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Theory of dissolution and precipitation waves—redux
Author(s) -
Ghaderi Zefreh Masoud,
Doster Florian,
Hesse Marc A.
Publication year - 2019
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.16573
Subject(s) - dissolution , partial differential equation , saturation (graph theory) , ion , dispersion (optics) , precipitation , thermodynamics , conservation law , chemistry , mathematics , mathematical analysis , mechanics , physics , meteorology , organic chemistry , combinatorics , optics
We present a local equilibrium theory for the reactive transport of two salts that share an anion in an ideal solution. We revisit this classic problem using the theory of hyperbolic partial differential equations accounting for the volume of precipitates. We construct analytical solutions for the 2 × 2 system of conservation laws in the absence of hydrodynamic dispersion. The character of the system depends on the saturation of the salts, that is, whether the fluid is saturated with both, either of the two or none of the salts. We provide a comprehensive analysis of the system and its solution. Each primitive variable, the amount of precipitate and the concentration of ions, remains constant along one class of waves that propagate in the system. The analysis of the system allows identification of seven bifurcations with respect to the intermediate state.