Nonequilibrium transport of solute in soils and geological media is commonly attributed to two main processes: (1) the rate-limited mass transfer of aqueous species to or from the regions with limited or no advective flow; and (2) the time-dependent chemical reaction at the surfaces of solid materials. The first process is often referred to as transport-related nonequilibrium or physical nonequilibrium and the second process is referred to as reactionrelated nonequilibrium or chemical nonequilibrium. As a result of pedogenic processes, soils and geological media are often characterized by extensive chemical and physical heterogeneities. Soil heterogeneity has a profound effect on the transport of chemicals in the soil profile. The physical heterogeneity is mainly attributed to the highly nonuniform pore space as a result of the soil aggregates, soil layers, as well as cavities developed from natural and anthropogenic activities. The highly irregular flow field resulting from the spatial variance of pore sizes and connectivity is a major driving force of the nonequilibrium transport of solutes in soils (Biggar and Nielsen, 1976; Dagan, 1984). Conceptually, the nonequilibrium transport of nonreactive solutes in structured soils can be described as a rapid movement of water flow and solutes within preferential flow paths and a diffusive mass transfer of solutes to a stagnant region. This mobile-immobile dual-region concept is the foundation of the mathematical models used for simulating the physical nonequilibrium transport (van Genuchten, 1981; Reedy et al., 1996; Simunek et al., 2003).

In general, the nonequilibrium mass transfer of solutes in soils proceeds in two stages: (1) external or film diffusion from flow water to the solid interface; and (2) internal diffusion through the porous network of soil aggregates (Brusseau, 1993). Film diffusion is of importance only at low flow velocities. Under environmental conditions, diffusive mass transfer in the micropores inside soil aggregates is an important process influencing the mobility of reactive metals in soils. The intra-aggregate diffusion serves as a reservoir in the transport of contaminants by spreading them from flowing water to the