The kinetics of re-equilibration of the anionic surfactant sodium dodecylbenzene sulfonate at the air solution interface have been studied using neutron reflectivity. The experimental arrangement incorporates a novel flow cell in which the subphase can be exchanged (diluted) using a laminar flow while the surface region remains unaltered. The rate of the re-equilibration is relatively slow and occurs over many tens of minutes, which is comparable with the dilution time scale of approximately 10-30 min. A detailed mathematical model, in which the rate of the desorption is determined by transport through a near-surface diffusion layer into a diluted bulk solution below, is developed and provides a good description of the time-dependent adsorption data. A key parameter of the model is the ratio of the depth of the diffusion layer, H-c, to the depth of the fluid, H-theta, and we find that this is related to the reduced Peclet number, Pe*, for the system, via H-c/H-f = C/Pe*(1/2). Although from a highly idealized experimental arrangement, the results provide an important insight into the "rinse mechanism", which is applicable to a wide variety of domestic and industrial circumstances.