LETTER pubs.acs.org/ac
Analyte Distribution at Channel Intersections of Electro-Fluid-Dynamic Devices Chang Liu,† Yong Luo,‡ Ning Fang,§ and David D. Y. Chen*,† †
Department of Chemistry, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada School of Pharmaceutical Science and Technology, Dalian University of Technology, Dalian, Liaoning, 116023, China § Ames Laboratory, U.S. Department of Energy and Department of Chemistry, Iowa State University, Ames, Iowa, 50011 ‡
bS Supporting Information ABSTRACT: Mass conservation is the guiding principle for analyte distribution at channel intersections of microfluidic devices, where analyte migration is mainly driven by an applied electric field, and in electro-fluid-dynamic (EFD) devices, where multiple fields and pressures can be applied simultaneously on the same channel network. This paper introduces another type of conservation, the conservation of effective volumetric flow rate, at channel intersections when the conductivity of the solution in the intersecting channels is maintained constant. This conservation principle provides an additional criterion needed to describe analyte migration in channels connecting to a common intersection and to predict how analyte is distributed into individual channels in the channel network of EFD devices, when multiple voltages and pressures are applied. The theoretical bases of effective volumetric flow rate balance are discussed, and the potential use of this principle in conjunction with the principle of mass conservation to predict the migration behavior of analytes is demonstrated. Junctions of different geometry in EFD devices are used to demonstrate the validity of these equations, and the measured velocities and numbers of microbeads in each channel agree with the predicted values.
C
hemical separation in microchannels of microfluidic devices has been demonstrated for two decades.1,2 The channel geometry used in various applications includes one-dimensional single channels, Y-shaped or cross-shaped intersecting channels, and highly complex channel networks.3,4 The ease of sample introduction and sample mixing by electroosmotic flow and the use of electrophoresis for chemical separation are important advantages for microfluidic devices. These devices have been used in a wide variety of disciplines, including clinical diagnostics5,6 and organic synthesis.7 Electro-fluid-dynamic (EFD) devices, in which both electric field and hydrodynamic pressure are applied simultaneously, can be used for particle separation8 and continuous chemical purification.9 Many of these applications are based on different net velocities of charged components in different channels joined at an intersection. When molecules are present in a moving medium in an EFD device, they could either migrate with the medium driven by nondiscriminative forces, such as pressure or electroosmosis, or migrate through the medium driven by discriminative forces from the applied electric field. The two types of movement could also happen simultaneously, giving a net migration determined by the sum of the velocity vectors of each movement. While differential migration of analytes in a single channel for chemical separation is well understood, separation using two-dimensional r 2011 American Chemical Society
channel geometries and the driving forces for analytes’ distribution into different channels are not understood. This work investigates how analytes at a channel intersection migrate into different channels and introduces the principle of conservation of effective volumetric flow rate, which describes the relationship of steady state velocities for charged components in intersecting channels. Both theoretical derivation and experimental validation are demonstrated. We also demonstrate the use of both mass conservation and effective volumetric flow rate conservation principles to predict analyte concentration in individual channels.
’ EXPERIMENTAL SECTION The EFD devices shown in Figure 1 were fabricated on soda lime glass (Nanofilm, Westlake Village, CA) using the standard photolithographic patterning and wet chemical etching method.10 The width of the main and lateral channels for the Y-shaped EFD device (Figure 1a) on the film mask were 80 and 40 μm, respectively. For the devices illustrated in Figure 1b, all channels have a width of 20 μm. The positive potentials were Received: November 27, 2010 Accepted: January 18, 2011 Published: January 26, 2011 1189
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concentration. Thus, for the channels linked together at the intersection, the conductivity in each channel is the same: σi = σ. From Kirchhoff’s law, at the junction point of n channels (n g 2), the total current at the intersection is zero, which can be written as n X Ji Si ¼ 0 ð1Þ i¼1
where Ji is the current density in each channel and Si represents the cross sectional area for the specific channel. The direction of current density, as well as other vectors discussed later, is along the channel direction due to the wall limitation. Thus, these vectors are all expressed as scalars, and the values are defined as positive when the vector direction is toward the intersection. If Ohm’s Law J = σE is used in eq 1, it becomes n X Ei Si ¼ 0 ð2Þ i¼1
For pressure driven flow, the fluid in the EFD device is assumed incompressible, so the relationship of the fluid flow velocity can be written as: n X vf ,i Si ¼ 0 ð3Þ i¼1
Figure 1. Channel geometries used in this study. (a) Y-shaped device. The length of the main channel CF and lateral channels AC and BC are 3.6 and 3.0 cm, respectively. The positive potentials of 200 and 150 V were applied at points A and B. Point E is grounded, and the channel DE has the length of 1.5 cm. A volumetric flow rate of 0.020 μL/min was controlled at point F. (b) Cross-shaped device. Channels AD, BD, and CD have the same length of 0.6 cm, and a volumetric flow rate of 0.250 μL/min was controlled through the 4.4 cm long channel DE. The positive potential of 500 and 200 V were applied at points C and B, and point A was grounded. Intersection C in (a) and intersection D in (b) are monitored. (c) Flow directions of microbeads migrating through the intersection of the Y shaped channel strucure. (d) Flow directions of microbeads migrating through the intersection of the cross shaped channel strucure. The flow directions were determined by the applied electric fields and pressures.
provided by high-voltage power supplies (SL150, Spellman High Voltage Electrionics, Hauppage, NY), and the pressure induced flow velocity was controlled through a syringe pump (Harvard Apparatus, Holliston, MA). During the experiment, the sample solution was introduced through the reservoirs drilled on the chip. A Nikon Eclipse 80i microscope was used in this study, and the fluorescence signals were recorded by a Photometrics Evolve camera (Tucson, AZ). The optical band-pass filters were from Thorlabs (Newton, NJ), and their full width at half-maximum (fwhm) was 10 nm. Charged particles have been used to measure the net flow velocity in different channels.11 The sample used in this study was a 2% (w/v), 2.0 μm diameter carboxylate-modified fluorescent FluoSpheres bead solution (Invitrogen, Carlsbad, CA). The sample solution was diluted 1000 times and sonicated for 15 min before being loaded into the EFD device.
’ THEORETICAL BASIS In EFD devices, two or more microchannels are often joined together by an intersection, forming complex channel networks. The conductivity of the solution in the device can be considered uniform if a relatively high concentration of buffer solution is used throughout the device, and the analyte is present at a low
where vf,i is the fluid velocity in each channel. The motion of a charged particle or molecule that is moving in the channel of an EFD device is driven by both electric field and pressure induced fluid migration. Normally, the fluid flow within the microchannels is laminar.12 The net velocity of the charged particles or molecules in either channel can be written as: vi = veo,i þ vep,i þ vp,i = Eiμep þ vf,i, where electroosmotic velocity (veo) and electrophoretic velocity (vep) are proportional to the electroosmotic mobility (μeo) and electrophoretic mobility (μep), respectively. The fluid velocity vf,i is the sum of bulk flow vp,i and veo,i. From eqs 2 and 3, the net velocity of charged components in any channel can be rewritten as: vi ¼ Ei μep þvf ,i n X
¼-
j¼1,j6¼ i
n X
Ej μep Sj
Si
-
vf , j S j
j¼1,j6¼ i
Si n n X 1 1 X ¼ Sj ðEj μep þvf ,j Þ ¼ vj S j Si j¼1,j6¼ i Si j¼1,j6¼ i This equation can be rearranged to obtain the following: n X vi Si ¼ 0
ð4Þ
ð5Þ
i¼1
Equation 5 describes the general relationship of the net flow velocity for charged components in a channel intersection of an EFD device, showing the effective volumetric flow rate conservation principle. There is no specific requirement for direction or magnitude of the applied pressure or electric voltage, nor the geometry or number of the channels. Within the channel junction of an EFD device, where hydrodynamic pressure and electric field may be independently or simultaneously applied, the sum of term “viSi” is always zero. This term has the unit of m3/s and can be considered as an effective volumetric flow rate, because it describes the volume traveled by the molecules per 1190
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Table 1. Velocity of Microbeads in Individual Channels device
|v1|
|v2|
|v3|
|v4|
ratio determined
ratio predicted
Y intersection (μm/s)
47.9 ( 3.3
60.5 ( 2.6
26.3 ( 1.8
N/A
((|v2| þ |v3|)/(|v1|)) = 1.81
((|v2| þ |v3|)/(|v1|)) = 1.82
cross intersection (mm/s)
2.14 ( 0.47
1.58 ( 0.27
0.62 ( 0.17
0.14 ( 0.05
((|v1| þ |v4|)/(|v2| þ |v3|)) = 1.04
((|v1| þ |v4|)/(|v2|þ|v3|)) = 1.00
unit time and not the bulk solution volumetric flow rate. Detailed derivations of equations presented in this paper are presented in the Supplemental Information.
’ RESULTS AND DISCUSSION In order to verify if this theoretical prediction is valid in real situations, we used two types of common EFD device geometries to demonstrate the flow rate relationship in the three (Figure 1a) and four channel (Figure 1b) intersections. Y-shaped microfluidic devices have been used to introduce samples from interconnecting channels and to efficiently mix different solutions into a single channel.13 We have reported that a Y-shaped device can also be used to reverse the mixing process when appropriate pressure and electric field were applied. Such devices can be used as continuous purification tools for complete processing of small samples.9 The different migration behaviors of components migrating in the device was determined by the net velocity of the analyte in each channel. The conservation of effective volumetric flow rate equation derived here provides the theoretical basis for how analyte is distributed into individual channels at an intersection in these devices. The cross section of wet etching fabricated glass chips does not provide well-defined shapes;14 thus, the real crosssectional area ratio for the main and lateral channels in the Y-shaped device was estimated using the ratio of channel widths at the image plane. For main and lateral channels with dimensions of 120.1 and 65.9 μm, respectively, the ratio is 1.82. On the basis of eq 5, v1S1 þ v2S2 þ v3S3 = |v1|S1 - |v2|S2 - |v3|S3 = 0 and S2 = S3 as shown in Figure 1c; the ratio of (|v2| þ |v3|)/|v1| should be 1.82 as well. The velocities for 100 fluorescent microbeads in three channels of the Y shaped EFD device under hydrodynamic pressure and electric field were measured, and the results are listed in Table 1. The net flow directions for the microbeads in each channel were marked in Figure 1c. Figure 2 shows the image of the migration of microbeads in the Y shaped EFD device. The microbeads have the fastest velocity in Channel 2, resulting in the longest bright spot in the image within the exposure period. The ratio of the average velocity of individual particles in Channel 2 plus that Channel 3 vs the average velocity of particles in Channel 1 agrees well with the predicted value, as shown in the last column of Table 1. The cross-shaped microdevice, illustrated in Figure 1b, is widely used in capillary electrophoresis on chip.15 Because the four channels have the same width on the film mask, their cross sectional areas are considered to be the same after wet etching and wafer bonding fabrication. The net velocities of 100 fluorescent microbeads migrating in four channels were measured as well, when hydrodynamic pressure and electric field were simultaneously applied. The net flow directions for the microbeads in each channel are marked in Figure 1d. From the result listed in Table 1, we can conclude that the experimental velocity ratios agree well with those predicted by eq 5. Although the flow rate of the microbeads is different in each channel, the sum of the products of net velocity and cross sectional area is equal to zero. The measured velocities support
Figure 2. Image of microbeads flowing in all three channels with a fixed exposure time. Longer images are the results of faster flow rates.
the conservation of effective volumetric flow rate principle at the intersection of three channels and four channels in EFD devices. The conservation of mass principle indicates that the amount of the analytes moving toward the intersection should be equal to the amount moving away during a given time period: n X ni i¼1
t
¼
n X
vi c i S i ¼ 0
ð6Þ
i¼1
However, this general equation can only provide information about the conjugate variable vici but not vi or ci individually. There may be unlimited possible combinations of flow rates and concentrations that can satisfy this equation. The conservation of the effective volumetric flow rate equation (eq 5) provides the relationship of net velocities of the analytes with the channel cross sectional areas, under the condition of the uniform conductivity in all channels joined at the intersection. If these two equations are used simultaneously, the concentration of the molecular species can be obtained n P vj c j S j vi ci Si j¼1,j6¼ i ¼ P ð7Þ ci ¼ n vi S i vj S j j¼1,j6¼ i Equation 7 can be used to determine the concentration of the analyte in a channel where the concentration and net velocity of the analyte is difficult to measure directly or to predict the concentration or migration rate if the properties of other channels are known. 1191
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Analytical Chemistry Because microbeads were used as the analyte in this work, the number of particles present in the channels can be used in place of analyte concentration (see Supporting Information). A video taken during the experiment showed that, for 100 particles flowing into the intersection from Channel 1, 78 entered into Channel 2 and 22 entered into Channel 3, almost exactly as predicted by this theory. In the case of the cross shaped intersection, a video showed that, of 100 particles entering into the intersection (94 from Channel 1 and 6 from Channel 4), 64 and 36 particales entered Channel 2 and Channel 3, respectively. These numbers are within the shot noise limit of the values predicted by eq 7. The conservation of the effective volumetric flow rate equation (eq 5) can also be used for nonuniform channels. At different cross-section positions, the product of net velocity and cross sectional area will give the same amount, which is a special condition of eq 5, when n = 2. The intersection studied here can be either a conventional channel junction or a more complex channel structure. Although the discussion in this paper is focused on 2-D microchannel networks, the conservation of effective volumetric flow rate is not limited to channels located on the same plane. The theoretical derivation is generally applicable, including the more complex 3-D channel networks. The only requirement for effective volumetric flow rate conservation is that the conductivity (σ) is assumed to be uniform in all channels joining together. This assumption is applicable when a relatively high concentration of buffer solution is used (capillary electrophoresis on chip) or the concentration of analyte is very low (single particle or single molecule imaging). If the conductivity for the solutions in all channels cannot be assumed to be uniform, eq 5 needs to be modified. Equation 2 can be rewritten as Σni = 1σiEiSi = 0, and eq 4 can be changed to vi = -(1/Si)Σnj = 1,j6¼i[(σj/σi)EjSjμep þ vf,jSj]. Thus, eq 5 can to be modified into Σni = 1[(σi/σ1)EiSiμep þ vf,iSi] = 0, where σ1 is the conductivity in any specific channel. However, because in most cases the different conductivities cannot be maintained when the channels are connected by the same intersection, it is difficult to make predictions unless the gradual changes in conductivites are accounted for.
’ CONCLUSIONS The effective volumetric flow rate is conserved at channel intersections of EFD devices when the conductivity in channels can be assumed to be uniform. The combination of this principle and the mass conservation principle can be used together to determine the analyte concentration at any channel, which can be difficult to predict or measure directly in some cases. These relationships predict that the distribution of analyte at the channel intersections is determined by the migration behavior of the species in each individual channel, because the sum of the effective flow rates for all channels must be zero. With proper arrangement of electric fields and pressure in each channel, analyte entering the channel intersection can be directed to enter a predetermined channel, facilitating continuous processing of sample mixtures into pure components or simplified fractions.
LETTER
’ AUTHOR INFORMATION Corresponding Author
*Tel: (604) 822-0878. Fax: (604) 822-2874. E-mail: chen@ chem.ubc.ca.
’ ACKNOWLEDGMENT D.D.Y.C. was supported by the Natural Sciences and Engineering Research Council of Canada, and N.F. was supported by the Director of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy (DOE). The Ames Laboratory is operated for DOE by Iowa State University under Contract No. EF-AC02-07CH11358. ’ REFERENCES (1) Arora, A.; Simone, G.; Salieb-Beugelaar, G. B.; Kim, J. T.; Manz, A. Anal. Chem. 2010, 82, 4830–4847. (2) Salieb-Beugelaar, G. B.; Simone, G.; Arora, A.; Philippi, A.; Manz, A. Anal. Chem. 2010, 82, 4848–4864. (3) Thorsen, T.; Maerkl, S. J.; Quake, S. R. Science 2002, 298, 500– 584. (4) Lebel, L. L.; Aissa, B.; Paez, O. A.; Khakani, M. A. EI; Therriault, D. J. Micromech. Microeng. 2009, 19, 125009. (5) Kline, T. R.; Runyon, M. K.; Pothiawala, M.; Ismagilov, R. F. Anal. Chem. 2008, 80, 6190–6197. (6) Martinez, A. W.; Phillips, S. T.; Carriho, E.; Thomas, S. W.; Sindi, H.; Whitesides, G. M. Anal. Chem. 2008, 80, 3699–3707. (7) Mason, B. P.; Price, K. E.; Steinbacher, J. L.; Bogdan, A. R.; McQuade, D. T. Chem. Rev. 2007, 107, 2300–2318. (8) Jellema, L. C.; Mey, T.; Koster, S.; Verpoorte, E. Lab Chip 2009, 9, 1914–1925. (9) Liu, C.; Luo, Y.; Maxwell, E. J.; Fang, N.; Chen, D. D. Y. Anal. Chem. 2010, 82, 2182–2185. (10) Woolley, A. T.; Mathies, R. A. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 11348–11352. (11) Gai, H.; Li, Y.; Silber-Li, Z.; Ma, Y.; Lin, B. Lab Chip 2005, 5, 443–449. (12) Brewer, L. R.; Bianco, P. R. Nat. Methods 2008, 5, 517–525. (13) Harrision, D. J.; Fluri, K.; Seiler, K.; Fan, Z.; Effenhauser, C. S.; Manz, A. Science 1993, 261, 895–897. (14) Rodriguez, I.; Spicar-Mihalic, P.; Kuyper, C. L.; Fiorini, G. S.; Chiu, D. T. Anal. Chim. Acta 2003, 496, 205–215. (15) Jacobson, S. C.; Moore, A. W.; Ramsey, J. M. Anal. Chem. 1995, 67, 2059–2063.
’ ASSOCIATED CONTENT
bS
Supporting Information. Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org. 1192
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