Modeling the effects of diffusion limitations on nitrogen-15 isotope dilution experiments with soil aggregates

An assumption inherent in isotope dilution methodologies is that of homogeneous distribution of label. This assumption may not hold, however, because of mass transfer limitations in most soil systems. The effects of mass transfer limitations on isotope dilution in soil aggregates with radii up to 0.36 cm were examined using spherical diffusion-reaction models designed to simulate ¹⁵NH₄⁺ isotope dilution experiments measuring gross production and consumption of NH₄⁺ across a 24-h period. Equations that described transport and reaction of NH₄⁺ assumed Fickian diffusion, linear, equilibrium adsorption, zero-order production of natural abundance ¹⁵N, and either pseudo-first-order or zero-order consumption of NH₄⁺. In the case of pseudo-first-order consumption, rate calculations were sensitive to the adsorption coefficient (emphasizing the need to interpret results as apparent rates), but not to other transport parameters. In the case of zero-order consumption, both production and consumption rates were always underestimated. Errors increased as aggregate size increased and as effective diffusivity decreased. Increasing the consumption to production rate ratio increased the error in production rate estimates. Allowing the applied label to diffuse into soil aggregates for 24 h prior to initial time sampling decreased errors by a factor of about three (to <-8% relative error) in the largest aggregate size class. These simulations reemphasize the need to optimize experimental protocol when designing isotope dilution experiments in structured soils and suggest an equilibration period prior to initial time sampling will improve accuracy of reaction rate estimates obtained from isotope dilution experiments.