Large deviations in Taylor dispersion

Kahlen, Marcel; Engel, A.; Broeck, C. Van den

doi:10.1103/physreve.95.012144

Cited by 13 publications

(13 citation statements)

References 24 publications

(31 reference statements)

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“…That is to say, diffusion enhances the transport process. Although random hop rates between nearby streamlines may be the same 47 , the velocity fields along nearby streamlines are by no means always similar. Streamlines undergo a sudden “compression” when entering a narrow throat, which is a typical structure in porous media.…”

Section: Resultsmentioning

confidence: 99%

Ubiquity of anomalous transport in porous media: Numerical evidence, continuous time random walk modelling, and hydrodynamic interpretation

Yang

Wang

2019

Sci Rep

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Anomalous transport in porous media is commonly believed to be induced by the highly complex pore space geometry. However, this phenomenon is also observed in porous media with rather simple pore structure. In order to answer how ubiquitous can anomalous transport be in porous media, we in this work systematically investigate the solute transport process in a simple porous medium model with minimal structural randomness. The porosities we consider range widely from 0.30 up to 0.85, and we find by lattice Boltzmann simulations that the solute transport process can be anomalous in all cases at high Péclet numbers. We use the continuous time random walk theory to quantitatively explain the observed scaling relations of the process. A plausible hydrodynamic origin of anomalous transport in simple porous media is proposed as a complement to its widely accepted geometric origin in complex porous media. Our results, together with previous findings, provide evidence that anomalous transport is indeed ubiquitous in porous media. Consequently, attentions should be paid when modelling solute transport by the classical advection-diffusion equation, which could lead to systematic error.

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Section: Resultsmentioning

confidence: 99%

Ubiquity of anomalous transport in porous media: Numerical evidence, continuous time random walk modelling, and hydrodynamic interpretation

Yang

Wang

2019

Sci Rep

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“…which embodies the same result as in (1). In moving from the second line to the third one we have used the expression for the variance of the time spent in + given in (17). As anticipated, the total dispersion involves thermal fluctuations Tμ and a term related to the mobility switching which is proportional to the square of the applied force and the variance of the time spent in a state.…”

Section: (7)mentioning

confidence: 90%

“…(19) in Ref. [17]) if one identifies µF with the state dependent velocity u in [17]. Composing the two solvability conditions and returning to the original variables we have the following SDE for the effective dynamics…”

Section: Multiple-scales Techniquementioning

confidence: 99%

“…Similar terms were discussed quite some time ago by Van den Broeck and coworkers and by Mackey and co-workers, see e.g. [12][13][14], and recently reconsidered in the context of Taylor dispersion [15][16][17]. The effective diffusion of a protein was recently analyzed in [18] and applied to fluorescence correlation spectroscopy (FCS) measurements in [19].…”

Section: Introductionmentioning

confidence: 96%

“…Although established a long time ago these non-equilibrium steady-state relations appear to have been somewhat occluded, and the recent revival of interest has been motivated by other arXiv:1706.00784v2 [cond-mat.stat-mech] 12 Oct 2017 questions. The analysis of Taylor dispersion in [17] is for instance partly foreshadowed by an analysis of active Brownian motion (Janus particles) [21] using cumulant generating functions, from which expressions like Eq. (1) can be derived.…”

Section: Introductionmentioning

confidence: 99%

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Steady diffusion in a drift field: A comparison of large-deviation techniques and multiple-scale analysis

Aurell

Bò

2017

Phys. Rev. E

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A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while the effective diffusion has two terms. One is of the equilibrium type and satisfies an Einstein relation with the effective mobility while the other is quadratic in the applied force. In this contribution we present two new methods to obtain these results, on the one hand using large deviation techniques, and on the other by a multiple-scale analysis, and compare the two. We consider both systems with discrete internal states and continuous internal states. We show that the auxiliary equations in the multiple-scale analysis can also be derived in second-order perturbation theory in a large deviation theory of a generating function (discrete internal states) or generating functional (continuous internal states). We discuss that measuring the two components of the effective diffusion give a way to determine kinetic rates from only first and second moments of the displacement in steady state.

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Microchip Liquid-Phase Ion Trap for Online Mass Spectrometry Analysis

Dai,

Li,

Meng

et al. 2024

Anal. Chem.

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Liquid-phase ion trapping (LPIT) was proposed recently for ion manipulations in liquid channels. When coupled with mass spectrometry, LPIT exhibits considerable potential in applications such as target enrichment and bottom-up proteomics. However, further evolution of LPIT techniques requires flexible field designs including electric and fluid fields. In this study, LPIT was constructed and implemented on microfluidic chips. Utilizing conductive polymers, nonlinear potential distribution was achieved in the liquid channel, enabling the focusing of ions at distinct locations based on their effective charges and hydrodynamic radii. The integration of an electrospray ionization source facilitated coupling of the LPIT chip with a mass spectrometer. The working mechanism and parameter optimizations were explored through a combination of theoretical analysis and numerical simulations. Experiments showcased the LIPT chip's proficiency in enrichment and separation capabilities. The detection sensitivity of the following mass spectrometer could be improved by ∼10-fold. A good linearity (R 2 > 0.99) was obtained for reserpine in the range of 1−100 ng/mL. The separation capability was demonstrated using a mixture of 11 amino acids.

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Large deviations in Taylor dispersion

Abstract: We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of the long-time regime for Taylor dispersion.

Cited by 13 publications

References 24 publications

Ubiquity of anomalous transport in porous media: Numerical evidence, continuous time random walk modelling, and hydrodynamic interpretation

Ubiquity of anomalous transport in porous media: Numerical evidence, continuous time random walk modelling, and hydrodynamic interpretation

Steady diffusion in a drift field: A comparison of large-deviation techniques and multiple-scale analysis

Microchip Liquid-Phase Ion Trap for Online Mass Spectrometry Analysis

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