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The Quarterly Journal of Mechanics and Applied Mathematics 1985 38(2):297-321; doi:10.1093/qjmam/38.2.297
© 1985 by Oxford University Press
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INFLUENCE OF AN IN-PLANE MAGNETIC FIELD ON THE STABILITY OF SHEAR FLOW OF MEMATIC LIQUID CRYSTALS

G. D. SMITH and P. K. CURRIE {dagger}

( Department of Mathematical Physics, University College Dublin )

It is generally known that in the shear flow of nematic liquid crystals with either {alpha}2<{alpha}3<0 or {alpha}3>{alpha}2> 0, the director adopts the Leslie angle orientation Q0away from the influence of the boundary. However, when a magnetic field is present, this main-stream orientation will be affected, and here we investigate the dependence of the orientation on the direction of the field and the relative strengths of magnetic field and shear flow. It is found that such an orientation angle fails to exist for some directions and strengths of the magnetic field and we show, in these cases, how all the solutions to the steady equations in the plane of shear ultimately become unstable. The asymptotic behaviour of the apparent viscosity and the first and second normal-stress differences as either the shear rate and/or the field strength become very large is also examined.


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