(6fd) Intelligent Systems, Active Colloids, and Advanced Responsive Materials

Active colloids provide diverse and as yet untapped opportunity to engineer novel intelligent systems at microscopic and mesoscopic scales in fields ranging from targeted drug delivery, micro- to meso-scale robotics, active microfluidic devices, among others. Far from thermodynamic equilibrium, even seemingly simple active colloidal systems exhibit complex and counter-intuitive properties including negative viscosities, “turbulent” behavior at low Reynolds numbers, and highly enhanced transport. The field is ripe for new research that exploits this complexity to develop active colloidal systems that perform useful functions. To harness these properties, fundamental underpinnings must be developed to predict, tailor, and control their behaviors. I will provide theory to guide the development of active systems critical to realizing this vision.

I specialize in leveraging the methods of applied mathematics and numerical simulation, combined with highly integrated collaboration with experimentalists, to provide fundamental understanding and strategies to develop advanced functionality in soft materials and complex fluid systems. This positions me to perform groundbreaking research in intelligent systems utilizing active matter. I will use boundaries and spatial confinement to assert precise control over the behavior of active systems. For example, fluid interfaces present rich opportunity for enhanced transport and structure formation to engineer advanced functionality. Active colloids move along complicated, curvilinear trajectories near interfaces. Furthermore, they can become physically adhered to fluid interfaces, confining their motion to two-dimensional (potentially non-planar) surfaces. Once adhered, active colloids are subject to capillary and Marangoni forces, which can have a drastic impact on their behavior. The influence of hydrodynamic, capillary, and Marangoni forces can be widely tuned to produce desired behavior by changing the shape of the interface or adding surfactant to adjust the mechanical properties of the interface. These three forces are completely inherent to active systems at fluid interfaces. Introducing external fields (e.g., magnetic or electric) or anisotropy to the colloidal particles provide additional degrees of freedom. My vision is to harness this toolkit to make advanced, active, functional structures.

My background equips me to realize this vision. My past work has made me an expert in applying a variety of tools of applied mathematics and numerical analysis to engineering problems in transport phenomena and soft matter physics. These include finite element analysis, perturbation methods, boundary integral and singularity methods, and many others. However, my current work is all performed in very close collaboration with experimentalists. I have found this kind of communication between theory and experiment to be vital; experiments test the validity and assumptions of theoretical models, while theory can explain counter-intuitive observations in the lab and suggest new means of experimentation. I will continue to work in close collaboration with experimentalists to explain new observations in active matter systems as well as to conceive new directions for experimentation as suggested by theoretical findings.

Postdoctoral Advisor: Prof. Kathleen J. Stebe, University of Pennsylvania, Dept. of Chemical and Biological Engineering

Ph.D. Dissertation: Locomotion and Drift in Viscous Flows: Numerical and Asymptotic Predictions. Advised by Aditya S. Khair, Carnegie Mellon University, Dept. of Chemical Engineering

Teaching Interests:

In this data-driven era, intuition is of paramount importance to engineers to critically assess prediction. To develop these insights, we rely on powerful and fundamental concepts in many areas of mathematics, science, and engineering. I have a passion to teach these approaches to future generations of scientists and engineers, and I will design courses that provide effective and inclusive environments for learning. Tools of structured, active in-class learning provide means both to keep students engaged in the class content and to learn critical problem-solving skills. This style of learning departs from pure lecturing to allow students to reason through difficult problems with the help of the instructor, TAs, and peers. By using these pedagogical methods, I will instill the ability to use critical thinking and mathematical analysis to gain strong physical intuition about complex problems in engineering and to assess outcomes of machine learning and data-driven models. Providing such foundations to the next generation of scientists and engineers will equip them to push the limits in both industrial and academic environments.

I have had rich teaching experiences. During the first year of my postdoc, I had the privilege to teach an informal “mini-course” on micro-hydrodynamics and another on Green’s functions and their application to partial differential equations. Combined, they comprised 14 individual lectures of 90–120 minutes. The 15–20 attendees of these lectures included members of my research group as well as other interested graduate students from across the engineering school. To aid learning, I also constructed several informal exercises for students to discuss and work through during or after class. Aside from this, I have also given guest lectures in graduate and undergraduate courses on interfacial phenomena, fluid mechanics, and mathematical methods. During my PhD, I served as a mentor for a master’s student thesis project. Finally, I have provided informal one-on-one mentoring for graduate and undergraduate students throughout my academic career. I believe this past teaching experience has prepared me to teach and advise at the university level.