{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T14:54:05Z","timestamp":1783522445203,"version":"3.55.0"},"reference-count":55,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T00:00:00Z","timestamp":1756944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Sciences and Engineering Research Council of Canada (NSERC)","award":["RGPIN-2019-05087"],"award-info":[{"award-number":["RGPIN-2019-05087"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Membranes"],"abstract":"<jats:p>The biological performance and carbon dioxide (CO2) flux of the novel and emerging concept of a membrane carbonated microalgal biofilm photobioreactor (MC-MBPBR) for wastewater treatment were investigated using mathematical modelling in conjunction with the finite-difference method. A set of differential equations was established to model the performance of an MC-MBPBR. The impacts of CO2 partial pressure, wastewater characteristics, and biofilm thickness on the concentration profiles and fluxes of CO2 and nutrients (N and P) to the biofilm of the MC-MBPBR were systematically studied. The modelling results showed profound impacts of these parameters on process efficiency (CO2 transfer and N and P removals) and the existence of an optimal biofilm thickness for maximum CO2, N, and P fluxes into the biofilm. Penetration of CO2 through the biofilm into the bulk water phase might occur under certain conditions. An increase in gaseous CO2 and increased influent N and P concentrations led to higher CO2, N, and P fluxes. The optimal biofilm thickness varied with the change in wastewater characteristics and gaseous CO2 concentration. The modelling results were in relatively good agreement with experimental results from the literature. The proposed mathematical models can be used as a powerful tool to optimize the design and operation of the novel MC-MBPBR for wastewater treatment and microalgae cultivation.<\/jats:p>","DOI":"10.3390\/membranes15090269","type":"journal-article","created":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T15:31:21Z","timestamp":1756999881000},"page":"269","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Modelling of Diffusion and Reaction of Carbon Dioxide and Nutrients in Biofilm for Optimal Design and Operation of Emerging Membrane Carbonated Microalgal Biofilm Photobioreactors"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-5144-229X","authenticated-orcid":false,"given":"Meilan","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mechanical and Mechatronics Engineering, Lakehead University, 955 Oliver Road, Thunder Bay, ON P7B 5E1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1472-2701","authenticated-orcid":false,"given":"Baoqiang","family":"Liao","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, Lakehead University, 955 Oliver Road, Thunder Bay, ON P7B 5E1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Moreno Osorio, J.H., Pollio, A., Frunzo, L., Lens, P.N.L., and Esposito, G. 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