Dissipative soft modes in viscous nematodynamics

The paper analyses a possible occurrence of soft and semi-soft viscous modes in slow (low Reynolds number) flows of uniaxially anisotropic nematic liquids as described by the five parametric Leslie-Ericksen-Parodi (LEP) constitutive equations (CEs). As in the similar elastic case, the soft viscous modes theoretically cause no resistance to flow, nullifying the corresponding components of the viscous part of the total stress tensor, and do not contribute to the dissipation. That is why these modes can also be called dissipative soft modes. In some flows, these dissipative soft modes may cause the effect of “nematic superfluidity”. As in the theories of nematic elastic solids, this effect is caused by a marginal thermodynamic stability. The analysis is simplified in a specific local, rotating orthogonal coordinate system whose one axis is directed along the director. We demonstrate that depending on closeness of material parameters to the marginal stability conditions, LEP CEs describe the entire variety of soft, semi-soft and harder behaviors of nematic viscous liquids. When the only shearing dissipative modes are soft, the viscous part of stress tensor is symmetric, and LEP CE for stress, scaled with isotropic viscosity is reduced to a one-parametric, stress-strain rate anisotropic relation. When additionally the elongation dissipative mode is also soft, this scaled relation has no additional parameters and shows that the dissipation is always less than that in isotropic phase. Simple shearing and simple elongation flows illustrate these possible effects.