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

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

Zhanat Umarova (South Kazakhstan State University, Shymkent, Kazakhstan), Saule Botayeva (South Kazakhstan State University, Shymkent, Kazakhstan), Aziza Zhidebayeva (Silkway International University, Shymkent, Kazakhstan) and Nursaule Torebay (Silkway International University, Shymkent, Kazakhstan)
Copyright: © 2020 |Pages: 14
DOI: 10.4018/IJDST.2020040102

Abstract

The calculation of the characteristics of the selectivity in the membrane separation of mixtures, based on basic physicochemical characteristics of the solution, is a difficult task due to the large number of influencing factors. To solve this problem, for a theoretical evaluation of the selectivity of ultrafiltration membranes, modern distributed algorithms are used for a probabilistic approach, in which the mechanism of the separation process differs significantly from the separation mechanism in nanomembranes. As a result of the proposed models and modern distributed algorithms, estimates of the selectivity of nanofiltration membranes for individual ions were obtained. It was found that an important feature of mixing with the mixture flowing through the membrane is the dependence of the effective diffusion coefficient on time. Also, as a result of calculations by the proposed model, it was found that this feature is modeled by the coefficient of anomalous fractal diffusion in time, as well as by the displacement of the effective separation zone in the membrane.
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The Main Part

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

First, the matter comes from the depth of the continuous medium into the boundary diffusion layer. This stage is identified as a diffusion transference.

Secondly, the substance penetrates to the surface of the membrane through a Knudsen layer of thickness on the order of the mean free path of the molecules. In the Knudsen layer, the laws of diffusion transport are not valid.

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

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

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.

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