TY - JOUR
T1 - Models of geochemical systems from mixture theory
T2 - Diffusion
AU - Kirwan, A. D.
AU - Kump, Lee R.
PY - 1987/5
Y1 - 1987/5
N2 - The problem of diffusion of a geochemical component in a natural environment is investigated from the standpoint of mixture theory. The approach here differs from previous diffusion studies in that both the conservation of mass and momentum for the component is considered. This approach avoids parameterizing the diffusive flux in the mass equation by Fick's law. It is shown that when the momentum equation is included with the mass equation, the linear approximation for the space-time distribution of a solute in a binary system is the telegraph equation, well known from electrodynamics. This contrasts with the diffusion equation, which relies on introducing the Fick's law assumption into the conservation of mass equation for the solute. Solutions for both the diffusion and telegraph equation models are obtained and compared for the case of migration of a minor component into the seabed when the sediment-water interface concentration is a prescribed function of time. Although the stationary, steady state solutions of the telegraph and diffusion equations are identical, the former has a transient solution in which fluctuations propagate at finite speed. The Fickian assumption, in contrast, requires an infinite speed of propagation.
AB - The problem of diffusion of a geochemical component in a natural environment is investigated from the standpoint of mixture theory. The approach here differs from previous diffusion studies in that both the conservation of mass and momentum for the component is considered. This approach avoids parameterizing the diffusive flux in the mass equation by Fick's law. It is shown that when the momentum equation is included with the mass equation, the linear approximation for the space-time distribution of a solute in a binary system is the telegraph equation, well known from electrodynamics. This contrasts with the diffusion equation, which relies on introducing the Fick's law assumption into the conservation of mass equation for the solute. Solutions for both the diffusion and telegraph equation models are obtained and compared for the case of migration of a minor component into the seabed when the sediment-water interface concentration is a prescribed function of time. Although the stationary, steady state solutions of the telegraph and diffusion equations are identical, the former has a transient solution in which fluctuations propagate at finite speed. The Fickian assumption, in contrast, requires an infinite speed of propagation.
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U2 - 10.1016/0016-7037(87)90214-6
DO - 10.1016/0016-7037(87)90214-6
M3 - Article
AN - SCOPUS:0023482584
SN - 0016-7037
VL - 51
SP - 1219
EP - 1226
JO - Geochimica et Cosmochimica Acta
JF - Geochimica et Cosmochimica Acta
IS - 5
ER -