Faraday waves in smectic A liquid crystal layers

Abstract

We studied with linear stability analysis the onset of parametric waves on the surface of a smectic A liquid crystal. For thin Sm-A layers under an applied static magnetic field there are subharmonic-harmonic branches of surface waves at low modulating frequency of the driving acceleration and long wavelength. A semi-infinite Sm-A medium poses a dispersion relation with similar trends as for Newtonian liquids. When the external forcing is negligible there are two damped surface waves excited by thermal fluctuation of the interface, whereas in the absence of a magnetic field the dominant modes are of harmonic type for typical material parameters.

Phase Transition effect on the Parametric Instability of Liquid Crystals

“…A comprehensive experimental determination of the bulk Leslie viscosities of the most known liquid crystals in an ample interval of temperatures near their critical phase transition is scarce [53]. Their values can lead to the prediction of enhanced macroscopic hydrodynamic response on the parametric surface dynamics of liquid crystals [39,40], or polymer melts [57]. A similar experimental program may be set up for studying lyotropic liquid crystals to determine the viscosities and elastic parameters as a function of temperature.…”

“…In this section, we discuss the Faraday instability in smectic A liquid crystal layers [40]. We consider a smectic liquid crystal of average thickness L and infinite lateral extension in contact with a vapor.…”

“…The governing hydrodynamic equations of the velocity, viscous stress tensor, and the boundary conditions were reported in Refs. [40,53]. Following their use and with the help of the methods of Section 2, we derived the following recursive equation of the amplitude of deformation ζ n :…”

“…The basic study of this phenomenon poses challenges to hydrodynamic and statistical theories that need to be adapted or developed to explain the onset of the instability. The description of the Faraday instability has recently motivated the advance of new experiments [23][24][25][26] and theoretical approaches for anisotropic fluids such as liquid crystals [27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Also, it seems that its comprehensive experimental and theoretical investigation may have a major impact on the development of sensor technologies based on interfaces with biological or chemical components of practical interest.…”

Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

“…Larger frequencies were found to lead to subsequent peaks of co-existing subharmonic waves. A quantitative theoretical linear analysis of the dependence of the forcing acceleration and wave number on the strength of the external excitation frequency for the Faraday instability in smectic-A (Sm-A) liquid crystals was presented by Hern andez-Contreras [395]. A layer of Sm-A under a constant horizontal magnetic field applied in the direction of the wave-vector that orients the molecules in a stack of lamellar layers perpendicular to the air-liquid interface was considered.…”