Levich Institute Seminar Announcement, 10/03/2017
Steinman Hall, Room #312
(Chemical Engineering Conference Room)
Professor Pejman Sanaei
Courant Institute of Mathematical Sciences
"Mathematical Models for Membrane Filtration"
The purpose of this talk is to formulate and investigate new mathematical models for membrane filtration. The work presented is divided into two parts. In the first part, a new mathematical model for flow and fouling in a pleated membrane filter is presented. Pleated membrane filters are widely used in many applications, and offer significantly better surface area to volume ratios than equal area unpleated membrane filters. However, their filtration characteristics are markedly inferior to those of equivalent unpleated membrane filters in deadend filtration. While several hypotheses have been advanced for this poor performance, one possibility is that the flow field induced by the pleating leads to spatially nonuniform fouling of the filter, which in turn affects performance. In this work, we investigate this hypothesis by developing a simplified model for the flow and fouling within a pleated membrane filter. Our model accounts for the pleated membrane geometry (which affects the flow), for porous support layers surrounding the membrane, and for two membrane fouling mechanisms: (i) adsorption of very small particles within membrane pores; and (ii) blocking of entire pores by large particles. We use asymptotic techniques based on the small pleat aspect ratio to solve the model, and we compare solutions to those for the closest-equivalent unpleated filter.
In the second part, mathematical models are proposed to describe the effects of filter membrane morphology on filtration efficiency. A reasonable question that membrane filter manufacturers may ask is: what is the optimal configuration of filter membranes, in terms of internal morphology (pore size and shape), to achieve the most efficient filtration? In order to answer this question, a robust measure of filtration performance must be first proposed. Filter membrane performance can be measured in a number of different ways. As filtration occurs, the membrane becomes blocked, or fouled, by the impurities in the feed solution, and any performance measure must take account of this. For example, one performance measure might be the total throughput – the amount of filtered feed solution – at the end of filtration process, when the membrane is so badly blocked that it is deemed no longer functional. A simplified mathematical model is proposed, which (i) characterizes membrane internal pore structure via pore or permeability profiles in the depth of the membrane; (ii) accounts for various membrane fouling mechanisms; and (iii) defines a measure of filter performance; and (iv) predicts the optimum pore or permeability profile for the chosen performance measure.
BRIEF ACADEMIC/EMPLOYMENT HISTORY
PhD: New Jersey Institute of Technology (NJIT) (2013-2017)
Assistant Professor/Courant Instructor (September 2017-present): Courant Institute of Mathematical Sciences, New York University, New York.
RECENT RESEARCH INTERESTS
Mathematical Modeling, Numerical Analysis, Mathematical Modeling of Filter Membranes, Tissue Engineering, Applications of Mathematics to Industry, Biology and Physics.