Pattern Formation from Instabilities in Liquid Crystals

The invasion of one fluid into another of higher viscosity is unstable in a quasi-two dimensional geometry. In isotropic systems, this viscous-fingering instability typically produces complex patterns that are characterized by repeated branching of the evolving structure, which leads to the common morphologies of fractal or dense-branching growth. In anisotropic systems, in contrast, the growth morphology changes to a highly ordered dendritic growth characterized by stable needle-like structures. We investigate such morphology transitions between dendritic growth and dense-branching growth in an intrinsically anisotropic liquid; a lyotropic chromonic liquid crystal in the nematic phase. We show that the transition is remarkably sensitive to the interface velocity and the viscosity ratio between the less-viscous inner fluid and the more-viscous outer liquid crystal. We discuss the importance of a stable shear alignment and the emergence of defect structures in the liquid crystal in governing the morphology transition to dendritic growth.