(4eb) Fundamentals of Self-assembly and Contact-Line Motion

I am interested in studying two topics: Self-assembly and Contact-line motion. These are both fundamental problems in engineering, which have a range of applications, and exhibit very rich and interesting behaviour. I plan on investigating these theoretically through chemical/mechanical engineering tools such as statistical mechanics, thermodynamics and fluid mechanics, using computer simulations to aid the theory, and performing simple experiments to test the results. My interest in these problems, and my contributions to them thus far, are described below. My other interest is teaching. I enjoyed being a teaching assistant in graduate school and instructor of a class as a post-doc, and I am proud of the good student reviews I have received, and my rapport with the students.

Self-assembly is the future for creating ordered nano and micrometer scaled objects. It is also the method by which viruses assemble, and hence it has significant applications in the health industry. However, no simple theory can predict when or how self-assembly works. Which kind of subunit structures will assemble into the desired macro-structure? How long will the assembly take? How can assembly be hindered? What are the classes of structures that can be formed?  These are questions I seek to answer through modeling, computation, and simple experiments. In my post-doc (with Richard James, Aerospace Engineering and Mechanics, University of Minnesota), I have modeled self-assembly using a Smoluchowski equation with rotation, compared these results with Langevin simulations and constructed a macroscopic experiment on which these results can be tested. We have identified certain symmetric structures, which are natural to objects that self-assemble. Future research will focus on understanding the dynamics of assembly.

The second topic I am interested in is the relation between contact-line motion, solid-liquid slip, and contact-angle. Contact-line motion is important for inject printing, printed electronics, pesticides application (ones that spread more thinly and can be used more sparingly), and water-repelling glass. The fundamentals of the problem are still poorly understood. In my PhD (with Paul Steen, Chemical Engineering, Cornell University) I added a quasi-equilibrium thermodynamic balance to this fluids problem, which allowed for the first prediction of contact-line motion, based on the slip-length and equilibrium contact-angle. The theory allowed us to construct a simple experiment from which a slip-length was measured, which compared favourably with those in the literature. This theory works only for low Reynolds number flows, and there is interesting and industrially applicable work involving faster flow rates, which may become unstable or violate the quasi-equilibrium thermodynamic balance.