The ability of pulsatile fluid flow to enhance solute mass transfer and to separate different species has been demonstrated in the past for both open and annular pipe geometries. In the case of the open pipe, the reason for this phenomenon is the entrainment of fast-diffusing species in the region near the pipe wall while slower diffusers remain in the bulk of the fluid. Since the species tend towards different regions of the oscillatory flow, they will separate to an extent that depends on the frequency of the oscillation. Given this explanation, it is expected that the addition of another boundary would increase the entrainment of the fast diffuser and consequently enhance separation, and to this end a rod can be placed inside the pipe to form an annular fluid chamber. The inclusion of another boundary adds the possibility of including another frequency of oscillation. We intend to show that the best separation occurs when the inner and outer boundaries are moved at the same frequency, and explanations will be given based on the effect of the frequencies on the shapes of the velocity profiles.