Unidimensional solute transport incorporating equilibrium and rate-limited isotherms with first-order loss: 1. Model conceptualizations and analytic solutions

I derive analytic solutions to the advection‐dispersion equation for unidimensional solute or tracer transport. The tracer undergoes both sorption and first‐order loss. Sorption is via a linear Freundlich isotherm in tandem with rate‐limited exchange (after Lapidus and Amundson). An arbitrary tracer input is postulated, with pulse input and step input specializations given detailed consideration. Many distinct conceptual models of unidimensional transport are mathematically equivalent to this formulation, including a model of exchange between mobile and immobile water, and including models with selective first‐order removal processes. Ambiguities in interpreting model simulations of experimental data have two origins: more than one conceptual model is a contending simulator; a conceptual model may be mathematically overspecified with parameters. The implications of such ambiguities are discussed.