Document Type

Dissertation

Date of Award

8-31-2021

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Linda Jane Cummings

Second Advisor

Lou Kondic

Third Advisor

David Shirokoff

Fourth Advisor

Anand Uttam Oza

Fifth Advisor

Ian Griffiths

Abstract

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane filters, where the macroscale flow problem of Darcy flow through a pleated porous medium is coupled to the microscale fouling problem of particle transport and deposition within individual pores of the membrane; (2) dead-end membrane filtration with feed containing multiple species of physicochemically-distinct particles, which interact with the membrane differently; and (3) filtration with reactive particle removal using porous media composed of chemically active granular materials. Asymptotically-simplified models are used to describe and evaluate the membrane performance numerically and filter design optimization problems are formulated and solved for a number of industrially-relevant scenarios. This study demonstrates the potential of such modeling to guide industrial membrane filter design for a range of applications involving purification and separation.

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