Interfacial stress balances in structured continua and free surface flows in ferrofluids

Interfacial linear and internal angular momentum balances are obtained for a structured continuum and for the special case of a ferrofluid, a suspension of magnetic nanoparticles in a Newtonian fluid. The interfacial balance equations account for the effects of surface tension and surface tension gradient, magnetic surface excess forces, antisymmetric stresses, and couple stresses in driving interfacial flows in ferrofluids. Application of the interfacial balance equations is illustrated by obtaining analytical expressions for the translational and spin velocity profiles in a thin film of ferrofluid on an infinite flat plate when a rotating magnetic field is applied with axis of rotation parallel to the ferrofluid/air interface. The cases of zero and non-zero spin viscosity are considered for small applied magnetic field amplitude. Expressions for the maximum translational velocity, slope of the translational velocity profile at the ferrofluid/air interface, and volumetric flow rate are obtained and their use to test the relevance of spin viscosity and couple stresses in the flow situation under consideration is discussed