title: [Network form of the Kedem-Katchalsky equations for ternary non-electrolyte solutions. 1. Evaluation of Rij Peusner's coefficients for polymeric membrane].
abstract: BACKGROUND
  Peusner's network thermodynamics (PNT) enables symmetrical or hybrid transformation of membrane transport equations. For Kedem-Katchalsky equations (K-K) these transformations create the network form of these equations that contain new types of coefficients which can be calculated from the experimentally determined transport parameters, such as hydraulic permeability coefficient (Lp), solute permeability (omega) and reflection (sigma). For ternary and homogeneous solutions of non-electrolytes, transformations result in two symmetrical and six hybrid K-K network equations. The symmetrical forms of K-K network equations contain Peusner's coefficients Rij or Lij, whereas hybrid forms of K-K network equations contain Peusner's coefficients Hij, Nij, Kij, Pij, Sij or Wij.
  
  
  OBJECTIVE
  Derivation of network form of KK equations for homogeneous ternary solutions that contain nonelectrolytes Peusnera ratios Rij (i, j element of {1, 2, 3}) presented in the third-order matrix [R]. Evaluation of transport properties of the membrane using Peusner's coefficients Rij, the determinant of the matrix [R], somber elements belonging to Rij, quotients Rij/det [R] and quotients det [Rij]/det [R].
  
  
  METHODS
  A cellulose acetate hemodialysis membrane (Nephrophan) of known parameters for transport of aqueous glucose and ethanol solutions of was a research material. The PNT formalism and K-K equation for ternary nonelectrolyte solutions were a research tool in this paper.
  
  
  RESULTS
  The network form of K-K equations for ternary solutions was presented, that was obtained using the symmetric transformation of Peusner's thermodynamic networks. The resulting equations were used to interpret the transport of nonelectrolytes solutions consisting of solvent and two solutes. We calculated dependences of Peusner's coefficients Rij (i, j element of { 1, 2, 3}) and det [R] from the average concentration of one component of solution in the membrane (C1) with a constant value of a second component (C2) in conditions of solutions homogeneity. We also calculated dependencies of minors belonging to the elements Rij, the quotients Rij/det [R] and quotients det [Rij]/det [R] on the average concentration of one component of solution in the membrane (C1) at a constant value of the second component (C2).
  
  
  CONCLUSIONS
  Network form of K-K equations containing Peusner's coefficients Rij (i, j element of {1, 2, 3}) is a novel tool suitable for the examination of the membrane transport. The presented calculations showed that the values of coefficients R11, R21, R22, R23 and R13 are sensitive to the composition and concentration of the solutions separated by a polymer membrane.
authors.affiliation: Katedra Informatyki Ekonomicznej, Uniwersytet Ekonomiczny, Katowice, Polska. kornelia.batko@ue.katowice.pl
authors.forename: Kornelia M
authors.initials: KM
authors.lastname: Batko
authors.forename: Izabella
authors.initials: I
authors.lastname: Slezak-Prochazka
authors.forename: Andrzej
authors.initials: A
authors.lastname: Slezak
mesh_terms: D004058:Diffusion; D005947:Glucose / Q000737:chemistry; D015312:Hemodialysis Solutions / Q000737:chemistry; D006874:Hydrostatic Pressure; D008567:Membranes, Artificial; D008956:Models, Chemical; D009997:Osmotic Pressure; D010539:Permeability; D011108:Polymers / Q000737:chemistry*; D012996:Solutions / Q000737:chemistry
chemical_list: D015312:Hemodialysis Solutions; D008567:Membranes, Artificial; D011108:Polymers; D012996:Solutions; D005947:Glucose