On the problem of transient hydrodynamic instability of nematics in magnetic field: I. Instability at splay deformation
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ID CRYSTALS
On the Problem of Transient Hydrodynamic Instability of Nematics in Magnetic Field: I. Instability at Splay Deformation A. V. Golovanova and E. N. Ryzhovb a
Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, ul. Vavilova 28, Moscow, 119991 Russia email: [email protected] b Volgograd State Technical University, pr. Lenina 28, Volgograd, 400005 Russia Received April 3, 2013
Abstract—A dependence of the square of dimensionless magneticfield (MF) strength on the square of dimensionless wave vector of the domain structure, h 2(q 2 ) , is analytically derived for the transient hydrody namic instability arising at splay deformation under a MF. The domain formation is related to the fold catas trophe; the square of the critical field of domain formation, hD2 , is determined from the condition 2 2 2 2 2 ∂[h ( q )]/ ∂( q ) = 0. In the general case, the function h (q ) is a ratio of two polynomials whose coefficients for calamitics are determined by combinations of four dimensionless viscosities η2 η1 , η6 η1 , η7 η1 , and 2 η8 η1 . Under some assumptions, the quotient of the polynomials at large q is a quadratic function which allows one to experimentally determine the dimensionless viscosities η2 η1 , η6 η1 , η7 η1 , and α 2 η1 . DOI: 10.1134/S1063774514010052
INTRODUCTION The effect of the transient hydrodynamic instability of nematics in a magnetic field (MF) has been known for long [1–3]. This phenomenon is characterized by the appearance of a system of dark and bright stripes in the liquid crystal layer, when the latter is inserted into a MF stronger than the Freedericksz critical field H F for the layer. The system of stripes (which are vortex lines) was referred to as domain structure (DS) or a system of magnetohydrodynamic (MHD) domains. The difference of the MHD instability from the elctro hydrodynamic instability [4] is in the fact that in the former case DS is transient: upon switching the MF, the domains appear, develop, and then disappear. The MHD domains appearing at splay deformation in a typical thermotropic nematic nmethoxyben zylidenenbutylaniline (MBBA) were studied theo retically and experimentally in [1]. The dispersion dependences s(q 2 ) of the inverse domain switchingon time on the square of dimensionless wave vector q 2 were derived for various values of squared dimension 2 less MF strength h . It was shown that function s( q 2, h 2 ) (in the one constant approximation) is determined by combina tions of six Leslie viscosity coefficients αi and rota tional viscosity coefficient γ1. In addition, the depen dence q 2(h 2 ) was experimentally determined. An MBBA liquid crystal was chosen as a model system to analyze the function s( q 2, h 2 ), since all these coeffi
cients were measured for this substance [5]. It should be noted that, although the experimental dependence q 2(h 2 ) was obtained in [1], its shape was not deter mined analytically. This dependence was specified graphically as a curve intersecting function s(q 2) in the maxi
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