Dr. Keith Promislow

Professor
Michigan State University
Department of Mathematics
East Lansing, MI 48824
(517) 432-7135
(517) 432-1562 (Fax)
kpromisl@math.msu.edu
Google Scholar Citation Index

Applied Math Seminar

Math 254H

PREPRINTS and REPRINTS

Network formation in Ionomer Membranes

The device level modeling of polymer electrolyte membrane (PEM) fuel cells involves free boundary problems, phase change, stiff electrochemical reaction terms, and widely separated length and time scales. For some animated demos of fuel cells, check out the (MMSC) web page.
The Functionalized Cahn-Hilliard free Energy models network formation in polymer electrlolyte membranes and other amphiphilic materials. It balances solvation energy of ionic groups, counter-ion entropy, and elastic deformation of backbone polymer. The image at right red shows the development of network structures from random initial data. At middle left is a similar simulation in 3D, from a pore-driven region of parameter space, and at middle right is a still image with a higher volume fraction of solvent phase. At bottom left is a 2D simulation of the instabilities of a spherical drop. Blue indicates regions of high solvent (water) content and red (or clear in 3D) indicates regions of polymer phase. The flow maximizes surface area while minimizing bending moments. Simulations in 3D courtesy of A. Christlieb, J. Jones, and Z. Xu. Image compression by S. Promislow.