Subscriber access provided by KOREA ADV INS OF SCI & TECH

Analytical Chemistry is published by the American Chemical Society. 1155Sixteenth Street N.W., Washington, DC 20036

Article

Microfluidic Pycnometer for in Situ Analysis of Fluids in MicrochannelsJoo H. Kang, Bumjun Kim, and Je-Kyun Park

Anal. Chem., 2009, 81 (7), 2569-2574• Publication Date (Web): 02 March 2009

Downloaded from http://pubs.acs.org on March 31, 2009

More About This Article

Additional resources and features associated with this article are available within the HTML version:

• Supporting Information• Access to high resolution figures• Links to articles and content related to this article• Copyright permission to reproduce figures and/or text from this article

Microfluidic Pycnometer for in Situ Analysis ofFluids in Microchannels

Joo H. Kang, Bumjun Kim, and Je-Kyun Park*

Department of Bio and Brain Engineering, College of Life Science and Bioengineering, KAIST, 335 Gwahangno,Yuseong-gu, Daejeon 305-701, Republic of Korea

This paper presents a new particle migration principle anddemonstrates an analysis of solution density in a microf-luidic channel. A particle situated in a microfluidicinterface with different fluid density moves toward thelower-density fluid, driven by the asymmetric hydrostaticpressure acting on the submerged particle. Since thehydrostatic pressure is related to the diameter of a parti-cle submerged in a solution and the density of a solution,we expected that the particle injected into the middle ofthree inlets would show larger lateral deflection as theparticle size and density difference between two-injectedsolutions increase. In addition to hydrostatic pressuredifferences on the particle, we were concerned not onlyabout fluid momentum difference caused by solutiondensity and flow rate but also about rotational motion dueto asymmetric buoyancy driven by the density gradient.The fluid momentum difference affects an initial positionof the injected particles and its influence becomes en-larged according to the flow rate increases. The rotationalmotion of the particle had been evaluated using a com-putational tool. The experimental results and numericalexpectation proved our theoretical estimation, and herethis behavior explains a new principle termed pyklino-phoresis (Greek; pyk-, density; -klino-, gradient; -phore-sis, migration), which enables in situ analysis of microf-luidicliquidsamples.Ananalyticalmodelforpyklinophoresiswas provided as a proof-of-concept, and the analyticalresults of sucrose and volatile solutions were alsodemonstrated.

The measurement of solution density is required in manyapplications since each element and compound has a uniquedensity that reveals the concentration and the composition ofmixtures. Over the past century, several approaches have beendeveloped to determine the density of fluids, including thepycnometer,1 the vibrating tube density meter,2 and the hydrom-eter.3 Theses conventional tools for density analysis have beenwidely used to obtain various chemical and biological achieve-ments. As microfluidic technology expands in diverse fields such

as chemical synthesis, in situ analysis, and biological assay,4 anincreasing need exists for analysis of nanoliter liquid samples, evenfor tiny volatile compounds carried in microfluidic channels.Therefore, microfluidics-based analytical methods for tiny liquidsamples have recently attracted great attention and include theweighing of biomolecules,5 Raman spectroscopy,6 nuclear mag-netic resonance,7 and electrophoresis systems on a chip.8 Densityanalysis, however, despite several successful reports,5,9,10 still lacksinnovative methods that are easy to access and that are completelycompatible with current microfluidic reactors.11

In this paper, we describe a lateral microparticle migrationprinciple that we have named pyklinophoresis (PKP) (Greek; pyk-,density (pyknotita); -klino-, incline (klino); -phoresis, migration)that is driven by the pressure gradient asymmetrically acting onsubmerged particles. This phenomenon is related to hydraulics,but we have given it a new name because the submerged particleat the vertical interface of fluids is allowed only in microfluidicenvironments. A particle situated in the density gradient acrosssurroundings of the particle is subject to asymmetric forces drivenby the pressure difference between one side of the particle andthe other side. Since the forces are determined by the steepnessof the density gradient across the particle as well as by the particlesize, we are able to use this principle not only to separate particlesaccording to the size but also to discriminate the solutionproperties such as concentration and density. With the use of thisprinciple, we describe a microfluidic pycnometer for in situanalysis of fluid solutions including volatile methanol and ethanolin a microfluidic environment. We have proved a theoretical modelusing computational predictions and experiments. Since thisprinciple can be explained by combining several physical consid-erations, we have described additional driving effects on PKP in

* To whom correspondence should be addressed. E-mail: jekyun@kaist.ac.kr.Phone: +82-42-350-4315. Fax: +82-42-350-4310.

(1) Greenberg, O. Science 1906, 24, 314.(2) Ruben, S. Testing Apparatus and Method. U.S. Patent 1,570,781, January

26, 1926.(3) Linebarger, C. E. Hydrometer. U.S. Patent 1,424,730, August 1, 1922.

(4) deMello, A. J. Nature 2006, 442, 394–402.(5) Burg, T. P.; Godin, M.; Knudsen, S. M.; Shen, W.; Carlson, G.; Foster, J. S.;

Babcock, K.; Manalis, S. R. Nature 2007, 446, 1066–1069.(6) Ramser, K.; Enger, J.; Goksor, M.; Hanstorp, D.; Logg, K.; Kall, M. Lab

Chip 2005, 5, 431–436.(7) (a) Lee, H.; Sun, E.; Ham, D.; Weissleder, R. Nat. Med. 2008, 14, 869–

874. (b) Wensink, H.; Benito-Lopez, F.; Hermes, D. C.; Verboom, W.;Gardeniers, H. J. G. E.; Reinhoudt, D. N.; van den Berg, A. Lab Chip 2005,5, 280–284. (c) Gomez, M. V.; Reinhoudt, D. N.; Velders, A. H. Small 2008,4, 1293–1295.

(8) Belder, D.; Ludwig, M.; Wang, L.-W.; Reetz, M. T. Angew. Chem., Int. Ed.2006, 45, 2463–2466.

(9) Sparks, D.; Smith, R.; Straayer, M.; Cripe, J.; Schneider, R.; Chimbayo, A.;Anasari, S.; Najafi, N. Lab Chip 2003, 3, 19–21.

(10) Etchart, I.; Chen, H.; Dryden, P.; Jundt, J.; Harrison, C.; Hsu, K.; Marty,F.; Mercier, B. Sens. Actuators, A: Phys. 2008, 2, 266–275.

(11) Yen, B. K. H.; Gunther, A.; Schmidt, M. A.; Jensen, K. F.; Bawendi, M. G.Angew. Chem., Int. Ed. 2005, 44, 5447–5451.

Anal. Chem. 2009, 81, 2569–2574

10.1021/ac802492q CCC: $40.75 2009 American Chemical Society 2569Analytical Chemistry, Vol. 81, No. 7, April 1, 2009Published on Web 03/02/2009

this report. An innovative approach for demonstrating a newphysical principle is significant, not only for the development ofuseful applications such as the microfluidic pycnometer, but alsofor explaining the incomprehensible results we frequently en-counter in micro- or nanoscale environments.

THEORETICAL ESTIMATIONPKP driven by the hydrostatic force is distinguished from two-

phase fractionation, which is based on the difference of affinitybetween two immiscible liquid phases. In general, the hydrostaticforce acting on an immersed particle is produced by the symmetricpressure on the perpendicular to the curved area. However,because of the assumption that the submerged particle is sur-rounded by the homogeneous fluid, we need a new physicaldescription for the PKP phenomenon. As depicted in Figure 1, ifthe particle is placed under the density gradient between two fluidswith different solution densities, the pressure disparity producesan asymmetric force perpendicular to the fluidic interface. The

hydrostatic force on the submerged particle is the integral of thepressure over the surface of the particle as follows:12

Fh denotes the force on the spherical surface produced by thehydrostatic pressure on the particle, and γ represents Fg, whereF is the fluid density and g is the gravitational accelerationconstant. Under steady-state conditions around the particle, thex-component of Fh is given by

where δA is the infinitesimal area of a particle, δAx is theprojection of δA on an imaginary vertical plane, and zc is thevertical depth of the centroid of a particle below the fluidsurface.

(12) Khan, I. A. Fluid Mechanics; Oxford University Press: New York, 1995;Chapters 2-5.

Figure 1. The principle of pyklinophoresis (PKP) in the microfluidic two-phase laminar flow showing (a) top and (b) cross-sectional (O-O′)views. Solutions B and C are the same. The upper scheme in part b shows a particle surrounded by homogeneous solutions (FA ) FB). (c)Scheme of hydrostatic pressure acting on a submerged particle in a density gradient across the microchannel.

Figure 2. A microscopic image of (a) the fabricated microfluidic pycnometer and (b) an enlarged view of the extended channel at the outlet.The device consists of three inlets and a single outlet that contains an extended channel for the measurement of the particle positions. Allmicrochannels except for the extended portion are 20 µm in height and 100 µm in width.

Fh ) ∫Aγzc dA (1)

Fx ) ∫ pδAx ) ∫ γzcδAx ) γAxzc (2)

2570 Analytical Chemistry, Vol. 81, No. 7, April 1, 2009

As presented in Figure 1c, if the particle is divided by m thatis large enough compared to the diameter, Fhx can be expressedby summation of each Fhx(m) on the m section.

γ () Fg) is the function of x and y that is expressed by time,t(s). F can be calculated by eq 5.13

where F is the density in g/cm3, c is the concentration of sucrose(g/100 mL), and θ is the temperature in Celsius. c can beestimated using the equation as follows:14

where C0 is the initial concentration, h is the width of theinitial distribution (50 µm), w is the width of the channel(100 µm), and D is the diffusion coefficient of sucrose (4.3× 10-6 cm2/s).15

(13) Hirst, W.; Cox, R. A. Biochem. J. 1976, 159, 259–265.

Figure 3. The center-focused streamlines were presented with variation of the solution density at inlet A. Because one of the parametersdetermining the fluid momentum is the density of the solution, the center-focused streamlines are deflected toward the side of the lower densitysolution except for the equal density condition, part c. With the given condition of injecting a mixture of 50% methanol and ethanol in inlet B, wemeasured the centered streams, varying the composition of inlet A, which affects the initial positions of the particles flowing out from inlet C. Themeasured data were plotted in part f.

Fhx(x, y) ) ∑m)1

100

Fhx(m) (3)

Fhx(m) ) γ(x, y)Axzc (4)

γ(x, y) ) F(x, y)g ) 1.0004 exp{10-4[(43.52 -

0.039θ)c - 0.0612(θ - 4)2]}g (5)

C(t, x) ) 12

C0 ∑n)-∞

∞

{ erfh + 2nw - x2√Dt

+ erfh - 2nw + x2√Dt }

(6)

2571Analytical Chemistry, Vol. 81, No. 7, April 1, 2009

Employing the Fhx and Fick’s law, we estimated the lateraldeflection velocity of Vx.

where r is the radius of a particle and η is the dynamic viscosity(kg/ms). The particle velocity driven by the parabolic flowprofile along the microfluidic channel (Vy) was calculated usingeq 8. We disregarded vertical buoyancy and gravitational forcesbecause the height of the microfluidic channel is only slightly

Figure 4. Experimental results determined by particle positions in the extended microchannel around the outlet. Part a shows the particlepositions measured at the outlet channel along the increased injection flow rate, which support that particle migration is rapid and enhanced byfluid momentum difference between solutions A and B (or C). Part b describes that the larger particles show more rapid migration than thesmaller particles as predicted by the theoretical model. Parts c and d demonstrate the successful in situ concentration analysis of solutions(sucrose, methanol, and ethanol) in the microchannels. The density analysis results were obtained using 15 µm microparticles because thelarge particle is exerted by the strong PKP force.

Figure 5. The analytical model provides a theoretical estimate of particle traces in 100 µm wide microfluidic channels (x-y coordinates inFigure 1a) for (a) various sucrose concentrations in solution A and (b) various particle diameters. (a) The particle traces vary in accordance withthe solution density injected into inlet A. If the solution A contains the density same with the solutions B and C, the particles move along themicrofluidic channel, maintaining the initial position on the x-axis. When we vary the concentration of inlet A solution from 0% to 12%, theparticles are deflected toward the side of lower concentration. The density of the sucrose solution was calculated with a published formula.13

The formulas were solved by Matlab software. (b) As the particle size increases from 3 to 15 µm, the deflection of the particles is estimated tobecome larger according to the theoretical model. Combining theses numerical expectations, we can reach the conclusion that the larger particleand the steeper gradient are used in PKP experiments, the more increased deflection of the particle can be obtained. The initial position of theparticles is generally (50, 0) in x-y coordinates.

Vx(x, y) )Fhx(x, y)-6πrη

(7)

2572 Analytical Chemistry, Vol. 81, No. 7, April 1, 2009

larger than the particle diameter and sedimentation velocity ismuch less than the lateral PKP velocity.

We considered neither the surface tension between particle-fluid interfaces nor the Marangoni effect that is the flow of liquidcaused by the surface tension. This is because we used only twokinds of miscible solution in the microchannels, which do not allowan air-liquid interface.

EXPERIMENTAL SECTIONMicrofabrication. The particle separation was conducted

using a poly(dimethylsiloxane) (PDMS) microfluidic device havingthree inlets and a single outlet as presented in Figure 2. Themicrofluidic channels were designed to have 20 µm in height and100 µm in width, and the straightforward separation channel isabout 11 mm in length. Overall dimension and fabricationprocesses of the device are similar with our previous literature.14

The volume of the entire microfluidic channels is about 60 nL.Microfluidic Experiments. In density analysis, the reference

solutions at inlets B and C were 10% sucrose solution and 50%methanol/ethanol mixture, respectively. We measured the inter-mittent particle positions (approximately 300 particles for 30 min)while varying the concentration at inlet A. The sucrose andmethanol/ethanol were obtained from Sigma-Aldrich (St. Louis,MO) and J. T. Baker (Phillipsburg, NJ), respectively. Themethanol (F ) 0.7138, at 25 °C) and ethanol (F ) 0.7566)contained organic impurities that altered their inherent density.The density values of methanol and ethanol were measured by aconventional pycnometer (Pyrex Gay-Lussac Bottle, Cole-ParmerInstrument Company, IL) consuming 10 mL of each sample. Toprevent particle adsorption on the PDMS surface, all solutionscontained 0.02% Tween 20, which did not affect the total solutiondensity, and the PDMS microchannels were primed using Pluronicsurfactant (PF68; Sigma-Aldrich Korea, Kyunggi-do, Korea).16

Plain polystyrene particles with diameters of 10, 11, 12, and15 µm (Sigma-Aldrich Korea) were used in the experiment. Theflow rates at inlets A/B and at inlet C were 1.0 and 0.1 µL/min,respectively, and were controlled by the syringe pumps (HarvardApparatus, Inc., Holliston, MA). The flow rate ratios among A, B,and C were determined by considering the focusing width of thecenter stream, C, in the 100 µm wide microfluidic channel17

because the particles that flowed out of inlet C had to be exposedto solution A, as shown in Figure 1a. The particle positions weremeasured after the fluidic equilibrium (Figure 1 in the SupportingInformation) and were obtained from the captured images. Theimages were analyzed by i-Solution software (IMT i-Solution Inc.,Seoul, Korea). The PKP movement of the particles occurs in the100 µm wide microfluidic channel. However, the particle positionsare measured at the 1000 µm wide outlet channel because the

extended microfluidic channel enables one to measure thepositions of the fast-moving particles by reducing the flow rate,which are generally used in the microfluidic measurementtechnique.14

RESULTS AND DISCUSSIONTo prove the theoretical model using experimental results, we

used the PDMS microfluidic device as shown in Figure 2. Thedevice consists of three inlets and a single outlet, which isanalogous to the schematic model in Figure 1. Before we validatethe experimental results based on the hydrostatic force asdescribed in the theory section, we must consider severaladditional effects to explain the results. The first one is the forceproduced by the fluid momentum at the microfluidic intersectionbetween solutions A, B, and C. We used Newton’s second law ofmotion to state that the force exerted on the mass of the immersedparticles is equal to the rate of change of momentum:12

where V is the linear velocity of a fluid, Q is the fluidic discharge(VAx), and θ is the angle between inlet A and the main fluidicchannel. The force produced by the fluid momentum exertsinfluence on the initial positions of the particles and Fm on theparticle. We assessed the effect of the difference in fluidmomentum between solutions A and B as shown in Figure 3,which shows variation of the center streamlines affected by theasymmetric solution density on flow C. Solutions B and C are 50%methanol/ethanol mixture, and fluorescent dye (0.3 mM fluores-cein isothiocyanate) was added in solution C for visualization ofthe flow. The deflected center flow changes the initial point ofthe particle (x-component, 50 µm) to the points presented in Figure3f. These effects should be considered for correction of the initialpositions of the particles. In addition, as we increase the net flowrate, the particles rapidly migrate (Figure 4a) even at theconsiderably high flow rate of 16.8 µL/min (Reynolds number,Re ≈ 5.0). The results imply that the particle is deflectedimmediately on exposure to the different density solution alongwith the increased flow rate (V). Equation 9 proves the resultsbecause the net force driven by the fluid momentum is propor-tional not only to the density difference but also to the volumetricflow rate, Fm ∝ Q. The second additional effect on the particlesis the rotational movement induced by the asymmetric buoy-ancy on each half of the particle (Figure 2 in the SupportingInformation).18 Moreover, the reorientation of the vertical interfacebetween fluids is negligible (Figure 3 in the Supporting Informa-tion) because the aspect ratio of the microfluidic channel (h/w)used in this study is about 0.2, unlike that used in the previousresearch.19

The particle size effect in PKP was proved based on thetheoretical estimation presented in eq 3. As shown in Figure 4b,the particles are deflected from their initial path and driven byPKP according to their size. The deflected stream lines willconverge on the center line (i.e., at 50 µm in a 100 µm widemicrochannel) as could be expected from the analytical model in

(14) Kang, J. H.; Choi, S.; Lee, W.; Park, J.-K. J. Am. Chem. Soc. 2008, 130,396–397.

(15) Linder, P. W.; Nassimbeni, L. R.; Polson, A.; Rodgers, A. L. J. Chem. Educ.1976, 53, 330–332.

(16) Mcpherson, T.; Kidane, A.; Szleifer, I.; Park, K. Langmuir 1998, 14, 176–186.

(17) Lee, G.-B.; Hung, C.-I.; Ke, B.-J.; Huang, G.-R.; Hwei, B.-H.; Lai, H.-F. J.Fluids Eng. 2001, 123, 672–679.

(18) A qualitative simulation is available at http://www.mattiasfagerlund.com/DelphiODE/BuoyancyParticles.asp (accessed Feb 2009). The capturedmovie file is attached in the Supporting Information.

(19) Yoon, S. K.; Mitchell, M.; Choban, E. R.; Kenis, P. J. A. Lab Chip 2005, 5,1259–1263.

Vy(x) ) 32

v0(1 - 4(50 - x)2

w2 ) (8)

Fm ) (FAQAVA - FBQBVB)sin θ (9)

2573Analytical Chemistry, Vol. 81, No. 7, April 1, 2009

Figure 5. This rapid particle migration according to their size canbe applied to the particle sorting purposes as maintaining thelaminar flows in the channel, which cannot be obtained by thechaotic flow based sorting method such as hydrophoresis.20

Considering the application to nanoparticles, it will require arelatively long time to observe the complete movement ofnanoparticles driven by PKP, compared to that of the microparticlebecause the smaller particles are exerted by the weaker PKP force.Furthermore, we assessed the liquid solution analysis based onthe principle defined above, which discriminates concentrationand composition of the mixtures including the known chemicals.Figure 4c,d shows the discrimination results of the concentrationof solutions as determined by the lateral positions of the micro-particles. Compared with the theoretical estimate in Figure 5, theexperimental results demonstrate that our analytical modeldescribes the experimental tendency accurately. As we proved inour previous research,14 the numerical estimation of concentrationgradients using eq 6 can cause the results to differ from theexperimental one. This disparity in the concentration gradientsmay result in underestimation of the driving force acting on theparticle because the steep density gradient around the particleinduces the enhanced force driven by PKP as described in eqs 3and 4. In our theoretical model, we assumed that two flowsinjected through inlets A and B have a similar dynamic viscosity(η) so that we set η to have a constant. However, if η is quitedifferent from each other, we need to consider η as a function ofconcentration and time along the microfluidic channel. Figure 4dshows that the particle positions in the methanol/ethanol mixtureare deflected more than those of sucrose due to the lower dynamicviscosity of methanol/ethanol. Although the present analyticalmodel does not completely fit the experimental results becauseit is newly defined and requires well-defined formulas such asthat for isomagnetophoresis,14 combining the model with theadditional fluid momentum effect and rotational motion of theparticles can provide a further physical description that adequately

accounts for PKP. Considering applications using various kindsof solutions, a problem can result from choosing the referencesolution (inlets B and C) under certain experimental conditions.For example, if the solution of interest is nonpolar and dissolvespolymer particles, the reference solution should be similar withdifferent density, and the microparticles should be a silicon-basedsubstance that is not subject to the dissolving solution.

CONCLUSIONSIn situ analysis of microfluidic chemical and biological samples

generally requires high-cost optical manifolds, sensor componentswith complicated fabrication processes, and additional reporterchemicals. In particular, volatile solutions at a nanoliter scale makeit difficult to measure the properties relevant to density becauseof rapid vaporization. This new analytical principle can eliminatethese problems for micro/nano in situ analysis and allow compat-ibility with any form of microfluidic networks and simultaneousmonitoring of microfluidic chemical reactions. The PKP forcedescribed in this report is likely to stimulate interest in themicrofluidic results for the behavior of particles and cells inmiscible multiphase laminar flows.

ACKNOWLEDGMENTThis research was supported by the Korea Science and

Engineering Foundation (KOSEF) NRL Program Grant R0A-2008-000-20109-0 and by the Nano/Bio Science and TechnologyProgram Grant 2005-01291 funded by the Korea government(MEST). The authors also thank the Chung Moon Soul Centerfor BioInformation and BioElectronics, KAIST.

SUPPORTING INFORMATION AVAILABLEAdditional information as noted in text. This material is

available free of charge via the Internet at http://pubs.acs.org.

Received for review November 25, 2008. AcceptedFebruary 8, 2009.

AC802492Q(20) Choi, S.; Park, J.-K. Anal. Chem. 2008, 80, 3035–3039.

2574 Analytical Chemistry, Vol. 81, No. 7, April 1, 2009