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.