Version 1
: Received: 9 June 2022 / Approved: 13 June 2022 / Online: 13 June 2022 (12:54:53 CEST)
Version 2
: Received: 4 January 2023 / Approved: 5 January 2023 / Online: 5 January 2023 (03:38:02 CET)
Pereira, G.L.D.; Cardozo-Filho, L.; Jegatheesan, V.; Guirardello, R. Generalization and Expansion of the Hermia Model for a Better Understanding of Membrane Fouling. Membranes2023, 13, 290.
Pereira, G.L.D.; Cardozo-Filho, L.; Jegatheesan, V.; Guirardello, R. Generalization and Expansion of the Hermia Model for a Better Understanding of Membrane Fouling. Membranes 2023, 13, 290.
Pereira, G.L.D.; Cardozo-Filho, L.; Jegatheesan, V.; Guirardello, R. Generalization and Expansion of the Hermia Model for a Better Understanding of Membrane Fouling. Membranes2023, 13, 290.
Pereira, G.L.D.; Cardozo-Filho, L.; Jegatheesan, V.; Guirardello, R. Generalization and Expansion of the Hermia Model for a Better Understanding of Membrane Fouling. Membranes 2023, 13, 290.
Abstract
One of the most broadly used models for membrane fouling is the Hermia model, which separates this phenomenon into four blocking mechanisms, each with an associated parameter n. These mechanisms are complete blocking (n=2), intermediate blocking (n=1), standard blocking (n=3/2), and cake formation (n=3/2). The original model, which was obtained through experimental data, is given by an Ordinary Differential Equation (ODE) dependent on n. At the time, this ODE was only solved for these four values of n, which limits the effectiveness of the model when adjusted to experimental data. This paper aims to not only mathematically prove the original Hermia model but also to broaden the scope of this model for any real number n by using the original ODE, the equations of fluid mechanics, and the properties of single and multivariable calculus. The extended Hermia model (EHM) is given by a power law for any n≠2 and is given by an exponential function at n=2. To better test the model, we have performed the model fitting of the EHM and compared its performance to the original four pore-blocking mechanisms in 6 micro- and ultrafiltration examples. In all examples, the EHM performed consistently better than the four original pore-blocking mechanisms. Changes in the blocking mechanisms concerning transmembrane pressure (TMP), crossflow rate (CFR), crossflow velocity (CFV), membrane composition, and pretreatments are also discussed.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
