FEM numerical model study of heating in magnetic nanoparticles

Electromagnetic heating of nanoparticles is complicated by the extremely short thermal relaxation time constants and difficulty of coupling sufficient power into the particles to achieve desired temperatures. Magnetic field heating by the hysteresis loop mechanism at frequencies between about 100 and 300 kHz has proven to be an effective mechanism in magnetic nanoparticles. Experiments at 2.45 GHz show that Fe₃O₄ magnetite nanoparticle dispersions in the range of 10¹² to 10¹³ NP/mL also heat substantially at this frequency. An FEM numerical model study was undertaken to estimate the order of magnitude of volume power density, Q_gen (W m^-3) required to achieve significant heating in evenly dispersed and aggregated clusters of nanoparticles. The FEM models were computed using Comsol Multiphysics; consequently the models were confined to continuum formulations and did not include film nano-dimension heat transfer effects at the nanoparticle surface. As an example, the models indicate that for a single 36 nm diameter particle at an equivalent dispersion of 10¹³ NP/mL located within one control volume (1.0 × 10^-19 m³) of a capillary vessel a power density in the neighborhood of 10¹⁷ (W m^-3) is required to achieve a steady state particle temperature of 52 °C - the total power coupled to the particle is 2.44 μW. As a uniformly distributed particle cluster moves farther from the capillary the required power density decreases markedly. Finally, the tendency for particles in vivo to cluster together at separation distances much less than those of the uniform distribution further reduces the required power density.