ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Sharp-Interface Theory for Transitions Between the Isotropic and Uniaxial Nematic Phases of a Liquid Crystal

Eliot M. Fried
Washington University in St. Louis, Department of Mechanical and Aerospace Engineering

Thursday, May 3, 2007 15:00-16:00,
Building 101, Lecture Room B
Thursday, May 3, 2007 13:00-14:00,
Room 4550

Abstract: A sharp-interface theory has been developed to describe material interfaces between nematic and isotropic fluids. That theory accounts for flow, director elasticity of the nematic fluid, and anchoring energy at the interface. In this talk, we describe the extension of that theory to account for phase transformations between the isotropic and nematic phases of a liquid crystal. Such transformations involve the growth of one phase, nematic or isotropic, at the expense of the other--as described by the migration of the interface with respect to the underlying fluid. Of fundamental importance in the theory is a supplemental evolution equation arising from the notion of configurational momentum balance and accounting for the microphysics underlying the exchange of material between the phases. This equation provides an appropriate generalization of the Gibbs-Thomson relation familiar from theories for dendritic solidification. As an application, we study the behavior a spherical isotropic droplet surrounded by a radially oriented uniaxial nematic phase. Our generalized Gibbs-Thomson relation then reduces to a nonlinear ordinary differential equation. In addition to describing many essential features of isotropic-nematic phase transformations, this equation yields insight concerning the occurrence and stability of isotropic cores for hedgehog defects in nematic liquid crystals.

Speaker Bio: Eliot Fried is a Professor in the Department of Mechanical and Aerospace Engineering at Washington University in St. Louis. He received his PhD in Applied Mechanics from California Institute of Technology in 1991. His research interests include the mechanics of novel polymeric materials, molecular dynamics simulations of granular materials, and epitaxial growth in phase transitions. Professor Fried's publications have appeared in the Journal of Fluid Mechanics, Physical Review E, and the SIAM Journal on Applied Mathematics.

Presentation Slides: PDF

Contact: G. B. McFadden

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.

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