On the effect of an applied magnetic field on the shear-induced pattern formation in nematic polymer liquid crystals

Abstract

The effect of an applied magnetic field and of the boundaries on the stability of the shear flow of nematic polymer liquid crystals of the tumbling type with respect to the formation of the transient spatially periodic patterns that appears after the start-up of shearing is studied. The unidirectional shear of a nematic director initially uniformly oriented orthogonally to the sample plane and with strong anchoring is considered. The magnetic field is applied orthogonally to the sample plane or in the same direction of the flow. For a given value of the Ericksen number of the flow a critical value of the magnetic-to-viscous energy ratio shows up above which the uniform flow is stable. When the influence of the boundaries may be neglected, an internal Ericksen number that stays constant in a given material is considered such that the wavelength of the periodic pattern is a self-adjusted length. An internal generalized Ericksen number is defined such that it is a universal function of the magnetic-to-viscous energy ratio.

Perturbative analysis of the magnetic field effect on the stability of the shear flow of a nematic polymer

“…When a magnetic field is applied, the behaviour of the wavevector with Er and c c should reflect a non trivial interplay between these three energies. As found previously (15), the critical wavelength of the transient bands during shear is found to be invariant for constant (Er,h). …”

“…To attain a better description of the basic flow, the ansatze given in Equations (2) and (3) include beyond the lowest order terms giving the z dependence of v 0 z and h 0 compatible with the boundary conditions and considered previously (15), the next higher order terms also compatible with the symmetry of the problem. The ansatze used for the perturbations are:…”

“…In a previous paper (15), a linear stability analysis of the stationary solution of the equations for the shear flow of tumbling nematic polymers in the suppressed tumbling regime, with homeotropic boundary conditions and a magnetic field applied orthogonally to the sample plane, was reported. This analysis allowed a qualitative description to be obtained of the role of the magnetic field and of the boundaries in the stability of the flow with respect to the formation of the transient bands orthogonal to the shearing direction.…”

Rheological characterisation of a liquid-crystalline diol and its dependence with an applied electric field

“…In our experiment, due to the high conductivity of the sample, by increasing the value of the field above a critical value an over current resulted, and so the predicted saturation effect of the viscosity with the field could not be reached. Flow instabilities are not expected to play a role in our results due to the stabilising effect of the applied field [28].…”

Computational rheooptics of liquid crystal polymers

“…This phenomenon reflects the complexity of shearinduced instabilities and has been analyzed using molecular and macroscopic models [3,11,[22][23][24][25][26][27][28][29][30] and given the amount of theoretical and experimental data is a good test problem to validate and refine computational rheooptical models and will be used in this paper.…”