Modeling and simulation of magneto two-phase flow for magnetic drug targeting
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Motivated by magnetic drug targeting, we develop a magneto two-phase flow model to describe the dynamics of superparamagnetic iron oxide nanoparticles (SPIONs) suspended in a carrier fluid under the influence of an electromagnet. The strongly coupled system consists of a modified Navier-Stokes equation with an additional inertia term for the mass-averaged velocity, a transport equation for the SPION volume fraction density, and a quasi-static nonlinear elliptic equation for the magnetic potential. Using Onsager’s variational principle, we derive the relative velocity of SPIONs, accounting for nonlinear diffusion and transport under gravitational and magnetic fields. Eventually, we present and discuss numerical simulations which form a first step towards the validation of the model using experimental measurements.