Dynamics of Filaments during the Isotropic – Smectic A Phase Transition

We study the dynamics of filaments formed when certain materials undergo the isotropic-smectic A phase transition. The basis of this work is a solidification model derived from first principles, taking into account elastic, hydrodynamic and thermodynamic effects. The permeation process, which is solely responsible for the growth of the filament, is analyzed in detail. Various characteristics of the filament, such as growth rates, velocity profile inside the filament and transport along the filament, are calculated by studying the asymptotic limit of a slender body problem. We also derive, in this limit, the equation governing the dynamics of the centerline of the filament. Courant Institute of Mathematical Sciences, New York University, New York, NY 10012. Research supported by Air Force grant F49620-95-1-0065 and NSF grant DMS-9623137 Liquid Crystal Institute, Kent State University, OH 44242. Research supported by NSF under ALCOM grant 89-DMR20147