On the use of the dispersion model of fluid flow

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

“…The mathematical specification (1), (2) requires three independent dimensionless parameters, one of which is a removal rate, For any data fitting or validation, two further parameters For nondispersive (piston) flow, Ca = Cr. The concepts and interpretations of resident and flux concentrations have been discussed in detail by Brigham [1974•, by Kreft and Zuber [1978, 1979, and by Parker and van Genuchten [1984,1986]. Those researchers have noted that if C a satisfies an equation of the form (19), then so too does C r. (This is immediately apparent by noting that the differential operator (1-8/•) commutes with all of the operators in (19)).…”

Study of hydraulic parameters in heterogeneous gravel beds: Constructed wetland in Nowa Słupia (Poland)

“…Significant mathematical differences between models arise from different formulations of boundary and initial conditions. These issues were thoroughly discussed for practical applications by Kreft and Zuber (1978, 1979, 1986 and Parker and van Genuchten (1984). This paper provides a quantitative description of flow characteristics in the constructed wetland in Nowa Słupia, Poland.…”

Technical Commentary on “Estimation of Degradation rates by Satisfying Mass Balance at the Inlet”

“…Within the porous media we can measure only the resident concentration, not the flux one. Kreft and Zuber (1979) suggest in the case of radioactive tracers to measure C r and then to calculate C f , using Equation G5. Thus, we likely do not have a choice but to simulate the resident concentration.…”