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Front spreading with nonlinear sorption for oscillating flow
Author(s) -
Cirkel D. G.,
van der Zee S. E. A. T. M.,
Meeussen J. C. L.
Publication year - 2015
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 - 10.1002/2014wr015847
Subject(s) - convection , mixing (physics) , mechanics , nonlinear system , front (military) , flow (mathematics) , limiting , dispersion (optics) , rarefaction (ecology) , diffusion , physics , alternation (linguistics) , thermodynamics , classical mechanics , optics , geology , meteorology , linguistics , philosophy , mechanical engineering , paleontology , quantum mechanics , species richness , engineering
In this paper, we consider dispersive and chromatographic mixing at an interface, under alternating flow conditions. In case of a nonreactive or linearly sorbing solute, mixing is in complete analogy with classical dispersion theory. For nonlinear exchange, however, oscillating convective flow leads to an alternation of sharpening (Traveling Wave TW) and spreading (Rarefaction Wave RW). As the limiting TW form is not necessarily accomplished at the end of the TW half cycle, the oscillating fronts show gradual continuous spreading that converges to a zero‐convection nonlinear pure diffusion spreading, which is mathematically of quite different nature. This behavior is maintained in case the total (background) concentration differs at both sides of the initial exchange front.