capillary force valves

7/27/2019 Capillary Force Valves

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192 Capillary Flow

Transport of Droplets by Thermal CapillarityWetting and Spreading

References

1. Yih CH (1995) Kinetic-energy mass, momentum mass, and driftmass in steady irrotational subsonic ow. J Fluid Mechanics297:29–36

2. Huang W, Bhullar RS, Fung YC (2001) The surface-tension-driven ow of blood from a droplet into a capillary tube. ASME JBiomedical Eng 123:446–454

3. Chakraborty S (2005) Dynamics of capillary ow of blood intoa microuidic channel. Lab Chip 5:421–430

4. Law HS, Fung YC (1970) Entry ow into blood vessels at arbi-trary Reynolds number. J Biomechanics 3:23–38

5. Hoffman RL (1975) A study of the advancing interface I. Interfaceshape in liquid-gas systems. J Colloid Interface Sci 50:228–235

6. Sheng P, Zhou M (1992) Immiscible-uid displacement: contact-line dynamics and the velocity-dependent capillary pressure. PhysRev A 45:5694–5708

7. Tso CP, Sundaravadivelu K (2001) Capillary ow between par-allel plates in the presence of an electromagnetic eld. J Phys D34:3522–3527

8. Yang J, Lu F, Kwok DY (2004) Dynamic interfacial effect of elec-troosmotic slip ow with a moving capillary front in hydrophobiccircular microchannels. J Chem Phys 121:7443–7448

9. Yang L-J, Yao T-J, Tai Y-C (2004) The marching velocity of thecapillary meniscus in a microchannel. J Micromech Microeng14:220–225

10. Tas NR, Haneveld J, Jansen HV, Elwenapoek, van den Berg A(2004) Capillary lling speed of water in nanochannels. Appl PhysLett 18:3274–3276

Capillary Flow

Surface Tension Driven Flow

Capillary Force Valves

DANIEL IRIMIA

Massachusetts General Hospital,Harvard Medical School, Boston, MA, [email protected]

Synonyms

Capillary valves

Denition

Capillary force valves are uid control structures that usesupercial tension at the interface between different uidsto block and/or restore the entrance of uids in microchan-nels lled with a second immiscible uid. For most of themicrouidic applications the second uid is air, and the

liquid–air interface at a narrow hydrophobic stricture isused to prevent the liquid from entering a capillary.

Overview

Capillary forces result from the interaction of liquid, gasand solid surfaces, at the interface between them. Inthe liquid phase, molecules are held together by cohe-sive forces. In the bulk of the liquid, the cohesive forcesbetween one molecule and the surrounding molecules arebalanced. However, for the same molecule at the edge of the liquid, the cohesive forces with other liquid moleculesare larger than the interaction with air molecules (Fig. 1).As a result, the liquid molecules at the interface are pulledtogether towards the liquid. The overall effect of theseforces is to minimize the free surface of the liquid that isexposed to air. The proportionality between the decrease

in energy of the surface that results from decreasing thesurface is described by the surface tension :

γ =dGd A

where d G is the change in energy [Nm], d A is the changein area [m 2] and γ is the surface tension or surfaceenergy [N / m].Of interest for capillary forces is the contact betweenthree phases: liquid, solid and vapor (air). Three forcesare present, trying simultaneously to minimize the contactarea between the three phases. At equilibrium, the forcesat the triple interface are balanced (Fig. 2) and the rela-tionship between them is described by the Young–Dupree

Capillary Force Valves, Figure 1 Supercial tension forces at the inter-face between a liquid and air. For molecules in the liquid there is a balanceof the cohesive forces (F = 0), while for molecules closer to the interface,the cohesive forces with other molecules in the liquid are larger than theinteraction with air molecules (resultant forceF towards the bulk of theliquid)



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Capillary Force Valves 193

equation:

γ AS L = γ LS L + γ LA L × cos

where L is the length of the triple contact line and is

the contact angle between the liquid and the solid. It isinteresting to observe the vertical component pulling onthe solid surface in the case of wetting and pushing in thecase of non-wetting surfaces.Capillary forces are critical at the microscale. The surfacetension is responsible for the increased pressure in a bub-ble trapped in a capillary, and for the increased pressurerequired to push liquid into an empty non-wetting capillary(Fig. 3). The relation between surface tension and pressureis given by the Laplace equation:

P = γ C

where C is the curvature of the liquid surface. Depend-ing of the shape of the capillary, different formulas for thecurvature are available:

C =2

R

C =1

R1+

1 R2

where R is the curvature radius for the liquid in a circularcapillary and R1 and R2 are the curvatures in a non-circularcapillary.

Basic Methodology

The behavior of air and liquids in capillaries is of criti-cal importance at the microscale. After their fabrication,most of the channels in microuidic devices are lled withair. In general, before the microuidic devices are used

Capillary Force Valves, Figure 2 Capillary forces at the interactionbetween air, liquid and solid surfaces. Each of these forces works to min-imize the energy of the interface between liquid and solid, air and solid,liquid and air:F ls, F as , F la, respectively. At equilibrium, the horizontal pro- jection ofF la and F ls and F as cancel each other. The corresponding anglebetween F la and F ls is the contact angle between liquid and solid ( )

Capillary Force Valves, Figure 3 Capillary forces in hydrophilic capillar-ies result in increased pressure in trapped air bubbles. Capillary forces inhydrophobic capillaries prevent liquid from entering the capillary, and canbe overcome by larger pressure

for their designed purpose, the air inside the microuidicchannels has to be replaced by the working uid. How-ever, there are many applications where not all the airis replaced at once, and the advance of uid inside themicrouidic channels is controlled through capillary forcevalves.Two major strategies for making valves using the capillaryforces are through the use of (a) local changes of contactangle and (b) local changes of surface geometry.(a) The use of hydrophobic patches in a capillary relies onthe increased pressure that is required to push the liquidover the area of larger contact angle (Fig. 4). The increasedcontact angle between the liquid and the capillary in theregion of the hydrophobic patch results in a larger pres-sure necessary for moving the liquid over that region.After passing the patch, the pressure required for movingthe liquid returns to pre-patch values. The combination of hydrophobic patches on the bottom of the channel is of interest for microuidic devices where precise valving isrequired, or for liquids with different characteristics.One other particular effect of practical interest whenevercapillary forces are used is the difference between advanc-ing and receding angles for the same uid in the same cap-illary. This phenomenon is also known as hysteresis andmanifests itself as larger contact angle at the advancingedge of a liquid–solid interface compared to the equilib-rium contact angle which is itself larger than the contactangle at the receding edge of the liquid–solid interface(Fig. 5). The origin of this is partially in the roughness of the surface and can have interesting effects when movingcolumns of liquids through capillaries [1].



194 Capillary Force Valves

Capillary Force Valves, Figure 4 Schematics of a capillary valve usinga hydrophobic patch. The pressure required to move the liquid ( P 1 )is higher when the liquid–air interface reaches the region of increasedhydrophobicity ( P 2)

Capillary Force Valves, Figure 5 Hysteresis in contact angle. The con-tact angle at the advancing interface ( a ) is usually larger than the equi-librium contact angle ( e), and larger than the contact angle at the trailinginterface ( t)

(b) The larger contact angle at advancing interfaces canbe used in capillary valves as well, in combination withlocal change of the shape of the surface or the changein the diameter of the capillary (Fig. 6). This approachto controlling a liquid–air interface can be used alone orin combination with the hydrophobic patches. Althoughthe uid control is usually less precise for valves usingchanges in diameter compared to valves using hydropho-bic patches, their implementation in microuidic devicesis overall easier.

Key Research Findings

For the majority of microuidic devices the initial lling(priming) of the device with liquid or the formation of airbubbles inside can render the device unusable. However,

Capillary Force Valves, Figure 6 Schematics of capillary valves usingchanges in the diameter of the capillary. Rapid enlargement of a capil-lary changes the physical angle between the liquid interface and the solidsurface and can form a temporary barrier for the advancing liquid ( P 1).Reducing the diameter of a hydrophobic capillary reduces the radius of cur-vature of the interface and requires larger pressure ( P 2) to move the liquidand could also function as a valving mechanism

there are numerous examples that use the liquid–air inter-faces to control the ow of liquid for different applica-tions. Wall-less control of the ow of liquid streams hasbeen demonstrated on micropatterned hydrophobic sur-faces (Fig. 7) [2]. Micropatterned patches have been usedto precisely stop the liquid ow at a certain position insidea channel without the need for moving parts (Fig. 8) [3],and for the accurate metering of nanoliter volumes of liq-

uids in microchannels [4, 5]. Handling of minute volumesof uids and mixing inside a capillary have been reported.Through the use of passive valves to control the ow of uid and air bubbles expanded from side chambers, vol-umes of liquids down to 25 pL can be handled precisely(Fig. 9) [6]. The hydrophobic nature of the liquid–wallinteraction was critical for stable and complete separationof picoliter volumes of uid [7].Capillary valves are burst valves, i. e. once the liquidpasses through them they no longer function as valves.Resetting a capillary valve requires the formation of theliquid–liquid or liquid–gas interface at the location of hydrophobic interaction. This can be achieved by theinjection of gas or liquid, usually in a small volume, froma reservoir or generated on the chip [6, 8].

Future Directions for Research

Capillary valves have no moving parts, are simple andeasy to implement and thus are very attractive for low-cost microuidic devices. At the same time, several areasof improvement are under scrutiny, to increase the per-formance of the valve, to improve the integration and to



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Capillary Force Valves 195

Capillary Force Valves, Figure 7 Hydrophilic and hydrophobic patchesare used to control the ow of liquid streams (here rhodamine in water)in a wall-less conguration, just by relying on the surface tension of theliquid [2] ( Color Plate11)

Capillary Force Valves, Figure 8 Capillary burst valves are used to con-trol the sequential mixing of reagents in a Lab-on-a-CD type device. Thesolutions of enzyme, inhibitor and substrate were loaded in reservoirs thatwere connected to channels labeled R1, R2 and R3, respectively. R4 is areservoir for waste collection. The rotation of the disk at different speedscontrols the opening of the valves, and the sequence of mixing the enzymewith the inhibitor, followed by mixing with the substrate, and detection [3]

expand the range of applications. Continuous efforts aremade to enlarge the variety of liquids that can be han-dled by new approaches to surface patterning in micro-capillaries. The integration of an increasing number of valves for the implementation of complex reaction proto-cols is also an area of active research, especially, but notlimited to, Lab-on-a-CD type devices [9]. Finally, whilemicrouidic devices are developed for applications out-side the laboratory, it becomes increasingly important to

Capillary Force Valves, Figure 9 A volume of 25 pL is isolated by thecreation of two new liquid–air interfaces, through the use of two thermalactuators. Two air bubbles isolate the separated volume from the rest ofthe liquid in the main channel [6] ( Color Plate 19)

provide robust valve designs that would ensure function-ing over a wider range of temperatures, storage conditionsand operator training, etc.

Cross References

Lab-on-a-Chip (General Philosophy)Centrifugal MicrouidicsApplications Based on ElectrowettingElectrowettingBiosample Preparation Lab-on-a-Chip DevicesBoiling and Evaporation in MicrochannelsBubble Actuated Microuidic SwitchCapillary FillingControl of MicrouidicsDroplet and Bubble Formation in MicrochannelsElectrocapillaryElectrochemical ValvesElectrowettingFabrication of 3D Microuidic StructuresFluid MeteringIntegrated Microuidic Systems for MedicalDiagnosticsLab-on-Chip Devices for Chemical AnalysisMarangoni ConvectionMicrouidic CircuitsMicrouidic Sample ManipulationSurface Tension, Capillarity and Contact AngleTransport of Droplets by Thermal CapillarityWater Management in Micro DMFCs



196 Capillary Magnetophoresis

References

1. de Gennes P-G, Brochard-Wyart F, Quéré D (2004) Capillarityand wetting phenomena: drops, bubbles, pearls, waves; translatedby Axel Reisinger. Springer, New York

2. Zhao B, Moore JS, Beebe DJ (2001) Surface-directed liquid owinside microchannels. Science 291:1023–1026

3. Duffy DC, Gillis HL, Lin J, Sheppard NF, Kellogg GJ (1999)Microfabricated Centrifugal Microuidic Systems: Characteriza-tion and Multiple Enzymatic Assays. Anal Chem 71:4669–4678

4. Handique K, Burke DT, Mastrangelo CH, Burns MA (2001) On-chip thermopneumatic pressure for discrete drop pumping. AnalChem 73:1831–1838

5. Lee SH, Lee CS, Kim BG, Kim YK (2003) Quantitatively con-trolled nanoliter liquid manipulation using hydrophobic valv-ing and control of surface wettability. J Micromech Microeng13:89–97

6. Irimia D, Tompkins RG, Toner M (2004) Single-cell chemicallysis in picoliter-scale closed volumes using a microfabricateddevice. Anal Chem 76:6137–6143

7. Ajaev VS, Homsy GM (2001) Steady Vapor Bubbles in Rectan-gular Microchannels. J Colloid Interface Sci 240:259–271

8. Oh KW, Ahn CH (2006) A review of microvalves. J MicromechMicroeng 16:R13–R39

9. Madou M, Zoval J, Jia G, Kido H, Kim J, Kim N (2006) Lab ona CD. Annu Rev Biomed Eng 8:601–628

Capillary Magnetophoresis

Magnetophoresis

Capillary Reactor Droplet Microreactor

Capillary Valves

Capillary Force Valves

Capillary Zone Electrophoresis

Capillary Electrophoresis

Caspase Activation

Microuidics for Studies of Apoptosis

Cast-in-Place Polymeric Media

Stationary Phases in Microchannels

Catalyst Testing

Denition

A branch of combinatorial chemistry used for developindevelop in an empirical or semi-empirical manner new andmore efcient catalysts.Most often, in the heterogeneous catalysis the catalysts aresolids–usually metals, very often precious metals–whilethe reactants are liquid or gaseous. The catalysts are usu-ally composed of a number of (metal) components in var-ious combinations. The tests are performed in parallelunder the otherwise equal temperature and pressure condi-tions in a large number of microreactors. In each microre-actor the combination of the tested catalyst components isdifferent and this results in a different yield or selectivity of

the test reaction. This is usually evaluated by compositionanalysis of the reaction products. The results are stored ina combinatorial library and processed mathematically todetermine the optimum combination.

Cross References

Microuidic Systems for Combinatorial ChemistryCombinatorial Library

Cataphoresis

Electrokinetic Motion of Cells and NonpolarizableParticles

Cathode

Denition

Negatively charged electrode.

Cross References

Electrophoresis

Cathode Sputtering

Sputtering for Film Deposition



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capillary force valves

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