Spiral waves in nematic liquid crystals:mExperimental analysis of selection rules

Abstract

Archimedian spiral waves develop around umbilics, in an homeotropically anchored nematic sample. They are observed under the influence of a rotating magnetic field in the plane of the glass plates, and in presence of a destabilizing electric field. The geometrical characteristics of these experimental spirals (pitch, rotation frequency, etc.) are analyzed in parameter space. These spiral waves are numerically fitted with Archimedian spirals to good degree of accuracy. The transverse speed of zero curvature Bloch walls are deduced from these measurements. The existing domain of these spiral waves is limited, respectively, toward large (low) magnetic-field rotation speed, or low (large) magnetic-field intensities, by the asynchronous regime (by a Bloch-Ising transition of the walls). These experimental results are compared to two-dimensional interactive simulations of a Ginzburg-Landau equation. The measurements made in the low-field domain (which is a validity condition for the model derivation) confirm the applicability of the same selection criterion deduced by Burton, Cabrera, and Frank [Philos. Trans. R. Soc. London Ser. A 243, 299 (1951)] for the description of spiral shaped steps in cristalline growth, and more recently for the fronts of excitable media.