“…The Markle model is superior to the Nakanishi model in that it is capable of describing the change in the Mn 2+ removal rate with fluid conditions. In this model, it is necessary to assume that either the mass transfer or the oxidation reaction is the rate-limiting step to derive the pseudo-first-order reaction rate characteristics that are observed with activated carbon as a catalyst ( Li et al., 2019a ; Saito et al., 2020 ). On the other hand, the rate coefficient of Mn 2+ removal by activated carbon is little affected by differences in free chlorine concentration, especially in the high concentration range ( Saito et al., 2020 ), but it is affected by the presence of co-existing substances (explained in Section 4.1 ) and the mixing intensity of the reactor (explained in Section 4.2 ).…”