I show that a dilute, sterically stabilized lyotropic smectic liquid crystal, subjected to a sufficiently large velocity gradient in the plane of the layers, will undergo a phase separation, with regions of reduced layer spacing coexisting with regions devoid of any layer material. The critical shear rate for this transition should go as (layer spacing${)}^{\mathrm{-}3}$.

• Received 21 November 1991

DOI:https://doi.org/10.1103/PhysRevLett.69.112