Dispersion control in pressure-driven flow through bowed rectangular microchannels

Lee, Garam; Luner, Alan; Marzuola, Jeremy L.; Harris, Daniel M.

doi:10.1007/s10404-021-02436-9

Cited by 8 publications

(8 citation statements)

References 24 publications

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“…As we expected, the standard homogenization result on this timescale is substantially worse than both center manifold results. Alternatively, at higher frequency, with ω = 20π, (38) performs visibly worse than both standard homogenization (41) as well as the time-dependent center manifold results (40). These observations from the numerical simulation are consistent with our previous theoretical analysis.…”

Section: Improvements Compared With Previous Studiessupporting

confidence: 89%

“…The left column shows the result for a small frequency, ω = π/5. The cross-sectional average of the numerical solution, the solution of effective equations (38) and (40) are almost indistinguishable. Recall that the standard homogenization result (41) requires t O( 1 ω ).…”

Section: Improvements Compared With Previous Studiesmentioning

confidence: 93%

“…We consider the problem in a channel domain (x, y) ∈ R × Ω, where the x-direction is the longitudinal direction of the channel and Ω ⊂ R d stands for the cross section of the channel. Some practical examples of the boundary geometry includes the parallelplate channel Ω = {y|y ∈ [0, L]}, the circular pipe Ω = {y|y 2 ≤ L}, the rectangular duct Ω = {y|y ∈ [0, L] 2 }, bowed rectangular channels [40]. The passive scalar is governed by the advection-diffusion equation with a general time-varying shear flow u(y, t) and no-flux boundary condition which takes the form…”

Section: Governing Equation and Nondimensionalization 211 Advection-d...mentioning

confidence: 99%

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Determinism and invariant measures for diffusing passive scalars advected by unsteady random shear flows

Lee¹,

McLaughlin²

2021

Preprint

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Here we study the long time behavior of an advection-diffusion equation with a general time varying (including random) shear flow imposing no-flux boundary conditions on channel walls. We derive the asymptotic approximation of the scalar field at long times by using center manifold theory. We carefully compare it with existing time varying homogenization theory as well as other existing center manifold based studies, and present conditions on the flows under which our new approximations give a substantial improvement to these existing theories. A recent study [30] has shown that Gaussian random shear flows induce a deterministic effective diffusivity at long times, and explicitly calculated the invariant measure. Here, with our established asymptotic expansions, we not only concisely demonstrate those prior conclusions for Gaussian random shear flows, but also generalize the conclusions regarding determinism to a much broader class of random (non-Gaussian) shear flows. Such results are important ergodicity-like results in that they assure an experimentalist need only perform a single realization of a random flow to observe the ensemble moment predictions at long time. Monte-Carlo simulations are presented illustrating how the highly random behavior converges to the deterministic limit at long time. Counterintuitively, we present a case demonstrating that the random flow may not induce larger dispersion than its deterministic counterpart, and in turn present rigorous conditions under which a random renewing flow induces a stronger effective diffusivity.

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Section: Improvements Compared With Previous Studiessupporting

confidence: 89%

Section: Improvements Compared With Previous Studiesmentioning

confidence: 93%

Section: Governing Equation and Nondimensionalization 211 Advection-d...mentioning

confidence: 99%

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Determinism and invariant measures for diffusing passive scalars advected by unsteady random shear flows

Lee¹,

McLaughlin²

2021

Preprint

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“…Consequently, approximating such a geometry by a semicircular one, for better mathematical tractability, looks quite reasonable. This, together with the fact that geometry plays a very important role in hydrodynamic dispersion (Lee et al 2021), persuaded the authors to focus on the problem of hydrodynamic dispersion within semicircular microchannels in the present study. To this end, the generalized dispersion model (Sankarasubramanian & Gill 1973) is invoked to track an injected solute band of arbitrary axial distribution and general shape in the cross-sectional area from the time of injection considering a steady and fully developed flow.…”

Section: Introductionmentioning

confidence: 94%

Unsteady convective–diffusive transport in semicircular microchannels with irreversible wall reaction

Azari

Sadeghi

2022

J. Fluid Mech.

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The unsteady dispersion of a solute band by a steady pressure-driven flow in a semicircular microchannel is theoretically studied via the generalized dispersion model. Considering an irreversible first-order reaction at the curved wall while assuming a no-flux boundary condition at the flat wall, analytical solutions are obtained for the exchange, convection and dispersion coefficients as well as the dimensionless forms of solute concentration and mean solute concentration. The solutions are obtained assuming an initial solute band of arbitrary cross-sectional shape and axial distribution and the results are presented for both circular and semicircular shapes with the uniform distribution being a special case of the latter. Besides the general solutions, special solutions are also derived for uniform velocity and no-reaction cases. In the following, the influences of the initial concentration distribution and the Damköhler number, a measure of the reaction rate, on the transport coefficients and the concentration distribution are investigated in depth. It is demonstrated that the combination of the initial concentration distribution and the Damköhler number specifies the variations of the transport coefficients in the short term but the Damköhler number is the only parameter dominating the long-term values: the exchange and convection coefficients are increasing functions of the Damköhler number whereas the opposite is true for the dispersion coefficient. Moreover, we show that, provided the solute injection is appropriately positioned and shaped, liquid-phase transportation with little dispersion is possible in typical microchannels utilizing semicircular geometry.

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“…where C = αw/E with α given in (36) for a flow conduit with Cartesian geometry. A typical microchannel with a thin deformable membrane as its top wall has C ≈ 1 − 10 µm/kPa (experimental fit) [129]. Equation ( 40) can be solved as a separable first-order ODE to obtain:…”

Section: Analytical Models For the Coupled Problem And Their Solutionmentioning

confidence: 99%

Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits

Christov

2021

Preprint

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Microfluidic devices manufactured from soft polymeric materials have emerged as a paradigm for cheap, disposable and easy-to-prototype fluidic platforms for integrating chemical and biological assays and analyses. The interplay between the flow forces and the inherently compliant conduits of such microfluidic devices requires careful consideration. While mechanical compliance was initially a side-effect of the manufacturing process and materials used, compliance has now become a paradigm, enabling new approaches to microrheological measurements, new modalities of micromixing, and improved sieving of micro-and nano-particles, to name a few applications. This topical review provides an introduction to the physics of these systems. Specifically, the goal of this review is to summarize the recent progress towards a mechanistic understanding of the interaction between non-Newtonian (complex) fluid flows and their deformable confining boundaries. In this context, key experimental results and relevant applications are also explored, hand-in-hand with the fundamental principles for their physics-based modeling. The key topics covered include shear-dependent viscosity of non-Newtonian fluids, hydrodynamic pressure gradients during flow, the elastic response (bulging and deformation) of soft conduits due to flow within, the effect of cross-sectional conduit geometry on the resulting fluid-structure interaction, and key dimensionless groups describing the coupled physics. Open problems and future directions in this nascent field of soft hydraulics, at the intersection of non-Newtonian fluid mechanics, soft matter physics, and microfluidics, are noted.

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Dispersion control in pressure-driven flow through bowed rectangular microchannels

Cited by 8 publications

References 24 publications

Determinism and invariant measures for diffusing passive scalars advected by unsteady random shear flows

Determinism and invariant measures for diffusing passive scalars advected by unsteady random shear flows

Unsteady convective–diffusive transport in semicircular microchannels with irreversible wall reaction

Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits

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