Complex fluid behavior: coupling of the shear stress with order parameter tensors of ranks two and three in nematic liquid crystals and in tetradic fluids

The second rank alignment tensor characterizing the preferential orientation of rod-like or disc-like molecules can easily be detected via the birefringence associated with it. The third rank tensor specifying a local short range order with tetrahedral symmetry, as expected for water, on the other hand, is a practically hidden variable. The flow alignment and the back-flow effect in nematic liquid crystals are consequences of the coupling between the shear stress tensor with the second rank alignment tensor. The basic equations describing, within the framework of a dynamic Ginzburg–Landau theory, the conjectured coupling between the shear stress and a third rank order parameter tensor are presented. Some potentially observable consequences are indicated. In particular, the anomalous broadening of the shock front thickness measured for water at higher driving pressures can be explained by this coupling.