Current distribution in random resistor networks

Maps of electric current density and hydrodynamic flow in porous media: NMR experiments and numerical simulations

The electric current density in percolation clusters was mapped with the aid of a NMR microscopy technique monitoring the spatial distribution of spin precession phase shifts caused by the currents. A test structure and a quasi-two-dimensional random-site percolation model object filled with an electrolyte solution were examined and compared with numerical simulations based on potential theory. The current density maps permit the evaluation of histograms and of volume-averaged current densities as a function of the probe volume radius as relationships characterizing transport in the clusters. The current density maps are juxtaposed to velocity maps acquired in flow NMR experiments in the same objects. It is demonstrated that electric current and hydrodynamic flow lead to transport patterns deviating in a characteristic way due to the different dependencies of the transport resistances on the pore channel width.