The mathematical model of concentration polarization coefficient in membrane transport and volume flows

Arkadiusz Bryll,Andrzej Ślęzak

doi:10.1007/s10867-016-9432-5

Arkadiusz Bryll, Andrzej Ślęzak

Open Access

https://doi.org/10.1007/s10867-016-9432-5

Copy DOI

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 ζs when 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 ζs and a concentration Rayleigh number (RC) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.

Highlights

Cognitive and applicative research in membrane transport is carried out in different fields of science, technology, and medicine [1,2,3,4]
This paper presents two mathematical models: the former presenting the influence of the volume flux (Jv) on the value of coefficient ζs and the latter presenting the influence of the osmotic force (Δπ) and the hydrostatic force (ΔP) on the value of coefficient ζs
We aim to prove that the detailed investigation of coefficient ζs shows its dependence on the flux Jvm (Fig. 2), the concentration ΔC1 (Fig. 3), the hydrostatic and osmotic pressure ΔP (Figs. 4, 5 and 6), the volume flux Jvm and the concentration Rayleigh number Rc (Fig. 7)

Summary

Introduction

Cognitive and applicative research in membrane transport is carried out in different fields of science, technology, and medicine [1,2,3,4]. Membrane cells are organic membranes and specialists on cellular transport should take into account that some amounts of substance might not reach inside cells due to the phenomenon of concentration polarization It may happen in the event of ulcer treatment by applying membranes. The problem of the role of volume flows generated by osmotic forces (Δπ) and hydrostatic forces (ΔP) in forming concentration boundary layers was mentioned [27]. To develop this issue, we will study how the volume flux (Jv), the osmotic force (Δπ) and the hydrostatic force (ΔP) influence the value of coefficient ζs. This paper presents two mathematical models: the former presenting the influence of the volume flux (Jv) on the value of coefficient ζs and the latter presenting the influence of the osmotic force (Δπ) and the hydrostatic force (ΔP) on the value of coefficient ζs

Theory

Calculation results and discussion

Findings

Conclusions