Flows in rectangular microchannels driven by capillary force and gravity

Jong, Wen-Ren; Kuo, T.H.; Ho, Soon-Seng; Chiu, Huag-Jen; Peng, Shouchang

doi:10.1016/j.icheatmasstransfer.2006.09.011

Cited by 61 publications

(47 citation statements)

References 7 publications

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“…Strage et al, 2003), rectangular (e.g. Ichikawa et al, 2004;Jong et al, 2007;Zhu and Petkovic-Duran, 2010) and grooved/triangular (Yost and Holm, 1995;Romero and Yost, 2006;Baret et al, 2007). Moreover, the same approach has been taken for channels defined by hydrophilic paths on a hydrophobic substrate (Darhuber et al, 2001) and by the space between two parallel plates (Rosendahl et al, 2004) under the assumption of flow with low Reynolds number and liquid imbibing in a tube/slablike manner.…”

Section: Introductionmentioning

confidence: 99%

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

Ouali

McHale

Javed

et al. 2013

Microfluid Nanofluid

149

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The spontaneous capillary-driven filling of microchannels is important for a wide range of applications. These channels are often rectangular in cross-section, can be closed or open, and horizontal or vertically orientated. In this work, we develop the theory for capillary imbibition and rise in channels of rectangular cross-section, taking into account rigidified and non-rigidified boundary conditions for the liquid-air interfaces and the effects of surface topography assuming Wenzel or Cassie-Baxter states. We provide simple interpolation formulae for the viscous friction associated with flow through rectangular cross-section channels as a function of aspect ratio. We derive a dimensionless cross-over time, T c , below which the exact numerical solution can be approximated by the Bousanquet solution and above which by the visco-gravitational solution. For capillary rise heights significantly below the equilibrium height, this cross-over time is T c  (3X e /2) 2/3 and has an associated dimensionless crossover rise height X c  (3X e /2) 1/3 , where X e =1/G is the dimensionless equilibrium rise height and G is a dimensionless form of the acceleration due to gravity. We also show from wetting considerations that for rectangular channels, fingers of a wetting liquid can be expected to imbibe in advance of the main meniscus along the corners of the channel walls. We test the theory via capillary rise experiments using polydimethylsiloxane oils of viscosity 96.0, 48.0, 19.2 and 4.8 mPa s within a range of closed square tubes and open rectangular cross-section channels with SU-8 walls. We show that the capillary rise heights can be fitted using the exact numerical solution and that these are similar to fits using the analytical visco-gravitational solution. The viscous friction contribution was found to be slightly higher than predicted by theory assuming a non-rigidified liquid-air boundary, but far below that for a rigidified boundary, which was recently reported for imbibition into horizontally mounted open microchannels. In these experiments we also observed fingers of liquid spreading along the internal edges of the channels in advance of the main body of liquid consistent with wetting expectations. We briefly discuss the implications of these observations for the design of microfluidic systems.

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Section: Introductionmentioning

confidence: 99%

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

Ouali

McHale

Javed

et al. 2013

Microfluid Nanofluid

149

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“…(33). As [8] and [9] both showed good agreement of Eq. (33) with experimental values of L, this serves as validation of the present model for times larger than the characteristic time scale t chr .…”

Section: Comparisons With Other Models and Experimentsmentioning

confidence: 55%

“…In the model including wall friction, the velocity decreases with time and the fluid penetrates smaller and smaller distances into the capillary. Both Schwiebert and Leong [8] and Jong et al [9] derived expressions for surface tension driven flow between parallel plates. In both studies the length as a function of time can be given as…”

Section: Comparisons With Other Models and Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

Macroscopic conservation equation based model for surface tension driven flow

Adams

White

2008

Advances in Fluid Mechanics VII

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Due to the small scales encountered in MEMS and microfluidic devices, surface tension can play a significant role in the device physics. As such, many microscale devices have exploited surface tension forces to serve as passive valves and to move fluids. Surprisingly, few models for surface tension driven flow seem to have been developed.In this study a theoretical mathematical model for surface tension driven flow through a capillary of an arbitrary cross section is derived. The model is based on macroscopic mass and momentum balances, allowing for different physical insights to be drawn compared to approaches starting with the Navier-Stokes equations. Expressions for flow length and velocity are derived for both frictionless flow and for flow with wall friction. For frictionless flow the result of surface tension force is to increase the momentum of the fluid by constantly drawing mass into the capillary at a constant characteristic velocity. In the case of flow with wall friction, a characteristic time scale can be calculated. For times on the order of the characteristic time scale, the flow velocity exponentially decays from the characteristic velocity, whereas for larger times the velocity shows an inverse power law dependence. The model well predicts flow behaviour for previously published experiments in which the characteristic time is small. For systems in which the characteristic time is larger, the model may show improved performance over previous models.

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“…It is known that the capillary flow rates in a microfluidic channel are dependent on the contact angle of the channel surface (Jong et al 2007). Therefore, capillary flow rates were determined in straight microfluidic channels (5 cm).…”

Section: The Flow Behavior In Microchannelmentioning

confidence: 99%

Development and characterization of a capillary-flow microfluidic device for nucleic acid detection

Jin

Dai

et al. 2012

Microsyst Technol

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We have developed a capillary flow-driven microfluidic biosensor to meet the needs of diagnostics for resource-limited areas. The device combined elements of lateral flow assays and microfluidic technology resulting in a hybrid with benefits of both formats. The biosensor was achieved by bonding two pieces of polymethyl methacrylate with channels ablated by a CO 2 laser, and enclosing an absorbent pad. The channels were UV/ozone treated to increase hydrophilicity which enabled capillary flow. The absorbent pad allowed for continuous flow in the channels once filled. The application of biosensor was demonstrated by detection of DNA with a sandwich assay. The target DNA was hybridized with nucleic acid modified magnetic beads as well as Ru(bpy) 3 2? doped silica nanoparticles. Fluorescent signals were quantified in a holder fabricated to fit in a fluorescent microtiter plate reader. The capillary flow microfluidic was capable to detect 1 pmol target. The assay format which features rapid analysis and does not require the use of pumps could allow for inexpensive point of care diagnostics in the future.

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Flows in rectangular microchannels driven by capillary force and gravity

Cited by 61 publications

References 7 publications

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

Macroscopic conservation equation based model for surface tension driven flow

Development and characterization of a capillary-flow microfluidic device for nucleic acid detection

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