(4dp) Understanding Transport Processes in Electrokinetics through Applied Mathematics: Challenges and Opportunities

Electrokinetics can be utilized in a wide variety of applications including environmental remediation, bioseparations for the development of novel pharmaceuticals, and drug delivery, just to name a few. In bioseparations, a technique that is commonly used to separate biomolecules, such as proteins, is electrical field flow fractionation (EFFF). In this approach, an electrical field is applied perpendicular to the direction of flow in a channel causing the biomolecules most susceptible to the field to move to the walls of the channel faster, thus creating a very efficient separation. Another area in bioseparations where electrokinetics is utilized involves nanocomposite gels and electrophoresis to separate proteins, antibiotics, and DNA, for example. It has been shown that the addition of charged nanoparticles into hydrogels has the potential to modify the internal structure (morphology) of the gel and can lead to enhanced separation efficiency.

In my doctoral research I have focused on the mathematical modeling of the aforementioned systems to study the effects of morphology, physicochemical properties (i.e. valence, mobility etc.), and applied electrical field on the determination of optimal times of separation. Predictions of optimal times of separation can aid in the improvement of the design of devices and materials, such as the ones mentioned above, and lead to better separation efficiencies. In order to accomplish the tasks mentioned above, I have studied a variety of systems with various types of geometries (rectangular, cylindrical, annular, axially varying) and types of flows (Couette, Poiseuille). In addition, I have examined the dynamics of the previously described systems in order to better understand the effects of these parameters on transient analyses.

In this presentation, I will summarize my doctoral research, the research program I plan to develop, and my philosophies about teaching. Understanding the behavior of the aforementioned biological systems is a complex task. Therefore, developing models to aid in this understanding can significantly advance the field. To accomplish this, a mathematical toolbox filled with a wide array of techniques from analytical (partial differential and integral equations, linear operator method approaches) to computational (finite element, finite difference, computer programming) is necessary. I hope to develop a research program that utilizes my knowledge in applied mathematics and computational strategies to develop models to predict the transport behavior in bioengineering systems, such as the ones mentioned previously. This broad area of research not only allows for versatile projects, but also lends itself to collaborations with colleagues from other disciplines, such as mechanical engineering, materials science, and mathematics, for example. In addition, collaborations with other engineers who perform experiments in the area to validate these models will be helpful. Potential sources of funding will also be identified and presented.