Dispersion in pulsed systems—III

Eidsath, A.; Carbonell, Ruben G.; Whitaker, Stephen; Herrmann, Leonard R.

doi:10.1016/0009-2509(83)85037-4

Cited by 184 publications

(26 citation statements)

References 16 publications

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“…These groups represent the relative roles of convective transport to diffusive transport in the system. It can be noted that the problem outlined here is similar to the hydrodynamic induced convective dispersion problems considered by Whitaker, Carbonell, and co-workers [24,25] and, using the macrotransport approach [29], that of Brenner, Edwards and co-workers [33]. However, in those studies the Navier-Stokes equation was solved to determine the convective transport term, while in the present study, the Laplace equation is used to determine the driving force for the electroconvective transport term and in the present study transport occurs in both phases.…”

Section: Volume Averagingmentioning

confidence: 82%

“…Since the process of averaging leads to the loss of information with regard to the fine structural details of the porous media, a second problem, termed the closure problem, must be solved in a representative unit cell in order to determine effective coefficients for the averaged equations [18,19]. The method of volume averaging has been extensively applied to the analysis of thermal conduction [20], diffusion [21][22][23], and convective-dispersion in porous media [24,25]. For these problems, agreement between theory and experiments has been very good, and recent studies have shown good agreement with Monte Carlo simulations of diffusion in isotropic and anisotropic media [26,27].…”

Section: Introductionmentioning

confidence: 99%

“…In both theories, effective transport coefficients which describe transport over the macro length scale are determined from solution of closure problems in the Unit cells. Both macrotransport theory and volume averaging have been applied to problems of hydrodynamically induced dispersion in porous media where the Navier-Stokes equation is used to describe the hydrodynamic flow field and the media obstacles are impermeable to flow [25,33]. In these studies, the ratio of the effective dispersion coefficient to the molecular diffusion coefficient was found to depend nonlinearly upon the dimensionless Peclet parameter, i.e., the ratio of average velocity to molecular diffusion [18,34].…”

Section: Introductionmentioning

confidence: 99%

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The effect of obstacle conductivity and electric field on effective mobility and dispersion in electrophoretic transport: A volume averaging approach

Locke

2002

Electrophoresis

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The method of volume averaging has been used to determine the effective electrophoretic mobility and dispersion coefficients for molecular transport of point-like solutes in a two-phase porous medium where the electrical conductivity and the diffusion and mobility coefficients may vary in both phases. The formal theory, derived in previous work, is numerically evaluated for cases where the obstacle phase has a large or small conductivity relative to the fluid phase and where the diffusion coefficient of the solute in the obstacle phase can be large or small relative to that in the fluid phase. In agreement with previous Monte Carlo methods, the effective electrophoretic mobility is not a function of media conductivity or electric field when the obstacles are impermeable to solute transport or have small diffusion solute diffusion coefficients. However, the dispersion coefficient is a strong function of electric field and varies with obstacle conductivity when diffusive transport is small in the obstacles relative to the fluid. In contrast, the effective electrophoretic mobility is a function of electric field when conductivity of the obstacles is much larger than the fluid and when the obstacles are very permeable to solute but have low electrical conductivity.

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Section: Volume Averagingmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The effect of obstacle conductivity and electric field on effective mobility and dispersion in electrophoretic transport: A volume averaging approach

Locke

2002

Electrophoresis

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“…Now, the definition of the total dispersion tensor is similar to that one for the effective diffusivity, but with one extra term involving the hydrodynamic dispersion as follows: [32] …”

Section: Appendixmentioning

confidence: 99%

“…The existence of convection at the microscale modifies the macroscale governing equation as follows: [32] e g @hc Ag i Here hv g i is the surface velocity field defined as…”

Section: Dispersive Mass Transportmentioning

confidence: 99%

Effective mass diffusion and dispersion in random porous media

2015

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In this work, the effect of the stochastic nature of porous medium on porosity, effective diffusion and mass dispersion was investigated. To this end, a methodology to build idealized media composed by solid particles with random size has been introduced. Gaussian and uniform probability distribution functions were employed to design the size and orientation of rectangular cylinders and cubes. Predictions of effective parameters were performed by using numerical procedures based on the volume averaging method. From the porosity and effective diffusion analysis, it was found that a minimum number of particles minimizes fluctuations of predictions. Thus, a minimum sampling size to measure properties was inferred. The minimum number of particles depends on the probability distribution functions and the dimensionality of particles used (cylinders or cubes). The methodology to build porous media also allows the creation of anisotropic media, and its effect is marked over the longitudinal and transverse components of effective diffusivity tensor. But this is not the case for the mass dispersion tensor, where the flow direction is the main cause for anisotropy. In fact, the flow taking place at pore‐scale increases noticeable the randomness of predictions of mass dispersion, specifically when the number of particles or the particle Péclet number are increased. This effect is more significant on the transverse mass dispersion.

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Solutions of Uncharged Molecules

Probstein

1994

Physicochemical Hydrodynamics

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Dispersion in pulsed systems—III

Cited by 184 publications

References 16 publications

The effect of obstacle conductivity and electric field on effective mobility and dispersion in electrophoretic transport: A volume averaging approach

The effect of obstacle conductivity and electric field on effective mobility and dispersion in electrophoretic transport: A volume averaging approach

Effective mass diffusion and dispersion in random porous media

Solutions of Uncharged Molecules

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