Alignment-dependent growth of unstable patterns in liquid crystals

The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. In isotropic systems, disordered dense-branching morphologies arise from repeated tip-splitting of the evolving finger. In anisotropic systems, by contrast, the growth morphology changes to a highly ordered dendritic growth characterized by stable needle-like protrusions decorated with regular side-branches. 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 depends on three parameters; the interface velocity, the concentration of liquid crystal and the viscosity ratio between the less-viscous inner fluid and the more-viscous outer liquid crystal. Remarkably, we find that different aspects of the patterns are experiencing environments of different viscosities; the characteristics of the locally-determined most unstable wavelength are governed by a viscosity that is 20 times lower than that governing the relative length of the fingers. We discuss how these two different viscosities are related to the local alignment of the liquid crystal.