Term information
Membrane transport for binary non-electrolyte solutions , generated by the hydrostatic pressure difference (delta p) and the osmotic pressure difference (delta phi), can be described by the Kedem-Katchalsky equations. The K-K equations have been derived from the principles of linear thermodynamics of irreversable processes. Such transport is described by the equations for volume flow, (J_v) and the solute flow (J_s) (Kedem O., Katchalsky A., 1958; Katchalsky A., Curran P.F. 1965; Kedem O., Katchasky A. 1963): J_v = L_p delta p - L_p sigma delta phi J_s = omega delta phi + (1-sigma) c_bar J_v source: http://www.botany.pl/pubs-pdf/Acta%20Societatis%20Botanicorum/2009/W093_096.pdf
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <apply> <eq/> <ci> <msub> <mi>J</mi> <mi>v</mi> </msub> </ci> <apply> <minus/> <apply> <times/> <ci> <msub> <mi>L</mi> <mi>p</mi> </msub> </ci> <ci>δ</ci> <ci>p</ci> </apply> <apply> <times/> <ci> <msub> <mi>L</mi> <mi>p</mi> </msub> </ci> <ci>σ</ci> <ci>δ</ci> <ci>ϕ</ci> </apply> </apply> </apply> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <msub> <mi>J</mi> <mi>s</mi> </msub> <mo>=</mo> <mrow> <mrow> <mi>ω</mi> <mo>⁢</mo> <mi>δ</mi> <mo>⁢</mo> <mi>ϕ</mi> </mrow> <mo>+</mo> <mrow> <mfenced close=")" open="("> <mrow> <mn>1</mn> <mo>-</mo> <mi>σ</mi> </mrow> </mfenced> <mo>⁢</mo> <mrow> <msub> <mi>c</mi> <mrow> <mi>b</mi> <mo>⁢</mo> <mi>a</mi> <mo>⁢</mo> <mi>r</mi> </mrow> </msub> <mo>⁢</mo> <msub> <mi>J</mi> <mi>v</mi> </msub> </mrow> </mrow> </mrow> </mrow> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <msub> <mi>J</mi> <mi>v</mi> </msub> <mo>=</mo> <mrow> <mrow> <msub> <mi>L</mi> <mi>p</mi> </msub> <mo>⁢</mo> <mi>δ</mi> <mo>⁢</mo> <mi>p</mi> </mrow> <mo>-</mo> <mrow> <msub> <mi>L</mi> <mi>p</mi> </msub> <mo>⁢</mo> <mi>σ</mi> <mo>⁢</mo> <mi>δ</mi> <mo>⁢</mo> <mi>ϕ</mi> </mrow> </mrow> </mrow> </math>
J_v = L_p \delta p - L_p \sigma \delta \phi
J_s = \omega \delta \phi + (1-\sigma) c_{bar} J_v
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <msub> <mi>J</mi> <mi>v</mi> </msub> <mo>=</mo> <msub> <mi>L</mi> <mi>p</mi> </msub> <mi>δ</mi> <mi>p</mi> <mo>-</mo> <msub> <mi>L</mi> <mi>p</mi> </msub> <mi>σ</mi> <mi>δ</mi> <mi>ϕ</mi> </mrow> <annotation encoding="SnuggleTeX">\[ J_v = L_p \delta p - L_p \sigma \delta \phi \]</annotation> </semantics> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <msub> <mi>J</mi> <mi>s</mi> </msub> <mo>=</mo> <mi>ω</mi> <mi>δ</mi> <mi>ϕ</mi> <mo>+</mo> <mfenced close=")" open="("> <mrow> <mn>1</mn> <mo>-</mo> <mi>σ</mi> </mrow> </mfenced> <msub> <mi>c</mi> <mrow> <mi>b</mi> <mi>a</mi> <mi>r</mi> </mrow> </msub> <msub> <mi>J</mi> <mi>v</mi> </msub> </mrow> <annotation encoding="SnuggleTeX">\[ J_s = \omega \delta \phi + (1-\sigma) c_{bar} J_v \]</annotation> </semantics> </math>