Abstract
In this article, we report 3D numerical simulations of highly conductive non-magnetic particles dispersed in a moderately conductive matrix, subject to an AC magnetic field in a range of several hundred kHz. We address the issue of the scaling of current loops and heating power with respect to the volume fraction of the dispersed phase. Simulations are performed in two steps. First, a static electric potential gradient is imposed between two opposite faces of the simulation domain and an effective conductivity is computed in good agreement with percolation models. Second, the particles are constrained in a spherical sub-region and an AC magnetic field is imposed at the boundary of the domain. For small volume fractions, the induced Joule power is in good agreement with an analytical model of dilute dispersions. As the volume fraction increases, wider current loops form, until the percolation threshold is reached. Then the induced power in the spherical aggregate is well described by the power induced in an equivalent sphere with a volume-fraction-dependent conductivity.