Oberseminar Mathematik in den Naturwissenschaften

On the field-induced transport of magnetic nanoparticles in incompressible fluid flow

Combining Onsager’s variational principle with the equations of magnetostatics, we propose a thermodynamically consistent model for the motion of magnetized nanoparticles – suspended in an incompressible liquid and under the influence of magnetic fields. It couples evolution equations for magnetization, magnetic field, and particle density to Navier-Stokes-type momentum equations. We show the existence of weak solutions using a Galerkin approximation based on eigenfunction expansions of the associated Stokes, Maxwell, and Laplace operators. In the last part, numerical simulations in 2D are presented which are based on stable finite-element discretizations. They illustrate how magnetic nanoparticles are attracted by magnetic fields and how their magnetization interacts with the applied external field. This is joint work with P. Weiß (Erlangen).

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