Theoretical study of the instability of a homeotropic nematic submitted to an elliptical shear

Abstract

2014 Nous étudions l'instabilité qui se produit quand un nématique homéotrope est soumis à un cisaillement elliptique alternatif. A cet effet, nous développons une méthode permettant de tenir compte de la dépendance en temps aussi bien du régime non perturbé que des perturbations apparaissant lors de l'instabilité. D'autre part, nous appliquons la méthode au cas des échantillons minces. Nous obtenons ainsi une description détaillée de la façon dont varie le seuil quand change la forme de l'ellipse de cisaillement.

Hydrodynamic instabilities in a periodically sheared nematic liquid crystal

“…In the case n = 4, the threshold curves seem also to be well described by (5) (see Fig. 7) (we did not perform a systematic study in frequency and thickness).…”

“…The shear motion is applied to the upper plate; if the amplitudes xl, YI' Xn, Yn are « small », the flow in the liquid cell remains uniform (no convection) [3,5]. By progressive increase of xl, YI, Xn, Yn, we observe the following sequence:…”

“…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.…”

Cusp shaped hydrodynamic instability in a nematic

“…It is thus reasonable to relate the cusp in the threshold curve to the effect of the degeneracy around the E = 1 value. J. Sadik and coworkers [10] have recently proposed an analysis of this cusp. We will not reproduce their argument which is based on an extensive development of the above symmetry argument (in particular x --+ y and 0 --+ 7r/2 -4/) applied to the linear solu-tion of the nematodynamic problem.…”

“…For larger shear amplitudes, non linear contributions already appear in the alternating distortion below threshold [2]. In such conditions, the threshold can be written as a symmetric expansion of (2) in powers of X o/d and Yold (formula (55) of [10]) :…”