## 1. Introduction

[2] Many porous media exhibit different pore or flow domains due to layering, fracturing, or aggregation. In the following only two pore domains will be considered; domain 1 may represent a fracture or interaggregate pore space with faster flow and domain 2 with slower or no flow in the rock matrix or intraaggregate pore space. The difference in flow and transport of dissolved substances in the two domains may be accounted for by using a physical nonequilibrium concept [*Selim and Ma*, 1998]. Solute transport in porous media with transient water flow in multiple (unsaturated) domains typically will have to be solved numerically [*Gerke and van Genuchten*, 1996; *Simunek and van Genuchten*, 2008]

[3] Analytical solutions for solute transport involving physical nonequilibrium have mostly been restricted to dual-porosity media with a uniform water content and flow in the interaggregate or mobile aqueous domain and no flow in the intraaggregate or immobile domain. Transport in the longitudinal direction, by advection and dispersion, occurs solely in the mobile domain. There is diffusive solute transport between the two domains, which may be quantified by solving Fick's equation if the solid phase of the immobile domain consists of well-defined aggregates [cf. *van Genuchten and Dalton*, 1986; *Rappoldt*, 1990] or, more commonly, by assuming a linear first-order exchange process [*Lapidus and Amundson*, 1952; *Coats and Smith*, 1964; *van Genuchten and Wierenga*, 1976]. The solution can be readily extended for additional immobile domains [*Veling*, 2002]. *Bellin et al.* [1991] demonstrated that during nonequilibrium transport, the breakthrough curve (BTC) resulting from a Dirac input may have a double peak due to the separate processes of advective transport in the mobile domain and solute transfer between the mobile and immobile domains.

[4] Double peaks are more commonly associated with the concentration distribution versus time or position for transport in media with flow in both pore domains. Less attention has been paid to the analytical solution for transport in dual-velocity or dual-permeability media than for media with flow in just the mobile domain. The former represents a more general scenario. For example, there will be faster water flow in interaggregate pore space or fractures of a porous medium and slower flow in the intraaggregate pore space. The transport mechanism for solutes will be advection and dispersion in the two pore domains and diffusive transfer between the domains. A similar problem is solute transport in a stratified medium with flow parallel to the stratification and the two pore domains are coupled through dispersive solute transfer between the strata. *Dykhuizen* [1991] resorted to time moments to quantify transport in dual-velocity media noting that solutions for coupled equations and arbitrary boundary and initial conditions are difficult to obtain. In particular, the behavior at larger times could be conveniently approximated with asymptotic solutions. However, the procedure to decouple linear ordinary differential equations is well known in the mathematical literature and can be applied to systems with an arbitrary number of equations [*Zwillinger*, 1989; *Zill and Cullen*, 2006]. General solutions were obtained for diffusion in media with two porosities in companion papers by *Aifantis and Hill* [1980] and *Hill and Aifantis* [1980]. The approach was extended by *Hill and McNabb* [1989] for an arbitrary differential operator. The objective of this study is to derive explicit, nontrivial solutions for the solute concentration as a function of time and position for both domains including time moments of the BTC. The solutions will be applied to describe breakthrough curves obtained for solute transport in an aggregated Andisol soil.