Anal. Chem. 2006, 78, 6074-6080
Double-Cross Hydrostatic Pressure Sample Injection for Chip CE: Variable Sample Plug Volume and Minimum Number of Electrodes Yong Luo, Dapeng Wu, Shaojiang Zeng, Hongwei Gai, Zhicheng Long, Zheng Shen, Zhongpeng Dai, Jianhua Qin,* and Bingcheng Lin*
Laboratory of Microfluidics for Systems Biology, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, Dalian, Liaoning Province, P.R. China
A novel sample injection method for chip CE was presented. This injection method uses hydrostatic pressure, generated by emptying the sample waste reservoir, for sample loading and electrokinetic force for dispensing. The injection was performed on a double-cross microchip. One cross, created by the sample and separation channels, is used for formation of a sample plug. Another cross, formed by the sample and controlling channels, is used for plug control. By varying the electric field in the controlling channel, the sample plug volume can be linearly adjusted. Hydrostatic pressure takes advantage of its ease of generation on a microfluidic chip, without any electrode or external pressure pump, thus allowing a sample injection with a minimum number of electrodes. The potential of this injection method was demonstrated by a four-separation-channel chip CE system. In this system, parallel sample separation can be achieved with only two electrodes, which is otherwise impossible with conventional injection methods. Hydrostatic pressure maintains the sample composition during the sample loading, allowing the injection to be free of injection bias. Chip capillary electrophoresis (CE) has established its importance in lab-on-a-chip technologies as a major on-chip separation technique. The power of this technique lies in its ability to separate a sample with increased speed,1 reduced sample consumption,2 and higher throughput.3 To fulfill these superior performances, sample injection is a crucial element. This is in part because the injection determines the quantity of the sample plug, but also because it still determines the profile of the sample plug that is closely related to the peak shape and separation resolution.4 In a microchip format, capillary electrophoresis sample injection, in general, is performed in two discrete steps, sample loading and dispensing. The sample plug is formed in the loading step and then dispensed into the separation channel for electrophoresis * Phone/Fax: +86-0411-84379065. E-mails:
[email protected],
[email protected]. (1) Jacobson, S. C.; Culbertson, C. T.; Daler, J. E.; Ramsey, J. M. Anal. Chem. 1998, 70, 3476-3480. (2) Du, W. B.; Fang, Q.; He, Q. H.; Fang, Z. L. Anal. Chem. 2005, 77, 13301337. (3) Emrich, C. A.; Tian, H. J.; Medintz, I. L.; Mathies, R. A. Anal. Chem. 2002, 74, 5076-5083. (4) Fu, L. M.; Yang, R. J.; Lee, G. B. Anal. Chem. 2003, 75, 1905-1910.
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separation. So far, various types of sample loading have been developed. This versatility comes mainly from different types of sample loading force as well as the flexible design of the injector. Predominantly, the sample loading is driven by electrokinetic force because an electric field can be easily and precisely applied between the sample and the sample waste reservoir. Electrokinetic loading has been performed in “T”,5 “double-T”6 and “cross-T”7 injectors in floated,7 pinched,7 and gated8 formats. By addition of two arms to the loading and separation channels, repetitive loading can be realized.9 In addition, variable sample loading, depending on an additional focusing channel, which enables quantitative control of the sample plug volume and superior separation detection performance has been reported.4,10 Despite these achievements, electrokinetic loading inevitably introduces some types of injection bias,11,12 a phenomenon that can cause nonrepresentative sample injections. This unfavorable phenomenon can be triggered by various factors, including differences of mobility between the components in a sample,11 a solution of high ionic strength,13 variation of the ionic strength between the sample and the buffer,12 etc. Recently, Landers et al. investigated the injection bias and demonstrated that the pH shift of a sample due to electrolysis that occurred in the sample reservoir also significantly contributed to the injection bias,14 then, the authors proposed a pressure loading by a diaphragm pump based on reversible PDMS membrane valves, thus allowing successful avoidance of injection bias. (5) Harrison, D. J.; Manz, A.; Fan, Z. H.; Ludi, H.; Widmer, H. M. Anal. Chem. 1992, 64, 1926-1932. (6) Effenhauser, C. S.; Manz, A.; Widmer, H. M. Anal. Chem. 1993, 65, 26372642. (7) Jacobson, S. C.; Hergenroder, R.; Koutny, L. B.; Warmack, R. J.; Ramsey, J. M. Anal. Chem. 1994, 66, 1107-1113. (8) Jacobson, S. C.; Hergenroder, R.; Moore, A. W.; Ramsey, J. M. Anal. Chem. 1994, 66, 4127-4132. (9) Thomas, C. D.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 2004, 76, 60536057. (10) Fu, L. M.; Yang, R. J.; Lee, G. B.; Liu, H. H. Anal. Chem. 2002, 74, 50845091. (11) Alarie, J. P.; Jacobson, S. C.; Ramsey, J. M. Electrophoresis 2001, 22, 312317. (12) Alarie, J. P.; Jacobson, S. C.; Culbertson, C. T.; Ramsey, J. M. Electrophoresis 2000, 21, 100-106. (13) Satow, T.; Machida, A.; Funakushi, I. C.; Palmieri, R. J. High Resolut. Chromatogr. 1991, 14, 276. (14) Karlinsey, J. M.; Monahan, J.; Marchiarullo, D. J.; Ferrance, J. P.; Landers, J. P. Anal. Chem. 2005, 77, 3637-3643. 10.1021/ac0605142 CCC: $33.50
© 2006 American Chemical Society Published on Web 08/02/2006
Pressure, enabling elimination of the injection bias,14-17 is an alternative driving force for sample loading. On a microfluidic chip, pressure can be generated by a syringe pump via a chip-to-world interface consisting of tubing, sample reservoir, and epoxy glue for sealing.15 This configuration was able to provide sequential injections of a neutral FITC-estrogen sample, being famous for its susceptibility to the injection bias, with high reproducibility. Furthermore, it enabled a waste-removing function due to incorporation of an enlarged sample waste reservoir and several subreservoirs into the injector. On-chip pressure also can be generated by a PDMS membrane sealed on the sample reservoir.16 By periodical actuations of the membrane, a pulsed sample injection can be achieved. Varying the membrane actuation time, one can adjust the sample plug volume. Although pressure loading shows exciting advantages and great potential for quantitative analysis, generation of pressure in a microchannel, as demonstrated above, is not so simple. First of all, external equipment is needed, which increases the complexity and cost of the instrumentation,15,16,18 especially in the case that a high precision syringe pump is employed. In addition, external equipment needs to be coupled to the sample channel. This macroto-micro combination is a rather difficult task and has been discussed previously in detail by Futterer et al.19 For example, since the ratio of interface and microchannel volumes is extremely large (typically >1000), microbubbles and slight changes in the connection geometry or in the environment (particularly important for elastic tubing and elastomer chips) can provoke dramatic spurious flows in the channels, which strongly affect the stability of the sample handling. The authors proposed that dynamic control of reservoir pressures at the end of each channel was able to alleviate this situation. However, this approach needs complex integration of multiple controlling elements, while it introduces dead volume to flow ducts. Especially for a compact microchip integrated with large amounts of microchannel, application of this approach is not even feasible. The question naturally arises “Is there any way to generate a pressure in a microchannel without any external equipment so that the instrumentation for the chip CE injection can be simplified, the cost can be reduced, and the injection bias can be eliminated ?” In this study, we propose hydrostatic pressure, generated by liquid level difference between reservoirs, to address this issue. In fact, we have attempted a hydrostatic pressure sample loading on a classical cross microchip in our previous research,20 however, without much success. Hydrostatic pressure, being persistent in electrokinetic dispensing, pushes the sample continuously into the separation channel during the separation, which elevates the baseline and affects the separation. In addition, the effect of hydrostatic pressure’s decreasing, caused by preferential solution flow between reservoirs, on the injection performance was assumed to be minimal; however, this was not strictly proved. (15) Lin, C. C.; Chen, C. C.; Lin, C. E.; Chen, S. H. J. Chromatogr., A 2004, 1051, 69-74. (16) Solignac, D.; Gijs, M. A. M. Anal. Chem. 2003, 75, 1652-1657. (17) Backofen, U.; Matysik, F. M.; Lunte, C. E. Anal. Chem. 2002, 74, 40544059. (18) Bai, X. X.; Lee, H. J.; Rossier, J. S.; Reymond, F.; Schafer, H.; Wossner, M.; Girault, H. H. Lab Chip 2002, 2, 45-49. (19) Futterer, C.; Minc, N.; Bormuth, V.; Codarbox, J. H.; Laval, P.; Rossier, J.; Viovy, J. L. Lab Chip 2004, 4, 351-356. (20) Gai, H. W.; Yu, L. F.; Dai, Z. P.; Ma, Y. F.; Lin, B. C. Electrophoresis 2004, 25, 1888-1894.
This paper presents two novel microchip formats to perform hydrostatic pressure injection, on which the continuous sample flow can be diverted into an additional microchannel during the dispensing, thus allowing an isolated sample plug to be injected. In addition, mathematical expression of hydrostatic sample loading is given, which fundamentally indicates the pressure decrease has a minimal effect on the injection stability, repeatability, and reproducibility. On the basis of these essential improvements, the potential of the hydrostatic pressure injection can be released into chip CE, such as removal of the injection bias, a minimum number of electrodes, an absence of pumps, a variable sample plug volume, etc. This injection method also finds its advantage in multichannel chip CE system, which tremendously reduces the number of electrodes needed for parallel sample separation. EXPERIMENTAL SECTION Materials and Solutions. Sodium fluorescein was purchased from Tianjin Institute of Dye (Tianjin, China). Fluorescein isothiocyanate (FITC) was obtained from Ameresco (Solon, OH). Rhodamine 123, bovine serum albumin (BSA, 66 000 Da) and conalbumin (ConA, 78 000 Da) was obtained from Sigma (St. Louis, MO). Acrylamide, ammonium persulfate (APS), N,N,N′,N′tetramethylethylenediamine (TEMED), and 3-(trimethoxysilyl) propyl methacrylate were obtained from Acros (New Jersey). The working concentration of sodium fluorescein was 10-7 M, unless otherwise noted. The working concentration of the Rhodamine 123 sample was 10-7 M for single-point LIF detection and 10-5 M for fluorescence imaging. The buffer was 25 mM borate, pH 9.3. Rhodamine 123 dye was used as the probing dye for demonstrating the principle of the injection. This kind of dye readily demonstrates two peaks in electropherogram with borate buffer,21 and in this paper, the “Rhodamine 123 sample peak” indicates the latter. BSA and ConA were labeled with FITC as described elsewhere.22 The ultimate concentration of FITC-BSA and FITC-ConA was ∼5 × 10-7 M. Microchips and Instruments. Glass microchips were fabricated as described elsewhere.22 Microchannels were 50 µm wide and 20 µm deep. The diameter and height of each reservoir were 3 and 1.5 mm, respectively. For the cross chip (Figure 1A), the liquid volume distribution was BR and BWR, 10 µL; SR, 7 µL; and SWR, empty. The channel length distributions (distance from the intersection) were BR and BWR, 10 mm; SR and SWR, 4 mm. For the double-cross chip (Figure 1A′), the liquid volume distribution was BRs and BWR, 10 µL; SR, 7 µL; and SWR, empty. The channel length distributions were BRs and BWR, 10 mm; and SR and SWR, 4 mm. The distance between the controlling and separation channels was 40 µm. For the multichannel chip in Figure 7A, all the separation and controlling channels were 25 mm long. The length of other arms of the microfluidic network was 5 mm. For the multichannel chip in Figure 7B, all the buffer and buffer waste arms were 25 mm long. The length of the sample and sample waste arms was 5 mm. Single-point23 and line24 LIF detection systems were the same as reported previously. The equipment and procedures for (21) Qin, J. H.; Ye, N. N.; Yu, L. F.; Liu, D. Y.; Fung, Y. S.; Wang, W.; Ma, X. J.; Lin, B. C. Electrophoresis 2005, 26, 1155-1162. (22) Huang, H. Q.; Xu, F.; Dai, Z. P.; Lin, B. C. Electrophoresis 2005, 26, 22542260.
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Figure 1. Comparison of cross and double-cross chip hydrostatic injection. (A) Schematic of the cross chip. SR, BR, BWR, and SWR indicate sample reservoir, buffer reservoir, buffer waste reservoir, and sample waste reservoir, respectively. Cross area was used for fluorescence images in B, C, and D. (B) Fluorescence image of hydrostatic sample loading; HP, hydrostatic pressure. (C, D) Fluorescence images of electrokinetic dispensing; EK, electrokinetic force. (E) A typical “tailed” electropherogram. (A′) Schematic of the double-cross chip. Channel between BR1 and BR2 is the controlling channel. Due to steric hindrance of BR1 and BR (BWR/BR2), an “L” bending of the channel is designed and fabricated at the end of the separation and controlling channel. Double-cross area of the microchip was used for fluorescence images in B′, C′, and D′. (B′) Fluorescence image of hydrostatic sample loading. (C′, D′) Fluorescence images of electrokinetic dispensing. (E′) A typical tail-free electropherogram.
Figure 2. (A) Illustration of the hydrostatic pressure-pinching in a cross intersection; (B) schematic of a basic model of hydrostatic pressure flow in a microchannel; (C) fluorescence images of the hydrostatic pressure-pinching in the cross intersection at different sample loading times; (D) variation of fluorescence intensity of cross intersection (indicated by dashed rectangle in frame C) with sample loading time, n ) 3.
fluorescence imaging were the same as reported elsewhere.20 For proteins separation, the microchannels were coated with linear polyacrylamide to prevent adsorption.22 Hydrostatic Pressure Injection for Single-Point LIF Detection. Referring to Figure 1A′, a 10-µL portion of buffer solution was added into BR1. Immediately after the solution was automatically filled in the microchannel network due to hydrostatic pressure and the hydrophilicity of the microchannel inner faces, 10 µL of buffer solution was sequentially added into BR, BR2, and BWR, followed by an addition of a 7-µL sample of solution into SR. Then a single pulse of a vacuum was applied at SWR to aspirate the sample into SWR. After a 20-s stabilization of the microfluids in the channel networks, an electric field of the same magnitude (280 v/cm, unless otherwise noted) was simultaneously (23) Zhou, Z. M.; Liu, D. Y.; Zhong, R. T.; Dai, Z. P.; Wu, D. P.; Wang, H.; Du, Y. G.; Xia, Z. N.; Zhang, L. P.; Mei, X. D.; Lin, B. C. Electrophoresis 2004, 25, 3032-3039. (24) Gao, Y.; Shen, Z.; Wang, H.; Dai, Z. P.; Lin, B. C. Electrophoresis 2005, 26, 4774-4779.
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Figure 3. (A) Electropherogram of a sequence of double-cross hydrostatic pressure injections (n ) 33). Periodical loading and dispensing time is 10 s. (B) Overlay of runs 7, 13, 19, 25, and 31 for the double-cross hydrostatic pressure injection (denoted by arrows in frame A).
applied in the separation and controlling channels. The detection point was set at a distance of 4.5 mm from the intersection. Application of the vacuum pulse is to accelerate the sample loading, or more than 40 s is generally needed for a stable sample loading, owing to relatively small hydrostatic sample flow rate in the microchannels. To vary the sample plug volume, an electric field was applied in the controlling channel during the sample loading, and the other procedures were the same as described above. Hydrostatic Pressure Injection for Line LIF Detection. Referring to Figure 7A and B, a 10-µL portion of buffer solution was added into BWR. Immediately after the solution was automatically filled in the microchannel in the microchannel network, 10 µL of buffer solution was added into each BR, followed by an addition of a 7-µL sample of solution into each SR. Then a single pulse of vacuum was applied at each SWR. After a 20-s stabilization of microfluids in the channel networks, an electric field of the same magnitude (400 v/cm) was simultaneously applied in all the separation and controlling channels. The detection line was set at a distance of 20 mm from the intersection. RESULTS AND DISCUSSION This research was motivated by our previous study that described a microchip injection method featuring hydrostatic
Figure 6. (A) Transformation of the chip format for the double-cross hydrostatic pressure injection. The cross label in the reservoir indicates the electrode. (B) Electropherogram of artificial mixtures of FITC-labeled BSA and ConA. The BR was grounded and BWR was connected to the anode. Esep ) 526.3 V/cm. The detection point is set at a distance of 4 mm from the intersection.
Figure 4. (A) Fluorescence images of sample loading profile with varied controlling electric field. Letter “E” indicates electric field in the controlling channel during the sample loading. (B) Variation of the Rhodamine 123 sample peak with the controlling electric field in the range of 24 to 88v/cm. (C) Peak height/area versus controlling electric field for Rhodamine 123; n ) 3. (D) Peak height/area versus controlling electric field for Rhodamine 123; Esep ) 400v/cm, n ) 3. (E) Peak height/area versus controlling electric field for sodium fluorescein; Esep ) 400v/cm, n ) 3.
Figure 5. (A) Illustration of three-electrode operation mode. Arrowed lines in the microchannel indicate the direction of electric field during the electrokinetic dispensing. (B) Typical sequential injections obtained with three electrodes. The periodical sample loading and dispensing time is 10 s. Numbers below the baseline indicate the magnitude of the controlling electric field during the sample loading. Esep ) 400v/ cm.
pressure loading.20 The previous injection method is performed on a classical cross chip and the injection process is described as follows: SWR is emptied to generate a hydrostatic pressure from SR to SWR (Figure 1A). This pressure pushes the sample through the cross intersection (Figure 1B). An electric field is applied between BR and BWR. The sample plug in the cross intersection is then dispensed into the separation channel for electrophoresis separation (Figure 1C). During the separation, the hydrostatic pressure from SR to SWR still exists. It drives the sample flow
Figure 7. (A) Schematic of one type of multichannel electrophoresis system using hydrostatic pressure sample injection and the corresponding electropherogram. (B) Schematic of another type of multichannel electrophoresis system using hydrostatic pressure injection and the corresponding electropherogram. The cross label in the reservoir indicates the electrode. The concentrations of FITC and the sodium fluorescein sample were 5 × 10-5 and 2.5 × 10-5 M, respectively.
continuously into the separation channel, associated with a horizontal electric field (Figure 1D). As a result, a “tail” is readily presented after the sample peak in the electropherogram (Figure 1E). Obviously, the major flaw of this injection method is the introduction of the tail. This tail affects, sometimes even destroys, the separation, which severely compromises many unique advantages of hydrostatic pressure injection that may benefit chip capillary electrophoresis. In this study, we eliminate this tail by addition of a controlling channel into the cross injector. The controlling channel is located between the separation channel and SR (Figure 1A′) and the original cross chip is transformed to a double-cross one. In this new chip format, the hydrostatic pressure injection process is demonstrated below. SWR is emptied, and the hydrostatic pressure pushes the sample through the double-cross intersection (Figure 1B′). An electric field is applied in the separation and controlling channels simultaneously. Due to the electric field in the controlling channel, a continuous sample flow from SR is diverted into the controlling channel and cannot migrate into the separation channel. As a result, an isolated sample plug can be injected by electric field in the separation channel (Figure 1C′ and D′). Figure 1E′ is a typical Analytical Chemistry, Vol. 78, No. 17, September 1, 2006
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electropherogram obtained in this case. Comparing this electropherogram with Figure 1E, we can easily find that the tail is completely eliminated. In other words, a new type of chip capillary electrophoresis injection method, double-cross hydrostatic pressure injection, has been established. Hydrostatic Pressure Loading and Electrokinetic Dispensing. During the sample loading, hydrostatic pressure exists not only between SR and SWR, but also between the empty SWR and buffer reservoirs (BR and BWR). These pressures drive the buffer solutions into the SWR via the cross intersection. Therefore, three strands of flow converge at the intersection (Figure 2A), forming a pressure-pinching configuration,18 as demonstrated in Figure 1B. This pinching profile resembles that of electrokinetic pinching.11 In the electrokinetic pinched injection, the pinching profile is determined by Eb/Es (ratio of electric field in the buffer channel to sample channel).4,11 Similarly, the hydrostatic pressure pinching profile can be determined by P1/Ps and P2/Ps (Figure 2A), neglecting the diffusion at the interface of buffer and sample flow.25 In a microchannel (Figure 2B), hydrostatic pressure, P, can be quantified using the following equation,
P ) Fg∆H
(1)
where F is the density, g is the gravitational constant, and ∆H is the liquid level difference. The liquid level difference will induce hydrostatic flow in the microchannel. In a D-shaped microchannel, the equation for the average flow rate,26vh, is
vh )
∆HFgDh2
(2)
where Dh is the hydraulic diameter, η is the viscosity, and L is the channel length. Owing to this flow, the liquid level difference would be steadily decreasing. Considering a minimum time passing, dt, the decrease of the liquid level difference, -d∆H, can be determined through the following mass balance equation,
(-d∆H)πR2 ) 2vhS dt
(3)
where S is cross-sectional area of the microchannel, and R is the radius of the reservoir. Combining eqs 1, 2, and 3, the following equation can be readily deduced,
P ) P0e-(FgDh S/15.626ηπR L)t 2
(4)
(P0 ) Fg∆H0) where P0 is the initial hydrostatic pressure. This equation quantitatively describes the pressure decrease in a microchannel caused by continuous flow from a high level (25) Chen, S. H.; Lin, Y. H.; Wang, L. Y.; Lin, C. C.; Lee, G. B. Anal. Chem. 2002, 74, 5146-5153. (26) Boer, G.; Dodge, A.; Flurri, K.; Van der Schoot, B. H.; Verpoorte, E.; De Rooij, N. F. Micro Total Anal. Syst. 1998, 492.
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P1 P10 -(FgDh2S/15.626ηπR2)[(1/L1)-(1/Ls)]t ) e Ps P 0
(5)
P2 P20 -(FgDh2S/15.626ηπR2)[(1/L2)-(1/Ls)]t ) e Ps P 0
(6)
s
s
For our microchips, R is 1.5 mm; Dh, S, L1, L2, and Ls are estimated to be 27 µm, 828 µm2, and 24, 10, and 8 mm, respectively. F and η are taken to be that of the water, at 20 °C, 1.0 g/mL and 1.0 cP, respectively. Provided with a sample loading time of 300 s,
e-(FgDh S/15.626ηπR )[(1/L1) - (1/Ls)]t ) 1.0013 2
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2
and
e-(FgDh S/15.626ηπR )[(1/L2) - (1/Ls)]t ) 1.0004 2
(2 × 15.626)ηL
2
reservoir to a low one. It can be noted that the term P cannot be 0 in the case that the initial hydrostatic pressure exists. That means that the hydrostatic flow, mathematically, never stops. Obviously, this deduction is not the truth in practice; however, it implies that the hydrostatic flow can be sustainable for a long period of time on a microchip (experimentally, more than 40 min), facilitating its application in microfluidics. On the basis of eq 4, the mathematical expressions that describe the hydrostatic pressure pinching can be readily obtained as the following,
2
These results combining eqs 5 and 6 indicate that the variation of P1/Ps and P2/Ps -would be 1.3‰ and 0.4‰, respectively, during a 300-s sample loading. That means the hydrostatic pressure pinching can be regarded as constant in a 300-s sample loading. In fact, this theoretical prediction is not surprising. As pressure in the sample channel decreases, the pressure in the bilateral separation and controlling channels decreases as well. Thus, the ratio remains constant. To demonstrate this point, a 300-s sample loading was recorded. As demonstrated in Figure 2C, the sample loading profile at 30 and 300 s did not demonstrate significant variation. The fluorescence intensity of the intersection can be regarded as a constant (Figure 2D). These results, according to the theoretical prediction, have significant implications. Within 300 s, (1) the hydrostatic pressure loading is stable; (2) the hydrostatic pressure injection is independent of the sample loading time, thus no strict time control is necessary for sample loading, simplifying the operation of the injection; (3) the injection would be repeatable. Fifteen independent injections were performed. Relative standard deviation (RSD) of the peak height was 7.22%, which meets the general requirement of the practical application. In addition, we present here some discussions about on-chip hydrostatic pressure flow. On the basis of eq 2, we can calculate that the average hydrostatic pressure flow rate on our microchip was ∼70 µm/s, provided there was a ∆H0 of 1.5 mm and an L of 5 mm. This value is one or two orders less than a typical electroosmotic flow rate (∼400-2000 µm/s, depending on the electric field); thus, it generally can be neglected when electroos-
motic flow is presented simultaneously. The hydrostatic pressure flow rate also can be very large if increasing the ∆H0. For example, by tilting the microchip, a hydrostatic flow rate of 2400 µm/s can be obtained with a ∆H0 of 10 cm.27 But it should be noted that in this case, the stability of hydrostatic pressure flow will be compromised. The stability of the hydrostatic pressure flow can be characterized by a decreasing pressure rate, (-dP/dt), which can be expressed by the following equation,
From this equation, it can be easily found that the decreasing pressure rate is proportional to ∆H0. It also can be found that the decreasing pressure rate is getting smaller with increasing time, which means the on-chip hydrostatic pressure flow will be more and more stable. Hydrostatic pressure sample loading is ascribed to pressure loading; thus, it should be free of injection bias, as reported in various literature.15,16 Sequential injection, as reported,14-16 is an effective way to evaluate the injection bias. In this study, 33 sequential injections were performed (Figure 3A). The consecutive sample peaks demonstrate excellent reproducibility, except for the first three runs. The RSD of the peak heights was 3.74%; overlaid traces (Figure 3B) demonstrated little or no differentiation between runs. These results establish the fact that the injection method is free of injection bias, which is in good agreement with the prediction above. In addition, they also indicate that hydrostatic pressure decreasing has a minimal effect on the electrokinetic dispensing, at least within 10 min, which agrees with the theoretical calculation based on eq 4 (percent of pressure decrease in 10 min is
