Applied Mathematics Colloquium

Dynamics of Langmuir-Blodgett films: theory and experiment

James Alexander

A Langmuir film is a molecularly thin film on a surface.  Here we consider the behavior of such films on a flat water surface.  (Note: “we” consists of a team of mathematicians, a physicist, a chemical engineer, and several students/post-docs.)  The equilibrium state of a finite domain (= “blob”) of such a film is a circular disk.  We consider the dynamical behavior when such a domain is disturbed.  The tension at the boundary of the domain is the restoring force (so-called line tension, analogous to surface tension of a fluid), which competes against the viscosity of the underlying fluid.  A prominent problem is to measure the line tension.  The system is modeled as two coupled Navier-Stokes systems, which, because the Reynolds numbers are small, reduces to two coupled Euler flows.  Solutions are found which permit comparison with experiment.  An advance we make is to model the system globally, not just asymptotically at the end of relaxation to equilibrium.  This requires advances in numerical techniques to make the computation effective.  In this lecture, we describe the project, from conceptual beginning through to the quantitative dovetailing of theory with experiment.

Some published results:

Gaseous hole closing in a polymer Langmuir monolayer, Lu Zou,  Andrew J. Bernoff,  J. Adin Mann Jr., JCA, Elizabeth K. Mann, Langmuir 26(5), 3232-3236 (March 2, 2010).

Determination of inter-phase line tension in DMPC/D-cholesterol mixed Langmuir films, Fanindra Bhatta, Pritam Mandal, Andrew J. Bernoff, JCA, J. Adin Mann, Edgar E. Kooijman, David W. Allender, Elizabeth K. Mann, Biophys J, 96(3), 350a (March 2, 2009).

Determination of interphase line tension in Langmuir films, Jacob R. Wintersmith,  Lu Zou,  Andrew J. Bernoff,  JCA, J. Adin Mann Jr.,  Edgar E. Kooijman,  Elizabeth K. Mann, Phys. Rev. E, Phys. Rev. E, 75(6) (June, 2007).

Domain relaxation in Langmuir layers, JCA, Andrew Bernoff, Elizabeth K. Mann, J. Adin Mann, Jr., Jacob Wintersmith, Lu Zou, J. Fluid Mech. 571(1), 191-219, (January 25, 2007) (with online supplementary material).

Hole dynamics of polymer Langmuir films, JCA, Andrew Bernoff, Elizabeth K. Mann, J. Adin Mann, Jr., Lu Zou, Phys. Fluids 18(6),  (June 2006) (with online supplementary material).