Taylor dispersion and molecular displacements in Poiseuille flow

Codd, SL; Manz, B.; Seymour, Joseph D.; Pt, Callaghan

doi:10.1103/physreve.60.r3491

Cited by 56 publications

(62 citation statements)

References 14 publications

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“…Thus, the volume that gets exchanged only slowly, which is responsible for the stationary branch of the fork, is Ϸ300 nl. The observation of this forking emphasizes the complementary character of direct f low imaging (22)(23)(24)(25) and TOF f low imaging. The former provides a map of local velocity vectors, whereas the latter is able to distinguish between different f low paths and shows how well a certain volume element is connected to the f low field.…”

Section: Resultsmentioning

confidence: 99%

Microfluidic gas-flow profiling using remote-detection NMR

Hilty

McDonnell

Granwehr

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

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We have used nuclear magnetic resonance (NMR) to obtain spatially and temporally resolved profiles of gas flow in microfluidic devices. Remote detection of the NMR signal both overcomes the sensitivity limitation of NMR and enables time-of-flight measurement in addition to spatially resolved imaging. Thus, detailed insight is gained into the effects of flow, diffusion, and mixing in specific geometries. The ability for noninvasive measurement of microfluidic flow, without the introduction of foreign tracer particles, is unique to this approach and is important for the design and operation of microfluidic devices. Although here we demonstrate an application to gas flow, extension to liquids, which have higher density, is implicit.hyperpolarization ͉ xenon ͉ magnetic resonance imaging M iniaturized fluid-handling devices have attracted considerable interest recently in many areas of science (1). Such microfluidic chips perform a variety of functions ranging from analysis of biological macromolecules (2, 3) to catalysis of reactions and sensing in the gas phase (4,5). To enable precise fluid handling, accurate knowledge of the flow properties within these devices is important. Because of low Reynolds numbers, laminar flow is usually assumed. However, either by design or unintentionally, the flow characteristic in small channels is often altered (e.g., by surface interactions, viscous and diffusional effects, or electrical potentials). Therefore, its prediction is not always straightforward (6-8). Currently, most microfluidic flow measurements rely on optical detection of markers (9, 10), requiring the injection of tracers and transparent devices. Here we show profiles of microfluidic gas flow in capillaries and chip devices obtained by NMR in the remote-detection modality (11,12). Through the transient measurement of dispersion (13), NMR is well adaptable for noninvasive yet sensitive determination of the flow field and provides a potentially more powerful tool to profile flow in capillaries and miniaturized flow devices.NMR remote detection separates the encoding of NMR information from the detection of the actual signal. Information about a stationary object of interest is encoded into spin polarization of a mobile sensor by using radiofrequency (rf) pulses and field gradients. The spin sensor is then physically transferred to a different location for detection, which leads to a decisive enhancement of signal whenever geometrical constraints prevent the use of a sensitive NMR coil for detection directly at the sample site (11,12). In the present work, we studied gas flow in model microfluidic devices by using hyperpolarized 129 Xe as a spin-carrying nucleus (14). Experimental ProceduresImage information was encoded with an rf coil that completely encompassed the microfluidic device (Fig. 1). Such a coil arrangement ideally allows NMR-image information to be obtained from the entire microfluidic device. For measuring flow, it provides a decisive advantage over localized detection, which is achievable, for example,...

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Section: Resultsmentioning

confidence: 99%

Microfluidic gas-flow profiling using remote-detection NMR

Hilty

McDonnell

Granwehr

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

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“…At longer mixing times the propagator becomes considerably broadened because the probability increases that all particles will change their radial position significantly during m . The secondary peak occurring at small velocities is also observable in the 1-D propagators (28). This characteristic deviation from the rectangular shape is due to the restricted diffusion in the immediate vicinity of the wall, which is connected to a smaller probability of a velocity change.…”

Section: Laminar Flow Through Cylindrical Pipementioning

confidence: 96%

Spatiotemporal correlations in transport processes determined by multiple pulsed field gradient experiments

Stapf

Han

Heine

et al. 2002

Concepts Magn. Reson.

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Multiple interrogation of spin density distributions by repeated application of narrow pulsed magnetic field gradients is introduced as a general approach to investigate the time behavior of a spin system undergoing macroscopic motion. The joint n-time probability densities obtained from this procedure can be treated directly in terms of the evolution of positions. Alternatively, appropriately designed pulse sequences allow the selective encoding of higher order parameters of motion such as velocity or acceleration. These quantities can be determined repeatedly within one gradient pulse sequence and can be statistically related to each other. Corresponding pulse sequences are presented and 2-dimensional propagators, correlation functions, and correlation coefficients are compared as different means of representing these correlations. The formalism is applied to numerical simulations of the following situations: rotation of an object at constant speed and laminar flow through a cylindrical pipe and a model porous system.

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“…This is done by sampling the entire q-space at varying displacement times D to obtain the propagator for each time [12,14,15,47]. In the asymptotic time limit Gaussian propagators are recovered for dispersion in homogeneous porous media, demonstrating the applicability of the Brownian motion models and the normal ADE.…”

Section: Mr Measurement Of Dispersionmentioning

confidence: 99%

“…in which the t 2a scaling results from the increased spreading due to the variations in velocity as in Taylor dispersion [23,24,[46][47][48].…”

Section: Anomalous Diffusion: Fade Model Of Biofoulingmentioning

confidence: 99%

Finla Technical Report DE-FG02-03ER63576

Seymour¹

2007

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The magnetic resonance microscopy (MRM) work at Montana State University has extended the imaging of a single biofilm in a 1 mm capillary reactor to correlate T 2 magnetic relaxation maps displaying biofilm structure with the corresponding velocity patterns in three dimensions in a Staphylococcus epidermidis biofilm fouled square capillary. A square duct geometry is chosen to provide correlation with existing experiments and simulations, as research bioreactors tend to be of square or rectangular cross section for optical or microelectrode access. The spatially resolved velocity data provide details on the impact of biofilm induced advection on mass transport from the bulk fluid to the biofilm and through the capillary bioreactor. These issues are of significant importance in biosensor and bioseparations applications based on microfluidics or 'lab on a chip' technology, as well as a model for a flow in fractured geological media. Extension of published work in Journal of Magnetic Resonance applied concepts from the theory of fluid mixing to quantify the secondary flows induced by the spatially heterogeneous biofilm. The secondary flows are measured to be 20% of the axial velocity and indicate a significant alteration of transport from the bulk fluid to the biomass from diffusive to convective dominated. A paper has been published in Biotechnology and Bioengineering detailing the experimental results and analysis. The impact of microbial activity, particularly surface attached biofilms, on the transport of fluids in porous systems is relevant to fields as seemingly diverse as geophysics and medicine. Few direct experimental data on the impact of bioactivity on transport dynamics in three-dimensional media are available due to sample opacity. Non-invasive magnetic resonance microscopy (MRM) directly measures length and time scale dependent dynamics in porous media. Our research demonstrates by direct measurement of the propagator, i.e. the displacement conditional probability or van Hove scattering function, the transition from normal to anomalous hydrodynamic dispersion as a function of bioactivity. The microbial activity transforms the porous media from a homogeneous to heterogeneous structure, increasing system complexity as defined in terms of dynamics. Continuous time random walk (CTRW) based fractional advection-diffusion equation (ADE) models which generate anomalous or fractional dynamics are compared to the measured dynamics in both the propagator displacement space and the Fourier reciprocal displacement wavelength space. The data provide insight into the application and development of fractional calculus based models and indicates their direct applicability to biofilm impacted porous media transport. A manuscript reporting these results was published in Physical Review Letters. Unsaturated flow in porous media has been analyzed using magnetic resonance (MR) propagator measurements of scale dependent displacement. The data show a change in dynamics from Gaussian to non-Gaussian. Velocity and pore distrib...

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Taylor dispersion and molecular displacements in Poiseuille flow

Cited by 56 publications

References 14 publications

Microfluidic gas-flow profiling using remote-detection NMR

Microfluidic gas-flow profiling using remote-detection NMR

Spatiotemporal correlations in transport processes determined by multiple pulsed field gradient experiments

Finla Technical Report DE-FG02-03ER63576

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