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

Abstract. The e®ect of an applied magnetic ¯eld and of the boundaries on the stability of the shear °ow 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 ¯eld is applied orthogonally to the sample plane or in the same direction of the °ow. For a given value of the Ericksen number of the °ow a critical value of the magnetic-to-viscous energy ratio shows up above which the uniform °ow is stable. When the in°uence 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 de¯ned such that it is a universal function of the magnetic-to-viscous energy ratio.