Analysis and Calculation of the Probability Selectivity Using the Modern Distributed Algorithms: Modern Distributed Algorithms

Analysis and Calculation of the Probability Selectivity

The calculation of the selectivity characteristics of membrane separation mixtures is a complex task due to the large number of influencing factors. This is based on the basic physicochemical characteristics of the solution, permeate and reptant. In the paper (Horntrop, Katsoulakis, & Vlachos, 2001), a probabilistic approach was effectively used to solve this problem. The analysis obtained estimates of the selectivity of nanofiltration membranes for individual ions. This paper uses a probabilistic approach for the theoretical evaluation of the selectivity of ultrafiltration membranes. In these membranes, the separation process mechanism is significantly different from the separation mechanism in nano-membranes.

The process of penetration of the substance into the pores of ultrafiltration membranes can be divided into several stages. These stages are characterized by different probabilistic estimates.

First, the substance enters from the depth of the continuous medium into the boundary diffusion layer. This stage is identified as diffusive transfer.

Secondly, the substance penetrates to the surface of the membrane through the Knudsen layer. This layer has a thickness of the order of the mean free path of the molecules. In the Knudsen layer, the patterns of diffusion transfer are not valid.

Thirdly, the substance penetrates into the “exit” of the pores on the membrane surface.

And finally, in the fourth, the substance diffuses inside the pore.