Shear instabilities of freely standing thermotropic smectic-A films

In this Letter we discuss theoretically the instabilities of thermotropic freely standing smectic-A films under shear flow\cite{re:wu}. We show that, in Couette geometry, the centrifugal force pushes the liquid crystal toward the outer boundary and induces smectic layer dilation close to the outer boundary. Under strong shear, this effect induces a layer buckling instability. The critical shear rate is proportional to $1\mathrm{/}\sqrt{d}$, where $d$ is the thickness of the film.