A calculation of shear rate thresholds for homogeneous and roll type instabilities in nematics subjected to simple shear flow

Abstract

Describes a new method for obtaining accurate critical shear rates at which homogeneous and roll instabilities may occur in thin samples of nematic liquid crystal subjected to simple shear flow. The particular arrangement considered is that in which the anisotropic axis of the liquid crystal is initially uniformly aligned parallel to the bounding plates and perpendicular to the direction of the flow. Exact expressions for determining the threshold values for all nematic materials are first obtained. The authors illustrate how one employs the technique developed by obtaining accurate values for the material MBBA.

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

“…From a mathematical viewpoint the problem is now formally the same as that considered by Barratt and Manley [5]. Hence assuming that Dl°vl = ~ Epsinpx, where…”

“…One is a homogeneous instability, the Pieranski-Guyon instability, while the other is a rolltype instability. Pieranski and Guyon [1,2] and Leslie [3] investigate the former instability while Manneville and Dubois-Violette [4] and Barratt and Manley [5,6] examine both types of instability. In the absence of any applied magnetic field they predict the onset of a homogeneous instability.…”

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

“…Koch and co-workers predicted from symmetry considerations the shape of the threshold curves, fixing the boundaries between different flow regimes occurring in a homeotropic nematic submitted to a periodical shear [7]. 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].…”

A theoretical investigation of Benard-Couette instabilities in nematic liquid crystals

“…The occurrence of flow instabilities in thin layers of nematic liquid crystal, when subjected to a simple shear flow between a pair of horizontal flat plates, has been the subject of several experimental and theoretical investigations (see Pieranski and Guyon 1973, Manneville and Dubois-Violette 1976, Leslie 1976, Barratt and Manley 1981. More recently Dubois-Violette and Manneville (1978) and Barratt and Zuriiga (1982) examined the stability of Couette flow in a cylindrical geometry when the anisotropic axis of the liquid crystal is initially uniformly aligned parallel to the axis of rotation.…”