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Algebraic Equations for Solute Movement During Absorption
Author(s) -
Watson K. K.,
Jones M. J.
Publication year - 1984
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/wr020i008p01131
Subject(s) - dispersion (optics) , constant (computer programming) , absorption (acoustics) , diffusion , algebraic number , thermodynamics , algebraic equation , constant coefficients , boundary value problem , mathematics , mathematical analysis , differential equation , fick's laws of diffusion , mechanics , physics , computer science , optics , nonlinear system , quantum mechanics , programming language
Recently published analytical solutions for nonreactive solute movement in unsaturated porous materials are reviewed with the aim of developing simple algebraic equations that can be used with confidence for predicting solute disposition during absorption. Quasi‐analytical solutions for constant concentration and constant flux boundary conditions using a velocity independent hydrodynamic dispersion coefficient are reduced to a simple yet accurate form. The solutions for systems where the mechanical dispersion forms the dominant component during dispersion are also presented. Systems that lie between the extreme cases where both the molecular diffusion and mechanical dispersion have comparable significance are then analyzed and values of an empirical parameter, which is a necessary term in the resulting equation, determined from computer‐based numerical studies. Finally, equations developed from the alternative governing differential equation for solute movement based on a Fickian model are also detailed.