Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall

Lee, Ding; Hunt, Robert L.; McLaughlin, Richard M.; Woodie, Hunter

doi:10.1007/s40687-021-00257-4

Cited by 8 publications

(8 citation statements)

References 54 publications

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“…The corresponding effective equation has been reported in the literature of Taylor dispersion (Young & Jones 1991;Taylor 2012;Ding et al 2021):…”

Section: Comparison To the Taylor Dispersion And Reciprocal Propertymentioning

confidence: 99%

“…For example, sodium fluorescein is a tracer used commonly in fluid experiments, and its self-diffusion coefficient in water has been measured experimentally by several authors to be approximately 4-5 × 10 −6 cm 2 s −1 (Casalini et al 2011). However, in a sodium chloride stratified fluid, the diffusion coefficient of sodium fluorescein could exhibit a significant increase, reaching values 8-9 × 10 −6 cm 2 s −1 (Ding et al 2021).…”

Section: Introductionmentioning

confidence: 99%

“…Understanding how fluid flow, electric potential and diffusion interact in multispecies electrolyte solutions is essential for measuring accurately mutual diffusion (Price 1988;Leaist & Hao 1993;Ribeiro et al 2019;Rodrigo et al 2021Rodrigo et al , 2022, as well as for simulating the system with stratified fluids (Ben-Yaakov 1972;Yuan-Hui & Gregory 1974;Poisson & Papaud 1983;Ding et al 2021;Ding & McLaughlin 2023), and for controlling diffusiophoresis (Ault et al 2017;Alessio et al 2022) and modelling isotachophoresis (Bhattacharyya et al 2013;Gopmandal & Bhattacharyya 2015;GanOr, Rubin & Bercovici 2015) and chromatography (Biagioni, Cerbelli & Desmet 2022). Despite its importance, the interplay between these three factors has not been studied extensively in the literature, creating a knowledge gap.…”

Section: Introductionmentioning

confidence: 99%

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Shear dispersion of multispecies electrolyte solutions in the channel domain

Ding

2023

J. Fluid Mech.

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In multispecies electrolyte solutions, even in the absence of an external electric field, differences in ion diffusivities induce an electric potential and generate additional fluxes for each species. This electro-diffusion process is well-described by the advection Nernst–Planck equation. This study aims to analyse the long-time behaviour of the governing equation under electroneutrality and zero current conditions, and to investigate how the diffusion-induced electric potential and shear flow enhance the effective diffusion coefficients of each species in channel domains. The exact solutions of the effective equation with certain special parameters, as well as the asymptotic analyses for ions with large diffusivity discrepancies, are presented. Furthermore, there are several interesting properties of the effective equation. First, it is a generalization of the Taylor dispersion, with a nonlinear diffusion tensor replacing the scalar diffusion coefficient. Second, the effective equation exhibits a scaling relation, revealing that the system with a weak flow is equivalent to the system with a strong flow under scaled physical parameters. Third, in the case of injecting an electrolyte solution into a channel containing well-mixed buffer solutions or electrolyte solutions with the same ion species, if the concentration of the injected solution is lower than that of the pre-existing solution, then the effective equation simplifies to a multi-dimensional diffusion equation. However, when introducing the electrolyte solution into a channel filled with deionized water, the ion–electric interaction results in several phenomena not present in the advection–diffusion equation, including upstream migration of some species, spontaneous separation of ions, and non-monotonic dependence of the effective diffusivity on Péclet numbers. Finally, the dependence of effective diffusivity on concentration and ion diffusivity suggests a method to infer the concentration ratio of each component and ion diffusivity by measuring the effective diffusivity.

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“…The corresponding effective equation has been reported in the literature of Taylor dispersion (Young & Jones 1991;Taylor 2012;Ding et al 2021):…”

Section: Comparison To the Taylor Dispersion And Reciprocal Propertymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shear dispersion of multispecies electrolyte solutions in the channel domain

Ding

2023

J. Fluid Mech.

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“…A special case of flow is the shear flow ξ(t)v = (u(y)ξ(t), 0). This type of flow can originate from either a time varying pressure field, or by randomly moving portions of the boundary, in a high viscosity fluid [13]. Here, we assume that ξ(t) is a Gaussian white noise in time so that R(t, s) = g 2 δ(t − s).…”

Section: Feynman-kac Formula Based Approachmentioning

confidence: 99%

“…We follow the similar multiscale analysis procedure described in the appendix 7.1 of [13] or [30]. We seek the asymptotic approximation to Ψ(x, t) in the limit ǫ → 0 that has the following multiscale expansion,…”

Section: Random Periodic Flowmentioning

confidence: 99%

Correlation function of a random scalar field evolving with a rapidly fluctuating Gaussian process

Bronski¹,

Ding²,

McLaughlin³

2022

Preprint

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We consider a scalar field governed by an advection-diffusion equation (or a more general evolution equation) with rapidly fluctuating, Gaussian distributed random coefficients. In the white noise limit, we derive the closed evolution equation for the ensemble average of the random scalar field by three different strategies, i.e., Feynman-Kac formula, the limit of Ornstein-Uhlenbeck process, and evaluating the cluster expansion of the propagator on an n-simplex. With the evolution equation of ensemble average, we study the passive scalar transport problem with two different types of flows, a random periodic flow, and a random strain flow. For periodic flows, by utilizing the homogenization method, we show that the N-point correlation function of the random scalar field satisfies an effective diffusion equation at long times. For the strain flow, we explicit compute the mean of the random scalar field and show that the statistics of the random scalar field have a connection to the time integral of geometric Brownian motion. Interestingly, all normalized moment (e.g., skewness, kurtosis) of this random scalar field diverges at long times, meaning that the scalar becomes more and more intermittent during its decay.

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Correlation Function of a Random Scalar Field Evolving with a Rapidly Fluctuating Gaussian Process

Ding,

McLaughlin

2023

J Stat Phys

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Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall

Cited by 8 publications

References 54 publications

Shear dispersion of multispecies electrolyte solutions in the channel domain

Shear dispersion of multispecies electrolyte solutions in the channel domain

Correlation function of a random scalar field evolving with a rapidly fluctuating Gaussian process

Correlation Function of a Random Scalar Field Evolving with a Rapidly Fluctuating Gaussian Process

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