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Length and speed selection in dendritic growth of electrohydrodynamic convection in a nematic liquid crystal.

We present results on dendritic growth of electrohydrodynamic convection in a nematic liquid crystal subject to parallel magnetic and electric fields. Previous work found that these dendrites have many properties in common with crystalline dendrites. Nevertheless, crystalline dendrites are significantly different from the system studied here. Specifically, the length selection mechanism for these dendrites is substantially richer than that which controls crystalline dendritic growth. In contrast with the sharp selection mechanism operating in the case of crystalline dendrites, these dendrites show only partial selection. As the separation between electrodes and the magnetic field becomes larger, the selection becomes even less sharp. We quantify the selection by measuring two important characteristics of these dendrites, their length scale, as reflected by the tip radius of curvature, and their growth speed. We measure these quantities as functions of the most important control parameters: the spacing of the liquid crystal cell, the magnetic field, and the applied voltage. A nontrivial scaling relationship is found for the tip radius of curvature. These dendrites occur in a system containing only one state of matter, and they are defined not by an abrupt boundary but by a diffuse interface. We find that the width of that interface is determined solely by the applied magnetic field.