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(Cl - Cr), Jv = f(Cl - Cr), Js = f(Cl - Cr), ( Ψ S ) J v = f(Cl - Cr), ( Ψ S ) J s = 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.
Keywords: Kedem–Katchalsky equations; S-entropy production; double-membrane system; membrane transport; nonlinear model equations.