The viscosity tensor of a ferrofluid under flow

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Abstract
We obtain the expression for the viscosity tensor of a ferrofluid under external flow. The system is modeled as a suspension of rigid dumbbells with a dipole moment in the direction of their bond vector. Our starting point is the Kramers–Kirkwood expression for the stationary viscous pressure tensor whose average is computed with the stationary solution of the corresponding diffusion equation. We obtain the pressure tensor up to second order in the velocity gradient and for any value of the magnetic field. From the pressure tensor, we derive the viscosity tensor including non-Newtonian effects. The components of the pressure tensor are related to different viscosity coefficients which are analyzed for flow through a pore and for planar elongational flow.

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