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Transport of particles by magnetic forces and cellular blood flow in a model microvessel
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The transport of particles (diameter 0.56 μm) by magnetic forces in a small blood vessel (diameter D = 16.9 μm, mean velocity U = 2.89 mm/s, red cell volume fraction H c = 0.22) is studied using a simulation model that explicitly includes hydrodynamic interactions with realistically deformable red blood cells. A biomedical application of such a system is targeted drug or hyperthermia delivery, for which transport to the vessel wall is essential for localizing therapy. In the absence of magnetic forces, it is seen that interactions with the unsteadily flowing red cells cause lateral particle velocity fluctuations with an approximately normal distribution with variance σ = 140 μm/s. The resulting dispersion is over 100 times faster than expected for Brownian diffusion, which we neglect. Magnetic forces relative to the drag force on a hypothetically fixed particle at the vessel center are selected to range from Ψ = 0.006 to 0.204. The stronger forces quickly drive the magnetic particles to the vessel wall, though in this case the red cells impede margination; for weaker forces, many of the particles are marginated more quickly than might be predicted for a homogeneous fluid by the apparently chaotic stirring induced by the motions of the red cells. A corresponding non-dimensional parameter Ψ′, which is based on the characteristic fluctuation velocity σ rather than the centerline velocity, explains the switch-over between these behaviors. Forces that are applied parallel to the vessel are seen to have a surprisingly strong effect due to the streamwise-asymmetric orientation of the flowing blood cells. In essence, the cells act as low-Reynolds number analogs of turning vanes, causing streamwise accelerated particles to be directed toward the vessel center and streamwise decelerated particles to be directed toward the vessel wall.
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