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- Title
Theoretical Calculation of Concentration Polarization in the Ultrafiltration Purification of Technological Solutions Containing Trisodium Phosphate.
- Authors
Lazarev, S. I.; Abonosimov, O. A.; Kotenev, S. I.; Shestakov, K. V.
- Abstract
The objectives of this study are to perform the mathematical description of the formation of a sediment layer on the surface of membranes due to concentration polarization on the basis of the semi-integral method of solving the convective diffusion equation, to optimize the process of ultrafiltration and determine the sediment layer on the surface of a membrane, and to calculate the membrane operation time and the filtrate volume in a steady-state regime before regeneration. Minimization results show that the lowest function value of 1.32583 and 1.32112 is given by the Wolfram Mathematica software for the Na3PO4 concentrations of 0.5 and 1 kg/m3, respectively. It is established that concentration polarization attains the maximum admissible value of 1.32583 and 1.298 for the solutions with concentrations of 0.5 and 1 kg/m3 at 2.43 and 2.52 s from the beginning of the separation process, respectively. The propagation of concentration polarization throughout the entire channel length requires 5500 and 5710 s, respectively. Afterwards, the membranes require regeneration to maintain the necessary level of purification. In these time periods, 0.191 and 0.173 L of filtrate are formed.
- Subjects
ULTRAFILTRATION; HEAT equation; PHOSPHATES
- Publication
Theoretical Foundations of Chemical Engineering, 2022, Vol 56, Issue 6, p1015
- ISSN
0040-5795
- Publication type
Article
- DOI
10.1134/S0040579522060094