation coefficients specifying the transfer efficiencies between host gas and particle, and particle properties, including the thermal conductivity k. and viscosity 

With these restrictions, the mean forces on a particle are calculated by integrating the momentum flux over the particle surface 

Equations (2.46-48) can be generalized to account for nonspherical particles and polyatomic gases. 

The Boltzmann equation must be solved with appropriate boundary conditions to obtain f and f. The full Boltzmann equation has not been solved analytically or numerically. Current approximate methods for extracting the desired information from the Boltzmann equation are covered in detail in a recent reference [2.84]. In view of this review, discussion of these methods will not be given. It is sufficient to indicate some of the principal methods which have been employed. These are moment or integral methods for specific molecular scattering laws, the use of models (of which the BGK model is the simplest) for the collisions term J(fgfg), and direct simulation by Monte Carlo or molecular-dynamics techniques. 

All these methods have been applied to problems of interest in the study of ufp. 

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