Prediction of the Limiting Flux and Its Correlation with the Reynolds Number during the Microfiltration of Skim Milk Using an Improved Model

Abstract

Limiting flux (JL) determination is a critical issue for membrane processing. This work presents a modified exponential model for JL calculation, based on a previously published version. Our research focused on skim milk microfiltrations. The processing variables studied were the crossflow velocity (CFV), membrane hydraulic diameter (dh), temperature, and concentration factor, totaling 62 experimental runs. Results showed that, by adding a new parameter called minimum transmembrane pressure, the modified model not only improved the fit of the experimental data compared to the former version (R2 > 97.00%), but also revealed the existence of a minimum transmembrane pressure required to obtain flux (J). This result is observed as a small shift to the right on J versus transmembrane pressure curves, and this shift increases with the flow velocity. This fact was reported in other investigations, but so far has gone uninvestigated. The JL predicted values were correlated with the Reynolds number (Re) for each dh tested. Results showed that for a same Re; JL increased as dh decreased; in a wide range of Re within the turbulent regime. Finally, from dimensionless correlations; a unique expression JL = f (Re, dh) was obtained; predicting satisfactorily JL (R2 = 84.11%) for the whole set of experiments

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“…The growing interest in these milk protein fractions explains the development of milk microfiltration equipment. However, this process remains difficult to understand as a whole, in particular, because the existing models 25 only evaluate a precise range of operating conditions and do not take into account the different types of membrane technologies that can be used 26 . To meet this challenge, Baudrit et al 27 designed a method combining the use of the PO2/TransformON vocabulary and a Bayesian network, to structure heterogeneous data sources, assess the reliability of data sources, and provide relevant recommendations based on deductive and quantitative reasoning.…”

Permeate Flux in Ultrafiltration Processes—Understandings and Misunderstandings

“…Firstly, as noted in a recent paper concerning the microfiltration of skimmed milk, experimental research is essential in the development of any membrane process where the constituents exhibit a "flux paradox" [43]. As they noted, "experimental research on membrane technology is a must to predict proper operating conditions as the gel polarization model underpredicts the flux by 1 to 2 orders of magnitude in colloidal suspensions, hindering the selection of operating conditions that meet the needs of large-scale production".…”

Decision Support Tool for the Agri-Food Sector Using Data Annotated by Ontology and Bayesian Network

“…Milk microfiltration is applied to fractionate milk proteins (casein micelles and serum proteins) in order to produce innovative ingredients. This process remains difficult to understand as a whole, especially because existing models (Astudillo-Castro et al 2020) assess only a specific range of operating conditions and do not take into account the three used types of membrane technologies (Gésan-Guiziou, 2010): (1) ceramic membranes with uniform transmembrane pressure (UTP), (2) ceramic membranes with graded hydraulic resistance (eg GP® membranes) and (3) polymeric spiral wound membranes. The innovations in this article include (1) combining ontologies and BN to structure heterogeneous sources of data/knowledge, given the reliability of data sources, to provide relevant conclusions and recommendations based on deductive and quantitative reasoning; (2) the development of a new domain ontology representing skimmed milk microfiltration and a set of metadata to assess data source reliability; and (3) assessment of the workflow developed (Fig.…”