Flow near a sharp corner in a nematic liquid crystal

Solutions are presented for the orientation and flow of a positive nematic liquid crystal near a corner between two planes on which a variety of bound ary conditions may be imposed. The flow near the corner is induced by a general motion at a large distance from the corner, which can make the flow symmetric or antisymmetric with r espect to the bisector of the angle. The real situation may be a combinatio n of both. The viscosity, usually a damping mechanism, may be responsible for the gene ration of a geometrical progression of eddies. The smaller the angle betwee n plates, the more probable the existence of eddies. The critical wedge ang le for the appearance of eddies is also investigated. The conditions considered are rigid walls and no-slip conditions at the bou ndaries, which have been treated in order to get a perfect alignment of the directors. For the two specific examples analysed, PAA near 125 degrees C and MBBA near 25 degrees C, eddies only appear in MBBA for an angle between plates smaller than 60 degrees, when the flow induced near the corner is a ntisymmetric with respect to the bisector of the plates. In this case, the flow near the corner consists of a sequence of eddies whose size and intens ity fall off in geometric progression with a ratio depending only on the an gle between plates. PAA and MBBA present this qualitative change in behaviour because the visco sity coefficients are much smaller in magnitude in PAA than in MBBA. We con struct a nematic liquid crystal with Leslie coefficients, which vary monoto nically between the two sets of coefficients for PAA and MBBA. Writing the six viscosity coefficients as mu(i) = x mu(i)(P) + (1 - x)mu(i)(M), with i = 1, 6, where the superscript 'M' is for MBBA and 'P' is for PAA, we find t hat the critical wedge angle at which eddies would appear (in antisymmetric flow) decreases as x increases from zero to one. The critical wedge angle is zero for x > 0.974 approximately, so no eddies exist in these cases.