A general theory of Taylor dispersion phenomena

Dill, Loren H.; Brenner, Howard

doi:10.1016/0021-9797(82)90239-9

Cited by 46 publications

(15 citation statements)

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“…On the other hand, in the absence of surface-excess reaction (i.e. k = ( which coincides with the comparable expression obtained by Dill & Brenner (1982). (Dill & Brenner (1982) defined the dimensionless surface adsorptivity k by dividing c by the characteristic volume-to-surface ratio.…”

Section: A (Xy ) = 2 Exp(i (814) N-oosupporting

confidence: 85%

“…k = ( which coincides with the comparable expression obtained by Dill & Brenner (1982). (Dill & Brenner (1982) defined the dimensionless surface adsorptivity k by dividing c by the characteristic volume-to-surface ratio. In present circumstances this convention requires th a t k = c/2a, thereby yielding U* = V/(\+k) in (8.50), which explicitly reproduces the comparable expression of Dill & Brenner (1982).)…”

Section: A (Xy ) = 2 Exp(i (814) N-oosupporting

confidence: 83%

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Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems

Dungan

Shapiro

Brenner

1990

Proc. R. Soc. Lond. A

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Convective-diffusive transport of a chemically reactive solute is studied analytically for a general model of a multiphase system composed of ordered or disordered particles of arbitrary shapes and sizes. Use of spatially periodic boundary conditions permits analysis of particulate multiphase systems of effectively infinite size. Solute transport occurs in both the continuous and discontinuous bulk phases, as well as within and across the interfacial phase boundaries separating them. Additionally, the solute is allowed to undergo generally inhomogeneous first-order irreversible chemical reactions occurring in both the continuous and discontinuous volumetric phases, as well as within the interfacial surface phase. Our object is that of globally describing the solute transport and reaction processes at a macro- or Darcy-scale level, wherein the resulting, coarse-grained particulate system is viewed as a continuum possessing homogeneous material transport and reactive properties. At this level the asymptotic long-time solute macrotransport process is shown to be governed by three Darcy-scale phenomenological coefficients: the mean solute velocity vector ͞U *, dispersivity dyadic ͞D *, and apparent volumetric reactivity coefficient ͞K *. A variant of a Taylor-Aris method-of-moments scheme (Brenner & Adler 1982), modified to include solute disappearance via chemical reactions, is used to express these three macroscale phenomenological coefficients in terms of the given microscale phenomenological data and geometry. The general solution technique, illustrated here for a simple, ordered geometrical realization of a two-phase system, reveals the competitive influences of the respective volumetric/surface-excess transport and reaction processes, as well as the solute adsorptivity, upon the three macroscale transport coefficients.

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Section: A (Xy ) = 2 Exp(i (814) N-oosupporting

confidence: 85%

Section: A (Xy ) = 2 Exp(i (814) N-oosupporting

confidence: 83%

Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems

Dungan

Shapiro

Brenner

1990

Proc. R. Soc. Lond. A

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“…Spatial moment analysis has also been considerably generalized by Brenner and coworkers [Brenner, 1980;Brenner and Adler, 1982;Dill and Brenner, 1982;Shapiro and Brenner, 1988]. Brenner [1980] periodic" model of a porous medium.…”

Section: Aris' [1956] Spatial Moment Analysis Was Extended By Hornmentioning

confidence: 99%

Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers

Valocchi¹

1989

Water Resources Research

139

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Spatial moment analysis is used in this paper to study the asymptotic, long-time behavior of the depth-averaged solute plume for transport in a perfectly stratified aquifer. The solute is assumed to adsorb onto the aquifer solids according to a first-order reversible kinetic rate law; steady, unidirectional, horizontal flow is assumed with arbitrary vertical variation in pore water velocity, dispersion coefficients, and adsorption reaction parameters. We derive general formulas to calculate the effective dispersion coefficient governing the transport of the depth-averaged plume. The results demonstrate that overall longitudinal spreading of the plume results from three distinct factors: local Darcy scale longitudinal dispersion, vertical variations in the pore water velocity and retardation factor, and adsorption kinetics. For the example of a two-layer aquifer, a simple nonequilibrium index is derived which shows that deviations from local equilibrium diminish as the degree of heterogeneity of the retarded pore water velocity increases. It is also demonstrated that enhanced plume spreading can be caused by negative correlation between the vertically varying pore water velocity and retardation factor in addition to slow adsorption kinetics. Thus great caution is warranted in interpreting the results of field scale reactive tracer experiments.

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“…An essential building block of this approach is the mathematical description of particle motion in a pipe ow. In the ÿelds of engineering, a general theory, which describes particle settling from an oscillatory ow, has been established (Dill & Brenner, 1982, 1983), but in the ÿeld of lung physiology, this theory has not received much attention 1 due to the demanding mathematical treatment of the problem. Instead, most of the currently used models of gravitational deposition in the lung are based on the theory of particle sedimentation in steady pipe ow o ered by Pich (1972), entirely ignoring the importance of the oscillatory nature of ow.…”

Section: Introductionmentioning

confidence: 99%

A simple model for gravitational deposition of non-diffusing particles in oscillatory laminar pipe flow and its application to small airways

Kojić

Tsuda

2004

Journal of Aerosol Science

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A general theory of Taylor dispersion phenomena

Cited by 46 publications

References 1 publication

Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems

Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems

Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers

A simple model for gravitational deposition of non-diffusing particles in oscillatory laminar pipe flow and its application to small airways

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