Gradient magnetic field-driven ferrofluid pipe flows with pressure regulation, a model for a ferrofluid pump

The idea of ferrofluid pumping in pipes is extended to scenarios where a uniform magnetic field gradient is employed, yet without a pressure difference between the inlet and outlet of the pipe. The governing equations, including the phenomenological magnetization equation for ferrofluid pipe flow, are solved by a custom-developed OpenFOAM solver. After the validation of this solver, ferrofluid pipe flows under the application of a magnetic field gradient are numerically predicted. The findings reveal that both pumping volume and pressure distribution can be adjusted by varying the reference magnetic field intensity and field gradient. A stronger reference magnetic field and a steeper field gradient result in higher flow rates and accelerated pressure increases along the field gradient direction. In a circular tube with a radius of 1 mm, when the dimensionless magnetic field gradient is 0.1 and the magnetic Reynolds number is 1000, the maximum velocity can attain 10.2 μm/s, the flow rate can reach 0.016 μL/s, and the equivalent average pressure gradient achieves 0.15 Pa/s. Notably, in a gradient magnetic field, the effective viscosity of a ferrofluid flowing in a pipe can be significantly reduced, achieving approximately 70% of its intrinsic viscosity in this study. These promising results lay the groundwork for the design of ferrohydrodynamic pumps that harness the potential of constant magnetic fields.