A linear analysis of instabilities in Couette flow of nematic liquid crystals

Abstract

This paper presents a new method for determining the critical threshold values at which both homogeneous and roll-type instabilities may appear when thin layers of nematic liquid crystal are subjected to Couette flow. The anisotropic axis of the material is initially uniformly aligned parallel to the axial direction and the effect of a stabilising, axially oriented, uniform magnetic field is allowed for in calculations. Carrying out a linear stability analysis of the continuum equations, we employ a Fourier series method to derive an expression for determining the critical shear rate at which instability occurs. Thresholds for both homogeneous and roll instabilities are obtained and their variation with rotation rate and applied magnetic field strength is examined for the material MBBA.

Rheo-Nmr and Numerical Study of the Nematodynamics in Cylindrical Couette Geometry

“…The velocity field for a Newtonian cylindrical Couette flow has a single non-null component n W that, when only the inner cylinder rotates with the angular velocity o i , can be written as: 24]. It should be noted that the velocity profile (10) associated with a director uniformly aligned parallel to the vorticity axis is actually an exact solution of the Leslie-Ericksen equations [10]. Accordingly it may be seen as a good first approximation.…”

“…The assumption of a secondary cellular flow may be justified by experimental evidences and stability analysis presented in literature for analogous 64 L. Orian et al systems [10,17]. The numerical results are used to interpret the main features of a set of Rheo-NMR spectra obtained with PBLG (poly-L-benzylglutamate)/m-cresol 14%.…”

“…Barratt and Manley developed an accurate method to calculate the shear rate thresholds for homogeneous and roll type instabilities in nematics subjected to simple shear flow [8]. The response to Couette flow has also been investigated: Cladis and Torza focused their attention in Taylor-Couette instabilities in nematic liquid crystals [3,9]; Barratt and co-workers proposed a linear instability analysis for thin nematic layers subjected to Couette flow [10].…”