On the thin-film asymptotics of surface tension driven microfluidics

Calver, S. N.; Gaffney, Eamonn A.; Walsh, Edmond J.; Durham, William M.; Oliver, James M.

doi:10.1017/jfm.2020.532

Cited by 8 publications

(12 citation statements)

References 35 publications

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“…We do so using asymptotic analysis, a technique used by many authors to study surface tension (e.g. by Calver et al 2020) and by others to capture early time and late-time hydrodynamics phenomena (see, e.g. Hinton & Woods 2018;Kiradjiev et al 2019).…”

Section: Long-time Asymptotic Approximationsmentioning

confidence: 99%

“…The role of surface tension on fluids within different geometries has been investigated experimentally, analytically and computationally for different scientific purposes. For example, using experiments via microfluidics, Calver et al (2020) investigated the tuning of flows driven by surface tension in small geometries that connects two liquid drops. Using matched asymptotic expansion, they successfully validated the dependence relation of drainage time to channel aspect ratio.…”

Section: Introductionmentioning

confidence: 99%

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Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

et al. 2022

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The unsteady effects of transitioning surface tension, $\gamma (t)$ , on the dynamics of capillary imbibition in channels of arbitrary shape are analytically investigated with a focus on rectangular and circular channels. With proper scaling, two unsteady models for $\gamma (t)$ are defined and used to highlight this transient behaviour. The convoluted dynamics at the flow front are correctly captured in the governing equations, which are rigorously analysed using unsteady eigenfunction expansion. Then, the final solution and data are obtained by employing the Runge–Kutta fourth-order scheme elegantly applied simultaneously to two derived nonlinear ordinary differential equations. Ultimately, the results are more accurate compared with previous studies. Dynamics and kinematic similarity between rectangular and circular channels are investigated and discussed and the conditions for equivalence in both channels are highlighted. Using a small parameter ( $\epsilon$ ) that stretches the time scale, we successfully use a robust asymptotic analysis to develop and capture the long-time dynamics. Ultimately, we recover the Lucas–Washburn regime analysed in Washburn (Phys. Rev., vol. 17, 1921, pp. 273–283), Lucas (Kolloidn. Z., vol. 23, 1918, pp. 15–22) for steady surface tension where the variations of depth and rate with time result in $h\thicksim t^{1/2}$ and $v \thicksim t^{-1/2}$ . In the end, the three forces, namely the inertia, $F_{v}$ , the viscous, $F_{\mu }$ , and the surface tension, $F_{\gamma }$ , are briefly analysed and used to highlight three main distinct regimes. We show that at early times, $F_{v}/F_{\gamma } \thicksim 1$ , whereas at a long time, $F_{\mu }/F_{\gamma } \thicksim -1$ .

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Section: Long-time Asymptotic Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

et al. 2022

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“…The circuit in Figure 3B‐iii serially dilutes and mixes dyes; pipetting dyes into input drops increases local pressures so chamber a fills only with red dye, f only with blue, and b–e with dilute mixtures. Flow rates in circuits without external pumps depend on many factors (e.g., circuit geometry, density, viscosity, and interfacial tension), but can be predicted, [ 22 ] and—for a fixed footprint—are maximal when the contact angle of the source drop is 90° and the sink drop is completely flat. Geometrical changes can have a large impact: increasing conduit width from 590 to 880 µm in a dumbbell‐shaped circuit can increase flow rate sixfold.…”

Section: Flow With and Without External Pumpsmentioning

confidence: 99%

Microfluidics on Standard Petri Dishes for Bioscientists

et al. 2021

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Few microfluidic devices are used in biomedical labs, despite the obvious potential; reasons given include the devices are rarely made with cell‐friendly materials, and liquids are inaccessibly buried behind solid confining walls. An open microfluidic approach is reviewed in which aqueous circuits with almost any imaginable 2D shape are fabricated in minutes on standard polystyrene Petri dishes by reshaping two liquids (cell‐culture media plus an immiscible and bioinert fluorocarbon, FC40). Then, the aqueous phase becomes confined by fluid FC40 walls firmly pinned to the dish by interfacial forces. Such walls can be pierced at any point with pipets and liquids added or removed through them, while flows can be driven actively using external pumps or passively by exploiting local differences in Laplace pressure. As walls are robust, permeable to O2 plus CO2, and transparent, cells are grown in incubators and monitored microscopically as usual. It is hoped that this simple, accessible, and affordable fluid‐shaping technology provides bioscientists with an easy entrée into microfluidics.

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“…2012; Calver et al. 2020). On the other hand, the structuring of channels by parallel grooves has also been shown to improve the efficacy of microfluidic devices: for example, railed microfluidic channels have been used to create superhydrophobic surfaces (Yoshimitsu et al.…”

Section: Introductionmentioning

confidence: 99%

“…2017; Calver et al. 2020); directional transport of liquids in biological processes (Prakash, Quéré & Bush 2008; Zheng et al. 2010; Ju et al.…”

Section: Introductionmentioning

confidence: 99%

The effect of isolated ridges and grooves on static menisci in rectangular channels

2022

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We present theoretical and numerical results that demonstrate the sensitivity of the shape of a static meniscus in a rectangular channel to localised geometric perturbations in the form of narrow ridges and grooves imposed on the channel walls. The Young–Laplace equation is solved for a gas/liquid interface with fixed contact angle using computations, analytical arguments and semi-analytical solutions of a linearised model for small-amplitude perturbations. We find that the local deformation of the meniscus's contact line near a ridge or groove is strongly dependent on the shape of the perturbation. In particular, small-amplitude perturbations that change the channel volume induce a change in the pressure difference across the meniscus, resulting in long-range curvature of its contact line. We derive an explicit expression for this induced pressure difference directly in terms of the boundary data. We show how contact lines can be engineered to assume prescribed patterns using suitable combinations of ridges and grooves.

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On the thin-film asymptotics of surface tension driven microfluidics

Abstract: Abstract

Cited by 8 publications

References 35 publications

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

Microfluidics on Standard Petri Dishes for Bioscientists

The effect of isolated ridges and grooves on static menisci in rectangular channels

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