Diffusion then causes this initially sharp interface to broaden over time, either more or less rapidly according to the magnitude of the diffusion constant. Here, a tube (glass, with 12 mm diameter) was filled to a depth of 200 mm with soil that had been rehydrated with an aqueous solution of the micelle-templated gold nanoparticles (54 mg(Au)/ml), followed by a second layer of equal thickness consisting of soil that had been rehydrated with water (UHQ 18. Mathematically, this experiment is modelled by considering diffusion in two semi-infinite halfspaces, for an initial condition of a step-function concentration profile, with the step at d = d0 where d is the spatial direction perpendicular to the interface, in our case the vertical position along the tube. This has previously been solved analytically , giving a solution ,