Scaling law for cross-stream diffusion in microchannels under combined electroosmotic and pressure driven flow

Song, Hongjun; Wang, Yi; Pant, Kapil

doi:10.1007/s10404-012-1058-8

Cited by 14 publications

(10 citation statements)

References 29 publications

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“…A combined pressure-driven and electroosmotic flow is used to separate ionic species in a nanofluidic channel by Gillespie and Pennathur [20]. In a recent paper, Song et al [21] have studied analytically the convection-diffusion of an analyte in a rectangular channel under EOF and pressure driven flow. There they have considered the effect of both negative as well as a positive pressure gradient.…”

Section: Introductionmentioning

confidence: 99%

Combined electroosmosis-pressure driven flow and mixing in a microchannel with surface heterogeneity

Bhattacharyya

Bera

2015

Applied Mathematical Modelling

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a b s t r a c tWe investigate the combined pressure-driven electroosmotic flow near a wall roughness in the form of a rectangular block mounted on one wall of an infinitely long microchannel. The insulated rectangular block has a constant surface potential which is different from the surface potential of the remaining part of the channel walls. The characteristics for the electrokinetic flow are obtained by numerically solving the Navier-Stokes equations coupled with the Nernst-Planck equation for ion transport and the Poisson equation for electric field. Vortical flow develops above the block when the surface potential of the block is in opposite sign to that of the surface potential of the channel. The strength of the re-circulating vortex grows as the surface potential of the block increases. Vortical flow also depends on the Debye length when it is in the order of the channel height. The combined effects due to the geometrical modulation of the channel wall and heterogeneity in surface potential is found to produce a stronger vortex and hence a stronger mixing, as compared with the effect of either of these. The recirculating vortex, which appears on the upper face of the block, grows and the average electroosmotic velocity increases with the increase of the electrolyte concentration. The recirculating vortex does not appear when EDL is thick and the effect of over-potential of the block on electroosmosis is negligible. The loss of momentum near the obstacle is compensated by the electrostatic force near the EDL, which prevents flow separation upstream or downstream of the obstacle. The mixing performance of the present configuration is compared with several other cases of surface modulation. The impact of the imposed pressure gradient on the vortical flow due to surface heterogeneity is analyzed.

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Section: Introductionmentioning

confidence: 99%

Combined electroosmosis-pressure driven flow and mixing in a microchannel with surface heterogeneity

Bhattacharyya

Bera

2015

Applied Mathematical Modelling

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“…When it comes to micromixers, besides the above‐mentioned advantages, the analytical approaches offer a unique feature which is omitting the false diffusion associated with the discretization of the governing equations in numerical approaches . To the author's best knowledge, the most complete analytical solution of species transport in Y/T‐sensors is the one due to Song et al. This work deals with hydrodynamically fully developed conditions and assumes the Peclet number to be large enough to allow neglect of the axial diffusion effects.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, under the premise of a hydrodynamically developed flow, a 3D analytical solution is derived for species transport in an electrokinetic T‐sensor by taking the axial diffusion effects into account. We consider the actual variations of the velocity within EDL, unlike Song et al that applied a slip velocity at the wall to account for the electrokinetic effects. Even though specific calculations are done assuming a main channel of rectangular cross‐section, the mass transport analysis is general enough to be easily extended to almost any arbitrary geometry.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for species transport in a T‐sensor at low peclet numbers

Sadeghi

2016

AIChE Journal

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A 3D analytical solution is presented for the problem of mass transport in a T-sensor by taking the axial diffusion effects into account. The solution methodology is based on an eigenfunction expansion of the solute concentration and enjoys the variational calculus for the solution of the associated eigenvalue problem. The method is capable of handling a mixed electroosmotic and pressure-driven velocity profile and is executed assuming a rectangular channel crosssection although it can be easily extended to more complex geometries. Two simplified models, one based on a uniform velocity profile, valid for the channel half height to Debye length ratios of above 100, and the other based on a depthwise averaging of the species concentration to be used for cases in which the channel width to height ratio is above 5 are also presented. As a part of the latter, expressions are derived for the Taylor dispersion coefficient of the mixed flow in a slit microconduit. The most interesting finding of this study is that, when the diffusion mechanism significantly contributes to the axial movement of the species, the well-known heterogeneous mass transport evolves into a nearly uniform pattern in the depthwise direction and the mixing length noticeably increases.The predictions of the thin EDL solution are also presented to be compared with those of C50.

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“…The approach being undertaken in this work, however, is subject to inherent weaknesses of numerical analyses such as prohibitive computational costs, demanding large amount of data to deduce the governing law, and the difficulty of providing physical insights into the underlying transport mechanism. In addition, closely related to the very specific problem considered, numerical diffusion caused by the discretization of the governing equations may induce artificial broadening of the diffusion zone, leading to some errors in the analysis (Song et al 2013). Analytical solutions, on the other hand, are hardly achievable but can successfully remove the abovementioned shortcomings.…”

Section: Introductionmentioning

confidence: 98%

“…More recently, Jeong et al (2011) developed a novel electrokinetic micromixer based on a Y-shaped configuration that involved the use of a periodic secondary voltage. In a theoretical study, Song et al (2013) presented analytical solutions for cross-stream diffusion of species under combined electroosmotic and pressure-driven flow. In their work, the heterogeneous transport behavior and spatially dependent diffusion scaling law for a Y-sensor were extensively investigated.…”

Section: Introductionmentioning

confidence: 99%

A depthwise averaging solution for cross-stream diffusion in a Y-micromixer by considering thick electrical double layers and nonlinear rheology

Yazdi

Sadeghi

Saidi

2015

Microfluid Nanofluid

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List of symbolsFlow consistency index (Pas n ) n Flow behavior index n 0 Ion density at neutral conditions (m −3 )Axial coordinate of moving reference frame (m) Z Valence number of ions in solutionGreek symbols α Channel aspect ratio (=W/H) δDimensionless thickness of diffusion layer εFluidEffective viscosity (Pas)Abstract Both nonlinear rheology and finite EDL thickness effects on the mixing process in an electroosmotically actuated Y-sensor are being investigated in this paper, utilizing a depthwise averaging method based on the Taylor dispersion theory. The fluid rheological behavior is assumed to obey the power-law viscosity model. Analytical solutions are obtained assuming a large channel width to depth ratio for which a 1-D profile can efficiently describe the velocity distribution. Full numerical simulations are also performed to determine the applicability range of the analytical model, revealing that it is able to provide accurate results for channel aspect ratios of ten and higher and quite acceptable results for smaller aspect ratios down to four. The model is then used for a complete parametric study to determine the effects of the governing parameters on the mixing performance. It is observed that utilizing a fluid with a higher flow behavior index gives rise to a smaller mixing length. Moreover, whereas a larger EDL thickness is accompanied by an improved mixing efficiency, the opposite is true for the channel aspect ratio. The effective diffusivity is also found to be an increasing function of the EDL extent and a decreasing function of the flow behavior index.

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Scaling law for cross-stream diffusion in microchannels under combined electroosmotic and pressure driven flow

Cited by 14 publications

References 29 publications

Combined electroosmosis-pressure driven flow and mixing in a microchannel with surface heterogeneity

Combined electroosmosis-pressure driven flow and mixing in a microchannel with surface heterogeneity

Analytical solutions for species transport in a T‐sensor at low peclet numbers

A depthwise averaging solution for cross-stream diffusion in a Y-micromixer by considering thick electrical double layers and nonlinear rheology

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