Instabilities in smectics A submitted to an alternative shear flow - I.— Theory

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Abstract
We give a theoretical analysis of the instabilities which occur in a smectic A sample, when submitted to an a.c. shear flow with velocity normal to the layers. This shear flow induces an a.c. tilt of the layers and, above a critical amplitude θ0c, an instability arises and results in the formation of a quasi-periodic network of focal conics. A result of this analysis is that one can find two different regimes, for lower and higher frequencies. In the low-frequency regime the threshold tilt angle θ0c depends on frequency as ω 1/2. At higher frequencies, one gets a ω-3/2 dependence. It is also shown that this instability arises in the bulk of the sample, and not near the upper and lower plates as in the static case