Numerous previous studies have shown that the absorption rate $\beta$ is of first-order, but what is the reason?
Smith, R., 1983, Effect of boundary absorption upon longitudinal dispersion in shear flows, Journal of Fluid Mechanics. 134(-1), 161-177.
https://doi.org/10.1017/s0022112083003286
Mazumder, B. S., S. K. Das, 1992, Effect of boundary absorption on solute dispersion in pulsatile flow through a tube, Journal of Fluid Mechanics. 239(-1), 523-549. https://doi.org/10.1017/s002211209200452x
Mondal, K. K., B. S. Mazumder, 2005, On the solute dispersion in a pipe of annular cross-section with absorption boundary, ZAMM. 85(6), 422-430.
https://doi.org/10.1002/zamm.200210180
Rana, J., P. V. S. N. Murthy, 2016, Solute dispersion in pulsatile Casson fluid flow in a tube with wall absorption, Journal of Fluid Mechanics. 793, 877-914. https://doi.org/10.1017/jfm.2016.155
Sebastian, B. T., P. Nagarani, 2018, Convection-diffusion in unsteady non-Newtonian fluid flow in an annulus with wall absorption, Korea-Australia Rheology Journal. 30(4), 261-271. https://doi.org/10.1007/s13367-018-0025-7