The intraparticle diffusion model, introduced by Weber and Morris, is one of the most commonly used techniques to identify the diffusion mechanism. Where kint is the intraparticle diffusion rate constant and C is a constant, related to the thickness of the boundary layer. In the phenomenon of adsorption, a multilinearity expressing the existence of multiple sequential steps is given in several works.
The Weber-Morris equation is actually a power function with no magical properties. This function makes it possible to approximate a single kinetic curve only for the initial stage of the adsorption process, which results both from the analysis of the solution of Fick's 2nd law and from the analysis of the equation based on SRT. The problem, however, is that such data is difficult to obtain, especially for fast processes, and is unreliable. I would like to add that at rpm of the stirrer / shaker used in kinetic tests, the influence of external diffusion can be neglected.
An answer for you question can be found in the original paper of weber and morrions. The just did a graphic analysis.
For a better understanding of intraparticle diffuision i would recomment the paper of Boyd:
BOYD, G. E., ADAMSON, A. W., & MYERS, L. S. (1947). The exchange adsorption of ions from aqueous solutions by organic zeolites. II Kinetics. Journal of the American Chemical Society, 69(11), 2836–2848.
Edeskuty, F. J., & Amundson, N. R. (1952). Effect of Intraparticle Diffusion: Agitated Nonflow Adsorption Systems. Industrial & Engineering Chemistry, 44(7), 1698–1703. http://doi.org/10.1021/ie50511a058
Crank, J. (1975). The mathematics of diffusion (2nd ed.). Oxford: Clarendon Press.
In short, only the 1st part of the diffuisions follows the squar root of time. Due to pore filling the speed decrease. And after the initial linear part, normally a more complex equation for the analysis has to be used.
One can also use the description based on the analogy to catalytic non-stationary processes. However, solving the inverse problem for partial differential equation/s is difficult.