A Modified Fick’s First Law Incorporating a Flux Correction Factor for Nutrient Diffusion in Intertidal Sediments

This study examined the diffusion of nutrients (NH4+, NO3−, and PO43−) in the pore water of intertidal sediments in Lake Komuke (located in the northeastern part of Hokkaido on the coast of Okhotsk Sea) across nine stations, at 0 cm to 40 cm depths, from 19 May to 23 August 2015. A comparison was made between the traditional version of Fick’s first law and a modified version to understand nutrient diffusion in the intertidal flat. The novelty of this study lies in establishing a flux correction factor as a function of the activity coefficient in intertidal sediments. The outcomes of the standard and modified versions of Fick’s law exhibited observable physical differences between stations for all nutrients. However, the statistical analysis demonstrated significant differences only for NO3− and PO43− at stations D, E, and F, suggesting that there is no statistically meaningful difference in NH4+ flux. A statistical comparison of 27 pairs of fluxes obtained by the classical and modified versions of Fick’s first law indicated that 88.9% of the differences were not statistically significant between the two methods, and 11.1% were statistically significant. This shows the consistency of the modified method, firstly in reproducing the classical version of Fick’s law, and secondly in improving upon it, in a porous medium. These findings indicate that the modified version of Fick’s first law is an accurate methodology for evaluating nutrient diffusion dynamics in intertidal environments, and is potentially applicable to coastal salt marshes, with practical implications for environmental management and conservation efforts.