Diffusion experiments under stagnant conditions in a constant aperture and a variable aperture slot were made to obtain data for simulation of simultaneous flow and diffusion in fractures. This approach was necessitated by the need to avoid buoyancy-induced flow caused by density differences generated by the presence of a tracer. For this purpose, to avoid flow but negligibly influence diffusion the slots were filled with agar, which generates a 99% porous matrix, which negligibly affects diffusion but essentially stops flow. A simple photographic technique was used to follow diffusion and to determine the aperture distribution on the variable aperture slot. With the obtained data, numerical simulations were performed to illustrate how a solute diffuses from a source into the water seeping past. The results support the simple analytical solution that has been used to determine the escape of radionuclides from a damaged canister containing spent nuclear fuel in a geologic repository in fractured rock.