| Summary: | Using the classical Kedem–Katchalsky’ membrane transport theory, a mathematical model was developed and the original concentration volume flux (<i>J<sub>v</sub></i>), solute flux (<i>J<sub>s</sub></i>) characteristics, and <i>S</i>-entropy production by <i>J<sub>v</sub></i>, <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>ψ</mi> <mi>S</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>J</mi> <mi>v</mi> </msub> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> and by <i>J<sub>s</sub></i> <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <msub> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>ψ</mi> <mi>S</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>J</mi> <mi>s</mi> </msub> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> in a double-membrane system were simulated. In this system, M<sub>1</sub> and M<sub>r</sub> membranes separated the <i>l</i>, <i>m</i>, and <i>r</i> compartments containing homogeneous solutions of one non-electrolytic substance. The compartment <i>m</i> consists of the infinitesimal layer of solution and its volume fulfills the condition <i>V<sub>m</sub></i> → 0. The volume of compartments <i>l</i> and <i>r</i> fulfills the condition <i>V<sub>l</sub></i> = <i>V<sub>r</sub></i> → ∞. At the initial moment, the concentrations of the solution in the cell satisfy the condition <i>C<sub>l</sub></i> < <i>C<sub>m</sub></i> < <i>C<sub>r</sub></i>. Based on this model, for fixed values of transport parameters of membranes (i.e., the reflection (<i>σ<sub>l</sub></i>, <i>σ<sub>r</sub></i>), hydraulic permeability (<i>L<sub>pl</sub></i>, <i>L<sub>pr</sub></i>), and solute permeability (<i>ω<sub>l</sub></i>, <i>ω<sub>r</sub></i>) coefficients), the original dependencies <i>C<sub>m</sub></i> = <i>f</i>(<i>C<sub>l</sub></i> − <i>C<sub>r</sub></i>), <i>J<sub>v</sub></i> = <i>f</i>(<i>C<sub>l</sub></i> − <i>C<sub>r</sub></i>), <i>J<sub>s</sub></i> = <i>f</i>(<i>C<sub>l</sub></i> − <i>C<sub>r</sub></i>), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>Ψ</mi> <mi>S</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>J</mi> <mi>v</mi> </msub> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> = <i>f</i>(<i>C<sub>l</sub></i> − <i>C<sub>r</sub></i>), <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>Ψ</mi> <mi>S</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>J</mi> <mi>s</mi> </msub> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> = <i>f</i>(<i>C<sub>l</sub></i> − <i>C<sub>r</sub></i>), <i>R<sub>v</sub></i> = <i>f</i>(<i>C<sub>l</sub></i> − <i>C<sub>r</sub></i>), and <i>R<sub>s</sub></i> = <i>f</i>(<i>C<sub>l</sub></i> − <i>C<sub>r</sub></i>) were calculated. Each of the obtained features was specially arranged as a pair of parabola, hyperbola, or other complex curves.
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