Anomalous anisotropic transport of scalars in dilute ferrofluids under uniform rotating magnetic fields - Mixing time measurements and ferrohydrodynamic simulations

This study reports experimental observations and numerical simulations on the transport of scalars in ferrofluids under rotating magnetic fields (RMF). Mass transport experiments were conducted in a T-mixer capillary with RMF rotational axis parallel to capillary central axis. Significant mass transport enhancement was measured in the transverse direction as RMF frequency and/or magnetic nanoparticles concentration increased. RMF directional control of mass flux enhancement was anisotropic as molecular diffusion was the only transport mechanism parallel to the capillary axis. The significance of ferrofluid advection (spin-up flow) as mass transport enhancement was examined in light of the advection-diffusion transport and experimental results. Hence, the ferrohydrodynamic equations (FHD) of motion were solved for the lower spin viscosity limit [based on Rosensweig's interpretation of micro-eddies diffusion length scale], and upper limit as reported from earlier spin-up flow studies. FHD simulations predicted lower magnitudes of the linear azimuthal velocities with decreasingly trends as spin viscosity increased. These findings were in disagreement with previously reported ferrofluid flows calculated on the basis of spin diffusion theory. To clarify the inconsistency's origin and confirm reliability of numerical simulations, the spin field and asymmetric stresses were analyzed to conclude that the small length scale of the capillary could not accredit the role of spin-up flow effects via azimuthal velocities for the improved mixing observations. Mixing time measurements and analysis of the advection-diffusion equation pointed toward lack of current FHD theory to resolve scalar transport due to the nanoparticle-scale secondary circumferential micro-convective flows. A pragmatic approach was therefore proposed to estimate from mixing time measurements the anomalous anisotropic effective diffusion coefficients induced by rotating nanoparticles, and to correlate them to RMF frequency and/or nanoparticles concentration.