Membrane filters represent a multi-billion dollar industry worldwide and many major multinational companies maintain a keen interest in improving and optimizing the membrane filters they produce, in terms of both performance and cost. When seeking to improve filter performance, certain features of the porous membrane are key, e.g. membrane thickness, internal pore structure and shape, pore connectivity, and variation of pore dimensions in the depth of the membrane. During the filtration process, the membrane internal void area becomes fouled with deposited impurities and as a consequence, the filter performance deteriorates, in a manner that depends strongly on the filter's internal structure, as well as the characteristics of the feed solution. The complexity of the coupling between the membrane morphology, which evolves dynamically due to the deposition, and the details of the particle-laden flow, including possible stochastic behavior of the particles, make filtration and fouling a challenging predictive modeling problem. Many researchers have addressed these issues, using a range of modeling approaches, but very few models present a coherent, first-principles approach to deal with both stochastic effects of particle dynamics and variations in internal membrane structure.

The long term goal of this proposal is to improve and optimize the membrane filters, in terms of both performance and cost. This needs to understand how the internal structure and morphology of membrane filters evolve in multi-directional flow due to particle deposition, which in turn results in membrane fouling. The specific goal of this proposal is to formulate novel and idealized mathematical models to investigate the evolution of membrane filters with complex internal structures by using asymptotic and numerical techniques. 


Intellectual merit: Regarding publications as outcomes of the proposal, since the starting of the proposal in 2021, the PI has published 8 articles in top journals with wide readerships and excellent disseminations in the field, which are all peer reviewed journals. The PI was the principle investigator as well as the corresponding author for 7 of these articles. Two of these articles were selected as featured articles. One of these two articles was also accepted for a Scilight article to showcase the work, in which the PI supervised two former undergraduate students from New York University (NYU), who are now PhD students at other schools. In the other featured article, the PI supervised two other former undergraduate students from NYU. Out of the 8 published articles mentioned above, 5 of them are in the topic of membrane filtration, which are directly related to this grant. It is also worth it to mention that the PI mentored 2 undergraduate students from New York Institute of Technology (NYIT) for one of the published article. Although they both were not undergraduate students at the Department of Mathematics at NYIT, the concepts of their research in applied mathematics under the PI's mentorship, sought them to be accepted to Science Undergraduate Laboratory Internship at Brookhaven National Laboratory and a Summer program at Pennsylvania State University in Summer 2021. 

Broader Impacts: Regarding the PI's service to the broader mathematics and physics communities, the PI was reviewer for several distinguished journals. In addition, the PI was a mentor for the Graduate Student Mathematical Modeling Camp 2021 at University of Delaware (UD). Furthermore, the PI and his collaborator organized a focus session entitled ``Microflows Meet Soft Matter: Compliance, Growth, Instabilities and Beyond (DSOFT, DFD, GSNP)" at the American Physics Society-March Meeting 2021. The PI also presented at the same session. The PI was an invited speaker at the Annual Meeting of the Society of Mathematical Biology and the 14th Northeast Complex Fluids and Soft Matter (NCS14) Workshop in 2021. Furthermore, the PI recently gave four invited talks on filtration topic at NJIT, GSU and MI-UO. 

Aligned with this proposal, in March 2021, the PI was awarded a two-year internal grant from NYIT, which is Institutional Support for Research and Creativity Grants. The PI officially recruited 2 female undergraduate students (one of them is a US citizen), who have been supported by this grant since Summer 2021. The first student has been working on a porous media/tissue engineering problem and her primary results are very promising and under review at Bulletin of Mathematical Biology with minor revisions. She presented her discoveries at the APS-DFD in November 2021 as well as SIAM Annual Meeting 2022. In addition, the PI mentored her to draft a proposal and apply for the NSF Graduate Research Fellowship Program (GRFP). The second student was working on the deposition and erosion project, which is the continuation of the work initiated by the PI's former NYIT student who graduated with a bachelor's degree in Electrical and Computer Engineering in May 2021. He is now a PhD student in UD. 

Last Modified: 12/21/2022
Modified by: Pejman Sanaei