  We discuss general 2-fluid hydrodynamic equations for complex fluids, where
one kind is a simple Newtonian fluid, while the other is either
liquid-crystalline or polymeric/elastomeric, thus being applicable to lyotropic
liquid crystals, polymer solutions, and swollen elastomers. The procedure can
easily be generalized to other complex fluid solutions. Special emphasis is
laid on such nonlinearities that originate from the 2-fluid description, like
the transport part of the total time derivatives. It is shown that the proper
velocities, with which the hydrodynamic quantities are convected, cannot be
chosen at will, since there are subtle relations among them. Within allowed
combinations the convective velocities are generally material dependent. The
so-called stress division problem, i.e. how the nematic or elastic stresses are
distributed between the two fluids, is shown to depend partially on the choice
of the convected velocities, but is otherwise also material dependent. A set of
reasonably simplified equations is given as well as a linearized version of an
effective concentration dynamics that may be used for comparison with
experiments.
