Faculty Member: John. A. Pelesko
Project Description: For the past several years we have been studying the behavior of bubbles and droplets in the presence of electric and magnetic fields. This includes both mathematical modeling and experimental efforts carried out in the MEC Lab. Numerous undergraduate and graduate students have participated in these efforts, including two recent Ph.D. students, Derek Moulton and Regan Beckham. Some of their most recent work can be found on our team wiki at: http://capillaryteam.pbwiki.com/ . This summer, we plan to refresh our group with at least three new undergraduate students and at least one graduate student, hopefully a GEMS student. We plan to focus on three basic projects:
Electro-Capillarity - In this project, we study the interaction of electric fields with capillary surfaces. In particular, we look at how soap films are deformed in the presence of an electric field. Some photographs, taken using the high speed camera in the MEC Lab are shown on the left below. In this case, our goal was to understand both the static behavior of the film and the dynamic response of the film to an electric field. The mathematical model was formulated using variational calculus and resulted in a coupled systems of non-linear PDE's that were solved using asymptotic and numerical methods. Our goal for this summer is to extend this work and carry out a more careful comparison of experimental and theoretical results.
Magnetic Film Draining - The photographs on the right are close up snapshots of a soap film draining under the action of gravity. However, in this system, magnetic nanoparticles have been added to the soap film to make it susceptible to the influence of a magnetic field. In the leftmost photograph, no nanoparticles have been added. The colors indicate thinning of the film and "normal" soap film drainage is seen to occur. In the photos on the right, nanoparticles have been added to the solution and the film drains not only under the influence of gravity, but also in the presence of a magnetic field. In the MEC Lab, we have demonstrated what we call "reverse draining," i.e., the upwards draining of a soap film against the action of gravity. This work will be featured at an upcoming meeting of the American Physical Society. A preliminary mathematical model of this system has been formulated and simplified using standard techniques from the theory of thin films. Our goal for this summer is to push both the theory and the experiment to the point where a quantitative comparison becomes possible.
Electro-Elastic Capillarity - The third project we will pursue this summer is the addition of an elastic substrate to the electro-capillarity problems discussed above. In essence, we want to understand how droplets sitting on an elastic substrate deform in the presence of an electric field. Our goal for this summer is to develop a first, simple, experimental version of this problem and to formulate the corresponding mathematical model.
All of the problems above involve using tools and techniques from variational calculus, ordinary differential equations, partial differential equations, asymptotic methods, and numerical analysis. The interested student is not expected to be familiar with all of this material, but should be willing to learn! A GEMS graduate student participating in this project will be expected to help supervise undergraduate researchers and to participate in laboratory work. No prior experimental expertise is expected, but again a willingness to learn is essential.