Boundary conditions and extended constitutive relations for spin-flow coupling in dipolar fluids

Abstract

Boundary conditions are formulated, within the framework of irreversible thermodynamics, for the velocity, the angular velocity and the dipole vector parallel to the average electric dipole moment of a streaming dipolar fluid.  The local conservation and balance equations for linear and angular momenta and for the dipole vector  are complemented by extended constitutive relations for the symmetric and antisymmetric parts of the friction pressure tensor as well as for the flux tensors of the spin,  i.e., the internal angular momentum, and of the dipole. Following the original idea of Ludwig Waldmann (Z. Naturforsch, 22a, 1967, p. 1269), the surface entropy production is inferred from the entropy flux. The desired boundary conditions are the linear constitutive relations set up such that the standard requirement of non-negative entropy production holds true, also at the surface. Thus "diagonal" surface phenomenological coefficients, like various slip length coefficients, need not be negative. Furthermore, coupling coefficients obey Onsager-Casimir symmetry relations. Some applications are presented for the plane Couette-flow geometry.