From "Black Box" to a Real Description of Overall Mass Transport through Membrane and Boundary Layers.

Endre Nagy,Márta Vitai

doi:10.3390/membranes9020018

Abstract

The “black box” model defines the enhancement, the polarization modulus, and the intrinsic enhancement, without knowing the transport mechanism in the membrane. This study expresses the above-mentioned characteristic parameters, simultaneously taking into account the mass transport expressions developed for both the polarization and the membrane layers. Two membrane models are studied here, namely a solution-diffusion model characterizing solute transport through a dense membrane and a solution-diffusion plus convection model characterizing transport through a porous membrane due to transmembrane pressure difference. It is shown that the characteristic parameters of the “black box” model (E, or ) can be expressed as a function of the transport parameters and independently from each other using two-layer models. Thus, membrane performance could be predicted by means of the transport parameters. Several figures show how enhancement and the polarization modulus varied as a function of the membrane Peclet number and the solubility coefficient. Enhancement strongly increased up to its maximum value when H > 1, in the case of transport through a porous membrane, whereas its change remained before unity in the case of a dense membrane. When the value of H < 1, the value of E gradually decreased with increasing values of the membrane Peclet number.

Highlights

With rising numbers of various membrane separation processes, working with different transport principles, efforts for describing transport processes through the membrane layer have been substantially increased
The main point of this study is to show how the most popular, characteristic parameters of membrane separations can be predicted, taking into account the transport parameters of the feed boundary layer, and the transport parameters of the membrane layer
The discussion of how the enhancement, intrinsic enhancement factors, and polarization modulus vary as a function of the simultaneous effect of two-layer solute transports can be useful and instructive, and it can significantly contribute to a better understanding of the real meaning of membrane separation properties

Summary

Introduction

With rising numbers of various membrane separation processes, working with different transport principles, efforts for describing transport processes through the membrane layer have been substantially increased. For characterization of the separation process in this case, it uses the measured outlet concentration value for description of the separation, which is considered to be a response of the membrane separation unit to the inlet parameter values. This “black box” model has often been used for characterization of the membrane separation process (e.g., reverse osmosis [8] or pervaporation [12,13]) in the starting time period of the membranes’

Objectives

Results

Conclusion