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.
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