Modelling the oxidation of elemental sulfur in soils

Abstract

Direct and recursive estimation models for the oxidation rate of elemental sulfur (S°) in soil have been proposed, both essentially based on a constant oxidation rate per unit area of exposed surface. Fertilizer S° is taken to consist largely of blocky shaped particles, i.e. having similar dimensions along three axes, which can be treated as equivalent spheres. The most important implication in applying the rate assumption to these shaped particles is that the mass at any time is related to the cube of the time. This has been verified experimentally for oxidation by thiobacilli. Although the assumption is less likely for heterotrophs, experiments involving four soils conformed to the cubic relation.

Implications for the particle variables of size and size distribution have been given more limited testing. The data are generally consistent with theory, such as independence of the rate constant with particle size.

Assuming an activation energy for the oxidation process implies, in addition to the above, an exponential relation of rate constant with temperature. This is supported by experiment. Values for the activation energy are approximately 85 kJ mol⁻¹, and therefore consistent with the rate limiting step for the oxidation being a chemical or biochemical reaction, rather than a diffusion process.

Because absolute rate constants are generated by the models, they are useful for examining the effects of environmental variables not hitherto included. Empirical relationships, once established, can then be included in the model, such as the quadratic relation between rate constant and soil moisture, with the maximum at approximately field capacity.

The delay time (the time to reach maximum oxidation rate) was useful, together with the rate constant, for distinguishing species of oxidizing microorganisms. Typically, under optimum conditions at 25°C, thiobacilli have a delay time of several days and a rate constant of 50µg cm⁻² day⁻¹ S, while heterotrophs have a negligible delay time but a rate constant of only 5µg cm⁻² day⁻¹ S.

The cubic model with a single rate constant gave a surprisingly good fit to the oxidation rate over 12 months in New Zealand pastoral soils under field conditions of varying temperature and moisture. This was attributed to the balancing effect of moisture and temperature on the rate constant under the cool temperate climate. A knowledge of the annual average soil temperature is sufficient to provide advice on the optimum particle size for S° fertilizer.