From "Black Box" to a Real Description of Overall Mass Transport through Membrane and Boundary Layers.
MEMBRANES 2019;
9:membranes9020018. [PMID:
30678068 PMCID:
PMC6409853 DOI:
10.3390/membranes9020018]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/31/2018] [Revised: 01/15/2019] [Accepted: 01/16/2019] [Indexed: 11/24/2022]
Abstract
The “black box” model defines the enhancement, E the polarization modulus, C∗/Co and the intrinsic enhancement, Eo 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,Eo or C∗/Co) 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.
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