Viscous fingering in liquid crystals

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Abstract
We have studied the Saffman-Taylor instability in a Hele-Shaw cell containing the nematic liquid crystal 4,4’-n-octylcyanobiphenyl (8CB). Air injected into the center of the cell gives rise to viscous fingering patterns, which show a sequence of dense-branching, dendritic, dense-branching morphologies as a function of temperature. A qualitative explanation of these morphological transitions is given in terms of the flow alignment of the director field and the resulting anisotropic viscosity in the nematic phase of the liquid crystal. The fingering patterns were digitized; analysis of the resulting data shows that while the perimeter of the pattern is fractal, the pattern itself is not. The extent to which the pattern is space filling depends on the morphology and this quantity may serve to indicate the morphological transitions.