A solute's diffusivity is a key property in the design and analysis of mass transfer systems. A simple method to determine such coefficients in aqueous media is Armfield's diffusion apparatus, in which reservoir (donor) and bath (receiver) compartments are separated by a honeycomb array of liquid-filled cylindrical pores. The solute of interest, i.e., NaCl, diffuses from the reservoir and pores into the bath. The electrical conductivity of the bath solution, which is proportional to the NaCl molarity, is tracked as a function of time at constant temperature. A comprehensive mathematical model is presented which combines simultaneous solute transport in the three compartments, allowing estimation of the aqueous NaCl diffusivity from experimental data. The model improves existing theoretical analyses of such data and can be adapted to study other challenging systems.