Boundary conditions for fluids with internal orientational degrees of freedom: Apparent velocity slip associated with the molecular alignment

Boundary effects are investigated for fluids with internal orientational degrees of freedom such as molecular liquids, thermotropic and lyotropic liquid crystals, and polymeric fluids. The orientational degrees of freedom are described by the second rank alignment tensor which is related to the birefringence. We use a standard model to describe the orientational dynamics in the presence of flow, the momentum balance equations, and a constitutive law for the pressure tensor to describe our system. In the spirit of irreversible thermodynamics, boundary conditions are formulated for the mechanical slip velocity and the flux of the alignment. They are set up such that the entropy production at the wall inferred from the entropy flux is positive definite. Even in the absence of a true mechanical slip, the coupling between orientation and flow leads to flow profiles with an apparent slip. This has consequences for the macroscopically measurable effective velocity. In analytical investigations, we consider the simplified case of an isotropic fluid in the Newtonian and stationary flow regime. For special geometries such as plane and cylindrical Couette flow, plane Poiseuille flow, and a flow down an inclined plane, we demonstrate explicitly how the boundary conditions lead to an apparent slip. Furthermore, we discuss the dependence of the effective viscosity and of the effective slip length on the model parameters