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Comment on the combined pore blockage and pore constriction model
Journal of Membrane Science 297 (2007) 271
Letter to the Editor Comment on the combined pore blockage and pore constriction model It has come to our attention that an article we published recently in this journal (Duclos-Orsello et al. [1]) omitted an important reference to a previous publication (Bolton et al. [2]). This omission was completely accidental—the paper by Bolton et al. appeared in print after we had submitted our paper to the Journal for review, and we were completely unaware of this work until after our paper had appeared in print. Bolton et al. presented a fouling model that is equivalent to part of the model that we developed (although in a very different mathematical form). This letter briefly summarizes the two fouling models and shows that they are mathematically equivalent, and it provides full credit to Bolton et al. for the original development of this result. Several studies have found that classical fouling models: complete pore blockage, intermediate pore blockage, pore constriction (standard blocking), and cake filtration cannot adequately describe experimental flux decline data throughout the entire filtration time. Ho and Zydney [3] used a combined pore blockage and cake filtration model to account for initial fouling due to pore blockage and subsequent fouling due to growth of a protein cake layer over the initially blocked regions. The model uses three parameters to describe the flow rate versus time data, or the three parameters can be measured independently. This model predicts a smooth transition from pore blockage to cake filtration during filtration. Model validation was conducted using BSA and track-etched microfiltration membranes. Bolton et al. [2] generated five new fouling models that accounts for the combined effects of two different classical fouling mechanisms, including cake-complete, cake-intermediate, complete-standard, intermediate-standard, and cake-standard. The pore blockage and cake filtration model was found to be most useful to provide good fit for the filtration of IgG and BSA. The model by Bolton et al. [2] uses two parameters to describe the volume versus time data. These parameters represent an “average” behavior of the system throughout the filtration. The combined simultaneous complete pore blockage and pore constriction model developed by Bolton et al. [2] shows that the filtrate volume can be expressed by Jo −2Kb t V = 1 − exp Kb 2 + K s Jo t 0376-7388/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2007.02.022
where Kb , Ks are best fit parameters, Jo the initial flux and t is the filtration time. The model assumes that the combined mechanisms are going on sequentially across the membrane surface. Constriction of a single pore can occur until the pore is blocked by a foulant and then flow stops. More recently, a three mechanism model combining pore blockage, pore constriction, and cake filtration is developed by Duclos-Orsello et al. [1]. The model assumes that the combined mechanisms are going on simultaneously across the membrane surface. The volumetric flow rate through the membrane was assumed to be expressed as the sum of the flow through the unblocked (Qu ) and blocked pores (Qb ). The pore constriction occurs until the pore is blocked by foulant and the pore blockage continues to grow to form the cake layer. The rate of pore blockage was described by the pore blockage model accounting for the effects of pore constriction in slowing down the rate of pore blockage. This leads to the flow through the unblocked pores (Qu ): 1 αCb J0 t Qu = exp − (2) Q0 1 + βQ0 Cb t (1 + βQ0 Cb t)2 where Q0 is the flow rate through a clean membrane, Cb the feed concentration, and α, β are parameters that describe the rate of pore blockage and rate of pore constriction. Eq. (1) can be differentiated to obtain Eq. (2), with Kb = αJo Cb and βQo Cb = Ks Jo /2. References [1] C. Duclos-Orsello, W. Li, C.C. Ho, A three mechanism model to describe fouling of microfiltration membranes, J. Membr. Sci. 280 (2006) 856. [2] G. Bolton, D. LaCasse, R. Kuriyel, Combined models of membrane fouling: development and application to microfiltration and ultrafiltration of biological fluids, J. Membr. Sci. 277 (2006) 75. [3] C.C. Ho, A.L. Zydney, A combined pore blockage and cake filtration model for protein fouling during microfiltration, J. Colloid Interface Sci. 232 (2000) 389.
Chase Duclos-Orsello Millipore corporation, Bedford MA 01730, United States Chia-Chi Ho ∗ University of Cincinnati, 497 Rhodes Hall, Cincinnati, OH 45221, United States ∗ Corresponding
author. Tel.: +1 513 556 2438; fax: +1 513 556 3473. E-mail address: [email protected] (C.-C. Ho) 12 February 2007
(1)
Available online 20 February 2007
Letter to the Editor Comment on the combined pore blockage and pore constriction model It has come to our attention that an article we published recently in this journal (Duclos-Orsello et al. [1]) omitted an important reference to a previous publication (Bolton et al. [2]). This omission was completely accidental—the paper by Bolton et al. appeared in print after we had submitted our paper to the Journal for review, and we were completely unaware of this work until after our paper had appeared in print. Bolton et al. presented a fouling model that is equivalent to part of the model that we developed (although in a very different mathematical form). This letter briefly summarizes the two fouling models and shows that they are mathematically equivalent, and it provides full credit to Bolton et al. for the original development of this result. Several studies have found that classical fouling models: complete pore blockage, intermediate pore blockage, pore constriction (standard blocking), and cake filtration cannot adequately describe experimental flux decline data throughout the entire filtration time. Ho and Zydney [3] used a combined pore blockage and cake filtration model to account for initial fouling due to pore blockage and subsequent fouling due to growth of a protein cake layer over the initially blocked regions. The model uses three parameters to describe the flow rate versus time data, or the three parameters can be measured independently. This model predicts a smooth transition from pore blockage to cake filtration during filtration. Model validation was conducted using BSA and track-etched microfiltration membranes. Bolton et al. [2] generated five new fouling models that accounts for the combined effects of two different classical fouling mechanisms, including cake-complete, cake-intermediate, complete-standard, intermediate-standard, and cake-standard. The pore blockage and cake filtration model was found to be most useful to provide good fit for the filtration of IgG and BSA. The model by Bolton et al. [2] uses two parameters to describe the volume versus time data. These parameters represent an “average” behavior of the system throughout the filtration. The combined simultaneous complete pore blockage and pore constriction model developed by Bolton et al. [2] shows that the filtrate volume can be expressed by Jo −2Kb t V = 1 − exp Kb 2 + K s Jo t 0376-7388/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2007.02.022
where Kb , Ks are best fit parameters, Jo the initial flux and t is the filtration time. The model assumes that the combined mechanisms are going on sequentially across the membrane surface. Constriction of a single pore can occur until the pore is blocked by a foulant and then flow stops. More recently, a three mechanism model combining pore blockage, pore constriction, and cake filtration is developed by Duclos-Orsello et al. [1]. The model assumes that the combined mechanisms are going on simultaneously across the membrane surface. The volumetric flow rate through the membrane was assumed to be expressed as the sum of the flow through the unblocked (Qu ) and blocked pores (Qb ). The pore constriction occurs until the pore is blocked by foulant and the pore blockage continues to grow to form the cake layer. The rate of pore blockage was described by the pore blockage model accounting for the effects of pore constriction in slowing down the rate of pore blockage. This leads to the flow through the unblocked pores (Qu ): 1 αCb J0 t Qu = exp − (2) Q0 1 + βQ0 Cb t (1 + βQ0 Cb t)2 where Q0 is the flow rate through a clean membrane, Cb the feed concentration, and α, β are parameters that describe the rate of pore blockage and rate of pore constriction. Eq. (1) can be differentiated to obtain Eq. (2), with Kb = αJo Cb and βQo Cb = Ks Jo /2. References [1] C. Duclos-Orsello, W. Li, C.C. Ho, A three mechanism model to describe fouling of microfiltration membranes, J. Membr. Sci. 280 (2006) 856. [2] G. Bolton, D. LaCasse, R. Kuriyel, Combined models of membrane fouling: development and application to microfiltration and ultrafiltration of biological fluids, J. Membr. Sci. 277 (2006) 75. [3] C.C. Ho, A.L. Zydney, A combined pore blockage and cake filtration model for protein fouling during microfiltration, J. Colloid Interface Sci. 232 (2000) 389.
Chase Duclos-Orsello Millipore corporation, Bedford MA 01730, United States Chia-Chi Ho ∗ University of Cincinnati, 497 Rhodes Hall, Cincinnati, OH 45221, United States ∗ Corresponding
author. Tel.: +1 513 556 2438; fax: +1 513 556 3473. E-mail address: [email protected] (C.-C. Ho) 12 February 2007
(1)
Available online 20 February 2007