Stochastic Model of Diffusion Mass Transfer with Sources or Runoffs of Diffusing Substance - v. Shevelev, Valentin (International Journal of Engineering and Technology, 2018)
As a rule, the prediction of results of engineering procedures related to the diffusion of an infused component into the treated material confines to solving boundary problems for the diffusion equation defining the change in the average concentration of the infused component. That said, the stochastic component of diffusion mass transfer determined by stochastic boundary conditions and fluctuations in the concentration of diffusing substance in the transfer region is not taken into account, which may significantly affect the prediction of the engineering procedure results. As a consequence, the 1D stochastic model of diffusion mass transfer is developed for the transfer region with third-order stochastic boundary conditions source or runoffs of diffusing substance. The elaborated approach allows one to derive the equation for the probability density of the distribution of the vector characterizing the concentration distribution of diffusing substance in the transfer region against the discrete set of its physically infinitesimal partition volumes in which the local quasi-equilibrium shows. The equation for the multidimensional probability of the concentration distribution of diffusing substance in the transfer region is used to derive the system of equations and formulate the boundary conditions for the unary function of the concentration distribution of diffusing substance, and also define the physical parameters included in the system of equations. The equation for the unary function of the concentration distribution of diffusing substance is used to derive the discretized equations for the core concentration moments basic for deriving the continuant equations for the average concentration and dispersion of diffusing substance. The boundary problems are formulated for the average concentration and dispersion of diffusing substance in case of sources and runoffs of the same type. The approach to finding the parameters of physical infinitesimal volume is formulated.Â Â Â