Cusp shaped hydrodynamic instability in a nematic

Abstract

2014 Nous étudions les seuils de l'instabilité hydrodynamique d'un nématique homéotrope soumis à un cisaillement elliptique. Nous analysons le rôle du changement de symétrie causé par la variation de l'ellipticité du cisaillement au voisinage du cas dégénéré de la polarisation circulaire. Abstract. 2014 We study the hydrodynamic instability thresholds of a homeotropic nematic subjected to an elliptical shear. We analyse the role of the changes in the symmetry caused by the variation of the ellipticity of the shear around the degenerate circular polarization.

Hydrodynamic instabilities in a periodically sheared nematic liquid crystal

“…The validity of equation 4has already been tested with elliptical shear experiments (i.e. with xn = yn = 0 in (1)); it reproduces the shape of the threshold with a very good accuracy [4,6]. In this paper, we present measurements for various shears which agree with formulae (4) or (5).…”

“…Curve A (8) : boundary between uniform and roll regimes; (J) = 2 n 150 Hz; B (m) : boundary between roll and square regimes; co = 2 7r 150 Hz; C ( 0) : boundary between uniform and roll regimes; co = 2 1t 75 Hz; D (EI) : boundary between roll and square regimes; w = 2 7r 75 Hz. The full curves correspond to the values C, and C21 given in (6). Fig.…”

“…1) In eight-shaped shears, the instability thresholds are reached for lower amplitudes than in elliptical shear, as shown in figure 8. Moreover the directions of the rolls (angle between the rolls and X-axis) is nearly along X and remains constant, in contrast with the elliptical shear where it depends on the ellipticity [2, 3,4,6].…”

“…Let us finally notice that by continuously varying the ratio n between the two applied frequencies m. and n0153 in the case of eight-shaped shear, we only observe roll or square instabilities when n is equal to the ratio of two small integers. 6. Flower-shaped shears.…”

“…Nematic liquids submitted to an elliptical or linear shear present instabilities which have been widely studied [1][2][3][4][5][6]. We have investigated the exact importance of the ellipticity or of the linearity of the shear motion.…”