DEPARTMENT OF MATHEMATICAL SCIENCES

COLLOQUIUM

SEPTEMBER 4, 2015

**Speaker: **
Jay Alexander, University of Maryland

**Title: ***
Line tension of Langmuir-Blodgett films: theory and experiment
*

**Abstract:**
A(n) (Irving) Langmuir-(Kathryn) Blodgett film is a molecularly thin film on a surface. Our team (a couple of mathematicians, an experimental physicist, a chemical engineer, and several students/post-docs) considers the behavior of such films on a flat water surface. 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 restoring force is the so-called line tension at the boundary of the domain (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. We advance a model of the system as two coupled Navier-Stokes systems, which because the Reynolds numbers are small, reduce to two coupled Euler flows. We model the behavior of the system globally in time, then implement comparison with experiments, and significantly sharpen the measurement of line tension over previous results. This requires some new mathematical and numerical techniques. In this lecture, we describe the project—experiment and theory—from conceptual beginning through laboratory experiments and mathematical analysis 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).

Department of Mathematical Sciences

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