Parity Odd Viscosity in Ferrofluids*

Ferrofluids are a synthetic magnetic colloid consisting of magnetized nanoparticles surrounded by a repulsive surfactant layer which prevents clumping. When subjected to an external magnetic field the ferrofluid acquires a macroscopic magnetization density which leads to novel magnetic behavior. In this work, within a Hamiltonian framework, we introduce a new coupling between the fluid vorticity $vec{omega}$ and the magnetization $vec{M}$, proportional to $vec{omega}cdotvec{M}$. This coupling gives rise to an additional anti-symmetric stress tensor, and if the magnetization is relaxed to the direction of a uniform and static applied field, gives rise to a parity odd transport coefficient. We show that when confined to a Hele-Shaw cell this coupling reproduces the parity odd generalization of Darcy's Law, seen in [1]. We discuss possible origins of this new coupling, and a series of experiments are proposed that may extract the strength of this coupling in a ferrofluid confined to a Hele-Shaw cell.

[1] D. Reynolds, G. M. Monteiro, and S. Ganeshan. Generalized Darcy’s law for parity odd three-dimensional fluids (2021).