Influence of weak anchoring on flow instabilities in nematic liquid crystals

We analyse the homogeneous instabilities in a nematic liquid crystal subjected to plane steady Couette or Poiseuille flow in the case when the director is pre-aligned perpendicular to the flow plane taking into account weak anchoring at the confining surfaces. The critical shear rate decreases for decreasing anchoring strength and goes to zero in the limit of torque-free boundary conditions. For Poiseuille flow one has two types of instability depending on the values of the azimuthal ($W_a$) and polar ($W_p$) surface anchoring strengths. The critical line in $(W_a,W_p)$ space which separates the two instabilities regimes is obtained.