  We use a variational principle to derive a mathematical model for a nematic
electrolyte in which the liquid crystalline component is described in terms of
a second-rank order tensor. The model extends the previously developed
director-based theory and accounts for presence of disclinations and possible
biaxiality. We verify the model by considering a simple but illustrative
example of liquid crystal-enabled electro-osmotic flow (LCEO) around a
stationary dielectric spherical particle placed at the center of a large
cylindrical container filled with a nematic electrolyte. Assuming homeotropic
anchoring of the nematic on the surface of the particle and uniform
distribution of the director on the surface of the container, we consider two
configurations with a disclination equatorial ring and with a hyperbolic
hedgehog, respectively. The computed electro-osmotic flows show a strong
dependence on the director configurations and on the anisotropies of dielectric
permittivity and electric conductivity of the nematic characteristic of liquid
crystal-enabled electrokinetics. Further, the simulations demonstrate space
charge separation around the dielectric sphere, even in the case of isotropic
permittivity and conductivity. This is in agreement with the induced-charge
electro-osmotic effect described for isotropic electrolytes surrounding
dielectric spheres.
