A stochastic description of longitudinal dispersion in uniaxial flows

Broeck, C. Van den

doi:10.1016/0378-4371(82)90224-2

Cited by 47 publications

(17 citation statements)

References 7 publications

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“…A key component of this work is the general short-time expansion of the dispersion coefficient in terms of a Taylor series expansion of the velocity field. The result is analogous to the established approach for preasymptotic Taylor dispersion in a capillary [17,54] and dispersion in turbulent flow [55]. PGSE NMR has been demonstrated to characterize the time dependent Taylor dispersion in capillary flow in excellent agreement with the theory [38,54,56].…”

Section: Permeability and Preasymptotic Dispersionsupporting

confidence: 56%

Nuclear magnetic resonance measurement of hydrodynamic dispersion in porous media: preasymptotic dynamics, structure and nonequilibrium statistical mechanics

Codd

Seymour

2012

Eur. Phys. J. Appl. Phys.

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Measurement of displacement time and length scale dependent dynamics by pulsed gradient spin echo nuclear magnetic resonance in porous media directly provides the preasymptotic hydrodynamic dispersion coefficient. This allows for comparison with nonequilibrium statistical mechanics models of hydrodynamics dispersion in porous media. Preasymptotic dispersion data and models provide characterization of porous media structure length scales relevant to transport and are related to the permeability and sample heterogeneity.

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Section: Permeability and Preasymptotic Dispersionsupporting

confidence: 56%

Nuclear magnetic resonance measurement of hydrodynamic dispersion in porous media: preasymptotic dynamics, structure and nonequilibrium statistical mechanics

Codd

Seymour

2012

Eur. Phys. J. Appl. Phys.

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“…Since our gradients were generated in seconds to minutes, their evolution fell in the early to intermediate dispersion regime. Approximate theoretical descriptions valid for early, intermediate, and late times exist for many geometries, including rectangular channels,[26, 27] cylindrical tubes,[28] and channels with smooth cross-sections. [12, 23] We define the gradient length Δ as the length of the transition zone between 10% and 90% of the maximum concentration, which captures the most linear, and therefore usable, portion of the concentration profile.…”

Section: Resultsmentioning

confidence: 99%

Convection-driven generation of long-range material gradients

Hancock

et al. 2010

Biomaterials

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Natural materials exhibit anisotropy with variations in soluble factors, cell distribution, and matrix properties. The ability to recreate the heterogeneity of the natural materials is a major challenge for investigating cell-material interactions and for developing biomimetic materials. Here we present a generic fluidic approach using convection and alternating flow to rapidly generate multi-centimeter gradients of biomolecules, polymers, beads and cells and cross-gradients of two species in a microchannel. Accompanying theoretical estimates and simulations of gradient growth provide design criteria over a range of material properties. A poly(ethyleneglycol) hydrogel gradient, a porous collagen gradient and a composite material with a hyaluronic acid/gelatin cross-gradient were generated with continuous variations in material properties and in their ability to regulate cellular response. This simple yet generic fluidic platform should prove useful for creating anisotropic biomimetic materials and high-throughput platforms for investigating cell-microenvironment interaction.

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“…It has also recently been observed experimentally in a cone and plate rotational flow by confocal microscopy [20]. Flow in a pipe with uniform initial distribution of particles results in identical scaling for the axial MSD [15,17].…”

mentioning

confidence: 61%

“…. This result has been derived using a multitude of analytical methods based on the advection diffusion equation [11][12][13][14][15], the projection operator method [16], and the generalized Langevin equation [11,15,17,18]. Direct numerical simulations have recently reproduced this time and shear rate dependent behavior [19].…”

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confidence: 95%

Anomalous preasymptotic colloid transport by hydrodynamic dispersion in microfluidic capillary flow

2014

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The anomalous preasymptotic transport of colloids in a microfluidic capillary flow due to hydrodynamic dispersion is measured by noninvasive nuclear magnetic resonance (NMR). The data indicate a reduced scaling of mean squared displacement with time from the 〈z(t)(2)〉(c) ∼ t(3) behavior for the interaction of a normal diffusion process with a simple shear flow. This nonequilibrium steady-state system is shown to be modeled by a continuous time random walk (CTRW) on a moving fluid. The full propagator of the motion is measured by NMR, providing verification of the assumption of Gaussian jump length distributions in the CTRW model. The connection of the data to microrheology measurements by NMR, in which every particle in a suspension contributes information, is established.

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A stochastic description of longitudinal dispersion in uniaxial flows

Cited by 47 publications

References 7 publications

Nuclear magnetic resonance measurement of hydrodynamic dispersion in porous media: preasymptotic dynamics, structure and nonequilibrium statistical mechanics

Nuclear magnetic resonance measurement of hydrodynamic dispersion in porous media: preasymptotic dynamics, structure and nonequilibrium statistical mechanics

Convection-driven generation of long-range material gradients

Anomalous preasymptotic colloid transport by hydrodynamic dispersion in microfluidic capillary flow

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