Soil water isotherm model for particle surface sorption and interlamellar sorption

Abstract

Soil–water retention curve (SWRC) describes the relationship between soil matric potential and soil water content, which is recognized as the most important constitutive function for unsaturated soil that governs many hydrological and mechanical properties, such as fluid flow, hydraulic conductivity, chemical transport, and soil freezing and thawing, etc. Soil–water isotherm (SWI) measured from vapor adsorption technique captures the SWRC at medium to high matric potential range, where three physical mechanisms of soil–water retention (SWR) with distinct free energy levels are involved: adsorption on external particle surface, adsorption in interlamellar space, and capillarity. So far, there is not a single SWI model that can take all three mechanisms into full consideration in full matric potential range. Here a closed-form SWI model is formulated as the mathematical sum of three independent SWIs, which are external sorptive SWI, internal sorptive SWI, and capillary SWI; each corresponds to one of the aforementioned SWR processes. The generality and effectiveness of the proposed model are experimentally validated through a suite of 21 soils, covering all common soil types with plasticity index (PI) of 4–132. The proposed SWI model shows excellent performance as it nearly perfectly (R2 > 0.99) fits both the adsorption isotherm and the desorption isotherm for each soil, validating the generality of the model. The external specific surface area (SSA) obtained from the external sorptive SWI correlates well with that determined from the classic Brunauer–Emmett–Teller equation, while the internal SSA obtained from the internal sorptive SWI also coincides with that measured independently; both further confirm the capability of the proposed SWI model to distinguish between external surface adsorption and interlamellar adsorption.