## 1. Introduction

[2] Solute diffusion in soil refers to the transport of a dissolved constituent in aqueous phase from a higher concentration point toward a lower one. This concentration gradient driven process in soil determines the rate of solute transport in the vadose zone, which can influence the solute concentration meters away from the source [*Helmke et al.*, 2004].

[3] An accurate estimation of solute diffusion flux in soil (*J*) is imperative. This flux (*J*) is described by Fick's law of diffusion in water along with a tortuosity factor (*ξ*) to account for the reduced cross-sectional area and longer pathway [*Jury et al.*, 1991]:

where *D*_{0} is the solute diffusion coefficient in water, *D _{s}* is the solute diffusion coefficient in soil,

*C*denotes solute concentration, and ∂

*C*/∂

*z*denotes solute concentration gradient along the flux direction

*z*.

*J*,

*D*, and

_{s}*ξ*are defined in terms of the total cross-sectional area.

[4] The tortuosity factor (*ξ*) can be calculated from the ratio of solute diffusion coefficient in soil (*D _{s}*) to that in water (

*D*

_{0}), and both

*D*and

_{s}*D*

_{0}are experimentally determined [

*Millington and Quirk*, 1961]. However, measurement of solute diffusion coefficient (

*D*) in soil is a time-consuming and labor-intensive procedure [

_{s}*Dane and Topp*, 2002]. Besides, experimental measurement of

*D*is not an ordinary undertaking for those who frequently use this parameter [

_{s}*Shackelford and Daniel*, 1991]. Consequently, a number of empirical tortuosity factor models have been proposed to predict solute diffusion coefficients in soils to replace the laboratory work [

*Moldrup et al.*, 1996, 2001, 2007;

*Olesen et al.*, 2001a]. These models are based on soil attributes such as soil water content, matric potential, texture, bulk density, and particle-size distribution that are known to affect the tortuosity factors [

*Lim et al.*, 1998;

*Phillips and Brown*, 1965;

*So and Nye*, 1989].

[5] Solute diffusion in soil may also be viewed on a microscopic scale. Under ordinary conditions, the water molecules in the aqueous phase of soil are distributed in two forms: continuous capillary tubes (pore water) and pendular rings around soil particles (film water) [*Conca and Wright*, 1992; *Phillips and Brown*, 1965; *So and Nye*, 1989]. The concept of pore and film water is the theoretical basis of the conceptual models to predict the solute diffusion coefficients in soils [*Lim et al.*, 1998]. *Hu and Wang* [2003] used laser ablation-inductively coupled plasma-mass spectrometry to study diffusion in porous media. They found that at different soil water contents, the liquid phase is structured in different forms and geometric arrangements. At higher soil water contents (0.05 to 0.5 cm^{3} cm^{−3}), the liquid phase occupies the voids that formed continuously connected pores, while at lower soil water contents (0.005 to 0.05 cm^{3} cm^{−3}), the liquid phase is held in pendular form that results in a less continuous diffusive pathway. They indicated that the transition of liquid phase distribution from the continuously connected pores form to the pendular form can cause a sudden decline in solute diffusion coefficient.

[6] The tortuosity factor predictive models if validated may greatly simplify the estimation of solute diffusion coefficients in soil. Many studies have been conducted to test the applicability of the models, but none of them used comparable experimental conditions to systematically assess the effectiveness of the prediction models for soils with different textures and at various degrees of water saturation. The main objective of this study is to measure solute diffusion coefficients of three soils ranging from sand, sandy clay loam, and clay at various soil water contents to evaluate the strength and weakness of each model in terms of predictive capability, range of applicability, and requirement of input parameters.