Abstract
"The paper proposes a one-dimensional mathematical model for describing the movement of liquefying air and the movement of particles in the gas-solids fluidized bed apparatus. The modeling is based on the mathematical approach of the theory of counting Markov chains. The factor determining the material entrainment from the apparatus was introduced into the model by using a macro diffusion coefficient, which made it possible to supplement the matrix of transition probabilities with probabilities of random throwing of particles into neighboring cells of the chain. Numerical experiments performed with the developed model allowed us to obtain qualitatively consistent results with respect to the distribution of the solid phase and the gradual removal of particles from the apparatus. The results obtained allow to consider the proposed model as a reliable basis for the development of a computer method for calculating the expansion of the bed and the entrainment of particles from technological equipment. "