title: [Network form of the Kedem-Katchalsky equations for ternary non-electrolyte solutions. 6. Evaluation of Kij Peusner's coefficients for polymeric membrane].
abstract: BACKGROUND
  Peusner Network Thermodynamics (PNT) enables transformation of Kedem-Katchalsky (K-K) membrane transport equations from classical to network form. For ternary and homogenous nonelectrolyte solutions, transformation results in two symmetrical and six hybrid forms of network K-K equations. Symmetrical forms of these equations contain Peusner's coefficients Rij or Lij, whereas hybrid forms contain Peusner's coefficients Hij, Wij, Nij, Kij, Sij or Pij. Experimental transport parameters can be used to calculate Peusner's coefficients, i.e. hydraulic permeability (Lp), solute permeability (ω) and reflection (σ) parameters.
  
  
  OBJECTIVE
  The aim of this paper is to derive network form of K-K equations for homogenous ternary nonelectrolyte solutions that contain Peusner's coefficients K ij (i, j ∈ {1, 2, 3}). These coefficients form a third degree matrix of Peusner's coefficients [K]. Moreover, we aim to calculate dependences of K ij coefficients on average concentration of one component of solution in a membrane (C1 ) when value of the second one (C2 ) is fixed and to compare these dependences with appropriate dependences for coefficients R ij , L ij , H ij and N ij presented in 1-5 parts of the paper.
  
  
  METHODS
  A cellulose hemodialysis membrane (Nephrophan) of known transport parameters for aqueous glucose and ethanol solutions was a research material. The PNT formalism and classical form of K-K equations for ternary non-electrolyte solutions was a research tool in this paper.
  
  
  RESULTS
  The network form of K-K equations was presented using the hybrid transformation of Peusner's thermodynamic networks for ternary solutions that contain solvent and two dissolved substances. For homogenous solutions, we calculated dependences of Peusner's coefficients Kij and quotients Kij/Rij, Kij/Lij, Kij/Hij and Kij/Nij (i, j ∈ {1, 2, 3}) on average concentration of one component (C1) of the solution in a membrane when value of the second one is fixed (C2).
  
  
  CONCLUSIONS
  The network form of K-K equations that contain Peusner's coefficients Kij (i, j ∈ {1, 2, 3}) is a novel tool to study membrane transport. We showed based on calculations that coefficients K12, K21, K23 and K32 are sensitive for composition and concentration of solutions separated by a polymer membrane.
authors.affiliation: Katedra Informatyki ekonomicznej, Uniwersytet ekonomiczny, Katowice, Polska.
authors.forename: Kornelia M
authors.initials: KM
authors.lastname: Batko
authors.affiliation: Instytut Marketingu, Politechnika Częstochowska, Gliwice, Polska.
authors.forename: Izabella
authors.initials: I
authors.lastname: Slęzak-Prochazka
authors.affiliation: Katedra Zdrowia Publicznego, Politechnika Częstochowska, Częstochowa, Polska.
authors.forename: Andrzej
authors.initials: A
authors.lastname: Slęzak
mesh_terms: D002482:Cellulose / Q000737:chemistry; D000431:Ethanol / Q000737:chemistry; D008567:Membranes, Artificial; D008956:Models, Chemical; D010539:Permeability; D011108:Polymers; D006435:Renal Dialysis / Q000295:instrumentation*; D012996:Solutions / Q000737:chemistry*; D012997:Solvents / Q000737:chemistry; D013816:Thermodynamics
chemical_list: D008567:Membranes, Artificial; D011108:Polymers; D012996:Solutions; D012997:Solvents; D000431:Ethanol; D002482:Cellulose