Hydrodynamic instabilities in a periodically sheared nematic liquid crystal

Abstract

2014 Dans un liquide nématique soumis à divers types de cisaillements périodiques, nous observons des instabilités en rouleaux et en carrés. Nous comparons nos résultats expérimentaux aux courbes de seuil du modèle théorique de Koch, Rothen, Sadik et Schöri.

Pattern selection in nematics subjected to an elliptical shear

“…In the first one (cell I), the nematic layer is subjected to an elhptical shear by imposing displacements of the form X= XQCOSUI, Y= Yf^sinut respectively to the lower and upper plate [3][4][5]. In the second one (cell II) whole shear is appUed to the upper plate and the lower plate remains steady [6]. The différence be thèse two geometries is characterized by the présence of différent convective terms for the orientation induced by the velocity profile.…”

“…Above a larger réversible threshold, > NJ^, a two-dimensional pattern develops. It is formed by another set of rolls making an angle of about 90° with the initial ones ("bimodal patterns" which are usually called " square patterns" in [4][5][6]). Domains of hexagons sometimes appear near £ = 1 in the 2D structure not so far above N^.…”

“…The threshold condition derived in réf. [8] for a system of rolls characterized by a wavenumber q (\q\ = q^) making an angle with the Ox axis of the shear elhpse is o^'XiY,^ -Ac^^X^Yii X^ + Yi)/d^ If one now takes into account the dependence of the coefficients on the wavelength, the growth rate of a perturbation of wavenumber near q^, the critical wavenumber for the thin cells considered here, and making an angle ç with the easy axis can be written at the lowest order as i^{q,q>)=Xe-Ksm'<p-eoQ\ (3)(4)(5)(6)(7)(8)(9)(10) where e = (A^^ -Nl)/N^, Q = q-and we have chosen the easy axis (ipo) as référence for measuring The linear theory illustrâtes the raising of the orientational degeneracy by the anisotropy of the shear when £ # 1 in complète agreement with the expérimental results which show that the angle t/zg undergoes a jump of ir/2 when one crosses the £ = 1 condition [4,5].…”

“…We now wish to discuss the stability of thèse rolls with respect to the formation of oblique rolls [16]. For q = q^,& new set of rolls making an angle (p with the normal rolls obeys the foUowing amplitude équation: 3^,/9/ ={\E-K sin\)A^ -g^Mj'^^ -^NDI^OI'^^- (4)(5)(6)(7)(8)(9) Linearizing around A^^ = AQ^^ + hA^, A^ = ô^^ one gets the growth rate of the obUque rolls:…”

“…The case of a homeotropic nematic subjected to an elliptical shear has been the subject of a large number of expérimental [3][4][5][6] and theoretical [7][8][9] studies. Careful analysis of the thresholds associated to the différent planforms have been performed [4,5].…”