Dispersion of ferrofluid aggregates in steady flows

Using focused shadowgraphs, we investigate steady flows of a magnetically non-susceptible fluid interacting with ferrofluid aggregates comprised of superparamagnetic nanoparticles. The ferrofluid aggregate is retained at a specific site within the flow channel using two different applied magnetic fields. The bulk flow induces shear stresses on the aggregate, which give rise to the development of interfacial disturbances, leading to Kelvin-Helmholtz (K-H) instabilities and shedding of ferrofluid structures. Herein, the effects of bulk Reynolds number, ranging from 100 to 1000, and maximum applied magnetic fields of 1.2 × 105 and 2.4 × 105 A/m are investigated in the context of their impact on dispersion or removal of material from the core aggregate. The aggregate interaction with steady bulk flow reveals three regimes of aggregate dynamics over the span of Reynolds numbers studied: stable, transitional, and shedding. The first regime is characterized by slight aggregate stretching for low Reynolds numbers, with full aggregate retention. As the Reynolds number increases, the aggregate is in-transition between stable and shedding states. This second regime is characterized by significant initial stretching that gives way to small amplitude Kelvin-Helmholtz waves. Higher Reynolds numbers result in ferrofluid shedding, with Strouhal numbers initially between 0.2 and 0.3, wherein large vortical structures are shed from the main aggregate accompanied by precipitous decay of the accumulated ferrofluid aggregate. These behaviors are apparent for both magnetic field strengths, although the transitional Reynolds numbers are different between the cases, as are the characteristic shedding frequencies relative to the same Reynolds number. In the final step of this study, relevant parameters were extracted from the time series dispersion data to comprehensively quantify aggregate mechanics. The aggregate half-life is found to decrease as a function of the Reynolds number following a power law curve and can be scaled for different magnetic fields using the magnetic induction at the inner wall of the vessel. In addition, the decay rate of the ferrofluid is shown to be proportional to the wall shear rate. Finally, a dimensionless parameter, which scales the inertia-driven flow pressures, relative to the applied magnetic pressures, reveals a power law decay relationship with respect to the incident bulk flow.