Mathematical models to study the kinetics of potassium release from swell-shrink soils of Central India in relation to their mineralogy

Employing four mathematical models (first-order, parabolic-diffusion, Elovich and zero-order), kinetics of potassium desorption from eight soils with and without cropping were studied to evaluate their ability in explaining K release from soils. The decline in the soil test K in cropped soils over original soils was drastic in easily desorbable forms compared to that of strongly held forms like 3 M H₂SO₄ K. Results showed that parabolic diffusion as well as first-order kinetic equation explained the K release data well for both original and K depleted (cropped) soils. Elovich and zero-order equations were not suitable to describe the kinetic data. However, zero-order equation explained K release data better in case of K-depleted soils as compared to original soils. Soils with higher initial K contents registered higher release rate constants. Over the entire period of cropping the range of release rate (b) decreased from 1.26 to 1.53 × 10^?2 to values ranging from 1.12 to 1.30 × 10^?2 h^?1. In contrast, the first-order equation, parabolic diffusion showed higher b values for cropped soils as they represent the diffusion gradient. Mica and its biotite content in both silt and clay fractions showed significant correlation (r) with b values. Similarly with the rate of K release, clay content of soils maintained significant r whereas the silt content did not.