Relationship between thermal and electrical conductivity curves of soils with a unimodal pore size distribution: Part 1. A unified series-parallel resistor model

Abstract

Soil thermal conductivity (λ) and electrical conductivity (σ) characterize heat and electricity conduction through soils. Both λ and σ are affected by similar factors, such as soil water content (θ), texture, bulk density (ρb), temperature, structure, and organic matter content. Little is known about the quantitative relationship between λ and σ, and how soil texture and ρb modify the relationship. In this part one of a two-part series, we examine the correlation between λ(θ) and σ(θ) curves and develop a new model for normalized σ curves of soils with a unimodal pore size distribution. We introduce an Ohm’s law analogy to describe the λ and σ curves conceptually, based on a cubic cell unit model. A unified series–parallel resistor model considering θ and ρb effects is established for both λ(θ) and σ(θ) curves by considering heat and electrical conduction pathways (solid, solid–liquid, and liquid pathways) in the hydration, menisci, and continuous liquid ranges. Simultaneous measurements of θ, λ and σ with thermo-TDR sensors on two soils are used to examine the model performance at various values of ρb and θ. The modeled and measured λ (θ) and σ (θ) curves provide consistent trends, and the normalized λ and σ values vs. degree of saturation confirm the existence of an earlier reported “mirror image” phenomenon between the functions.