title: The mathematical model of concentration polarization coefficient in membrane transport and volume flows.
abstract: In this paper, the authors investigate the membrane transport of aqueous non-electrolyte solutions in a single-membrane system with the membrane mounted horizontally. The purpose of the research is to analyze the influence of volume flows on the process of forming concentration boundary layers (CBLs). A mathematical model is provided to calculate dependences of a concentration polarization coefficient (ζs) on a volume flux (Jvm), an osmotic force (Δπ) and a hydrostatic force (ΔP) of different values. Property ζs= f(Jvm) for Jvm> 0 and for Jvm≈ 0 and property ζs= f(ΔC1) are calculated. Moreover, results of a simultaneous influence of ΔP and Δπ on a value of coefficient ζswhen Jvm= 0 and Jvm≠ 0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient ζsand a concentration Rayleigh number (RC) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.
authors.affiliation: Department of Public Health, Częstochowa University of Technology, 36b Armia Krajowa Al., 42200, Częstochowa, Poland. tex@op.pl.
authors.forename: Arkadiusz
authors.initials: A
authors.lastname: Bryll
authors.affiliation: Department of Public Health, Częstochowa University of Technology, 36b Armia Krajowa Al., 42200, Częstochowa, Poland.
authors.forename: Andrzej
authors.initials: A
authors.lastname: Ślęzak
mesh_terms: D001692:Biological Transport; D002462:Cell Membrane / Q000378:metabolism*; D008954:Models, Biological; D009995:Osmosis
keywords: Concentration Rayleigh number; Concentration polarization; Kedem–Katchalsky equations; Membrane transport