Date of Award

12-2017

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

Committee Member

Dr. Christopher Cox, Committee Chair

Committee Member

Dr. Nicos Andreas

Committee Member

Dr. Qingshan Chen

Committee Member

Dr. Matthew Saltzman

Abstract

In this thesis, we present a 1D model for the complex phenomenon of cross-flow filtration. We begin by developing the governing equations and providing analytical solutions that can be found using Laplace transforms for both the simple clean filter case, and the more complex filter with fouling in the form of cake, and depth plugging of the filter media. A walk through of the set up and implementation of a simple web-based application is given, and the code to produce the web application for this model is included in an appendix. The web application acts as a calculator, accepting model parameters and returning graphical output on the client side while the numerical solution is calculated on the server side. Lastly technique of a least-squares finite element approach is applied to the governing equations to obtain approximate solutions now under the assumption that viscosity is not constant, but varies linearly with respect to time. The major contribution from this thesis is the development of a web-based application for simulation of cross flow filtration, set in a framework that can be applied for a wide variety of modeling problems. This thesis is a significant step towards the long term goal to combine multiple disciplines including fluid dynamics, mathematics, and computer science, to produce an effective and robust modeling tool.

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