This paper simulated the advection and diffusion behaviors of the moving magnetic fluid in the vessel in the high-gradient magnetic field using Navier–Stokes equations. The particles accumulation behavior and the streamlines and the contour of concentration are all affected by the susceptibility, intensity of magnetic field and its gradient, and the flow velocity and also by the difference in size of vessels. The typical accumulation behaves as a solid obstacle in the flow as result of the competing between magnetic and fluid drag forces, and gives rise to a rigidly bound core region followed by a wash away region near the vessel boundary under the condition of 10 mm vessel in width. While the vessel is near 1 mm in width, the magnetic force is exerted almost on the whole vessel area, the vortex is not seen, the wash away area disappears and the concentration changes in the whole vessel. The results of the analysis provide meaningful information on ferrofluid transport and stabilization for various magnetic drug targeting and the magnetic fluid sealing, and other use in industrial and medical fields.
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