UNDULATION INSTABILITY UNDER SHEAR IN SMECTIC A LIQUID CRYSTALS.

The undulation instability in a smectic A in the presence of shear flow parallel to the layers is studied evoking the dilation at the threshold where an undulation appears with a wave vector inclined at an angle theta to the direction of flow. An integral relation is found showing that the dilation is necessarily positive. A perturbation method is developed to calculate the dilation explicitly as a function of the angle theta and the shear rate. It is shown that an undulation with wave vector perpendicular to shear direction is not affected by the flow and has a minimum threshold dilation equal to the static value. It is concluded that a rectangular texture develops at higher dilations in agreement with the rectangular focal domain pattern observed experimentally.