Kinetic Freundlich equation applied to soils with a high residual phosphorus content

For soils with low plant-available phosphorous (P) content, the kinetics of P sorption can be described adequately using the kinetic Freundlich equation (Q = at(m) C-n), where a, m, and n are fitting parameters. When this equation is used for soils that already contain a large amount of plant-available P as a result of previous P additions, the problem arises as to how the initial P content, Q(0), (Q at t = 0) can be taken into account. In this study, we tested the applicability of the equation to soils with a high level of plant-available P and several ways to include Q(0), which was estimated using nonlinear regression. Adsorption isotherms for three Dutch soils (sandy soil, loamy sand, and sandy loam soil) were determined after 1, 3, 7, and 21 days. We have shown that for these soils, a higher value of Q(0) must be used for a longer equilibration time. A description of the increase of Q(0) with time of the form: Q(0) = x t(m) appeared to be applicable for the three soils tested. This leads to an extended kinetic Freundlich equation of the form: Q(Delta C) = (a C-n - x) t(m), where Q(Delta C) represents adsorbed P, determined from the amount that has disappeared from the shaking solution, and x is an additional fitting parameter.