Viscosities Diverge as1ωin Smectic-ALiquid Crystals

The nonlinear coupling between the velocity field and the layer-displacement field leads to a radical breakdown of the conventional hydrodynamical theory for smectic-$A$ liquid crystals. Three of the five viscosities are found to diverge as $\frac{1}{\omega }$ for small frequencies $\omega$ with the result that the sound attenuation scales as $\omega$ (not ${\omega }^2$ as predicted by conventional hydrodynamics). It is also found that there is a simple relationship between the three diverging viscosities. Reanalysis of existing data appears to confirm the present prediction for the sound attenuation.