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A derivation of the macroscopic solute transport equation for homogeneous, saturated, porous media: 2. Reactive solutes at low concentration
Author(s) -
Chu ShuYuan,
Sposito Garrison
Publication year - 1981
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr017i002p00333
Subject(s) - porous medium , thermodynamics , adsorption , convection–diffusion equation , dispersion (optics) , mass transfer , convection , balance equation , chemistry , porosity , materials science , physics , mechanics , mathematics , optics , statistics , markov model , markov chain , organic chemistry
The macroscopic transport equation for a reactive solute at low concentration in a homogeneous, saturated, porous medium is derived on the basis of a rigorous cumulant expansion applied to the equation of mass balance for the solute both in the liquid phase and in the solid phase. The derivation includes a detailed consideration of the molecular‐kinetic picture of adsorption. The commonly neglected fact that all adsorption phenomena in natural porous media also are exchange phenomena is emphasized, as is the important distinction between uniform and nonuniform adsorbing surfaces. For the uniform case, where there is only one type of adsorption site on the solid matrix, the expression for the macroscopic transport equation is identical in form with the standard dispersion‐convection equation incorporating a first‐order kinetic adsorption model. For the nonuniform case, where there is more than one type of adsorption site, the macroscopic transport equation derived in this paper and the conventional dispersion‐convection equation are no longer identical. The difference between the two equations is discussed briefly.