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Quasi two-dimensional random site percolation model objects were fabricatebased on computer generated templates. Samples consisting of two compartments,a reservoir of H$_2$O gel attached to a percolation model object which wasinitially filled with D$_2$O, were examined with NMR (nuclear magneticresonance) microscopy for rendering proton spin density maps. The propagatingproton/deuteron inter-diffusion profiles were recorded and evaluated withrespect to anomalous diffusion parameters. The deviation of the concentrationprofiles from those expected for unobstructed diffusion directly reflects theanomaly of the propagator for diffusion on a percolation cluster. The fractaldimension of the random walk, $d_w$, evaluated from the diffusion measurementson the one hand and the fractal dimension, $d_f$, deduced from the spin densitymap of the percolation object on the other permits one to experimentallycompare dynamical and static exponents. Approximate calculations of thepropagator are given on the basis of the fractional diffusion equation.Furthermore, the ordinary diffusion equation was solved numerically for thecorresponding initial and boundary conditions for comparison. The anomalousdiffusion constant was evaluated and is compared to the Brownian case. Some adhoc correction of the propagator is shown to pay tribute to the finiteness ofthe system. In this way, anomalous solutions of the fractional diffusionequation could experimentally be verified for the first time.Comment: REVTeX, 12 figures in GIF forma

Diffusion on random-site percolation clusters: Theory and NMR microscopy experiments with model objects