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Open AccessArticle

Simulation of S-Entropy Production during the Transport of Non-Electrolyte Solutions in the Double-Membrane System

1
Department of Innovation and Safety Management Systems, Technical University of Czestochowa, 42200 Czestochowa, Poland
2
Department of Business Informatics, University of Economics, 40287 Katowice, Poland
3
Department of Security Services, Faculty of Safety Engineering, VSB-Ostrava, 70030 Ostrava, Czech Republic
*
Authors to whom correspondence should be addressed.
Entropy 2020, 22(4), 463; https://doi.org/10.3390/e22040463
Received: 23 March 2020 / Revised: 13 April 2020 / Accepted: 17 April 2020 / Published: 18 April 2020
Using the classical Kedem–Katchalsky’ membrane transport theory, a mathematical model was developed and the original concentration volume flux (Jv), solute flux (Js) characteristics, and S-entropy production by Jv, ( ( ψ S ) J v ) and by Js ( ( ψ S ) J s ) in a double-membrane system were simulated. In this system, M1 and Mr membranes separated the l, m, and r compartments containing homogeneous solutions of one non-electrolytic substance. The compartment m consists of the infinitesimal layer of solution and its volume fulfills the condition Vm → 0. The volume of compartments l and r fulfills the condition Vl = Vr → ∞. At the initial moment, the concentrations of the solution in the cell satisfy the condition Cl < Cm < Cr. Based on this model, for fixed values of transport parameters of membranes (i.e., the reflection (σl, σr), hydraulic permeability (Lpl, Lpr), and solute permeability (ωl, ωr) coefficients), the original dependencies Cm = f(ClCr), Jv = f(ClCr), Js = f(ClCr), ( Ψ S ) J v = f(ClCr), ( Ψ S ) J s = f(ClCr), Rv = f(ClCr), and Rs = f(ClCr) were calculated. Each of the obtained features was specially arranged as a pair of parabola, hyperbola, or other complex curves. View Full-Text
Keywords: membrane transport; Kedem–Katchalsky equations; double-membrane system; nonlinear model equations; S-entropy production membrane transport; Kedem–Katchalsky equations; double-membrane system; nonlinear model equations; S-entropy production
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Ślęzak, A.; Bajdur, W.M.; Batko, K.M.; Šcurek, R. Simulation of S-Entropy Production during the Transport of Non-Electrolyte Solutions in the Double-Membrane System. Entropy 2020, 22, 463.

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