Pattern Formation in Liquid Crystals

What does viscous fingering have in common with crystal growth? It is not only the visual similarity of the patterns the two seemingly unrelated phenomena can generate under certain circumstances, but also the same underlying physics which controls both growth processes. The common behaviour - diffusion limited growth - leads to morphological instability in which a growing surface is unstable with respect to spacially periodic perturbations. Several theoretical and simulation studies have shown that the simple model is biased in its large scale morphology by the local anisotropy of the growth rules. Liquid crystals exhibit inherent anisotropies tunable with temperature in their bulk properties, which makes them extremely attractive for experimental studies of pattern forming processes. Electrohydrodynamic instabilities, transient patterns at the Frederiksz transition, directional solidification at an isotropic-nematic and cholesteric-smectic A phase transition, viscous fingering and dendritic "smectification" are discussed.