Abstract
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, and by Js 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(Cl − Cr), Jv = f(Cl − Cr), Js = f(Cl − Cr), = f(Cl − Cr), = f(Cl − Cr), Rv = f(Cl − Cr), and Rs = f(Cl − Cr) were calculated. Each of the obtained features was specially arranged as a pair of parabola, hyperbola, or other complex curves.
Highlights
One of the most important properties of each non-equilibrium thermodynamic system is the continuous production of S-entropy [1,2]
The temporal change in S-entropy is a consequence of the entropy exchange with the external environment and the entropy production in the system
This means that for irreversible processes occurring in open systems, the S-entropy rate of change is the sum of the rate of entropy exchange with the external environment and the rate of entropy production in the system as a result of irreversible processes (ψ S = di S/dt > 0) [1,2,3]
Summary
One of the most important properties of each non-equilibrium thermodynamic system is the continuous production of S-entropy [1,2]. With the use of the Curran–Kedem–Katchalsky method utilized in the following papers [10,11,12,13,14,15,16,17,20,21,22,23], a non-linear mathematical model of transport in the double-membrane osmotic-diffusive cell was developed This cell contains two membranes (Ml , Mr ) arranged in series and separating the compartments (l), (m), and (r), which contain the solutions of various concentrations, respectively, Cl , Cm , and Cr (at the initial moment Cl > Cm > Cr or Cl < Cm < Cr ). In order to search for new transport properties of the double-membrane system on the basis of the mathematical model, of the concentration the calculations (Cm ), volume flux (Jv ), solute flux (Js ), S-entropy produced by Jv , (ψS ) Jv and by Js ((ψS ) Js ), and osmotic and diffusion resistances (Rv , Rs )
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