Nanofluidic Device for Exact Electrokinetic

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A Pseudo 1-D Micro/nanofluidic Device for Exact Electrokinetic Responses Junsuk Kim, Ho-Young Kim, Hyomin Lee, and Sung Jae Kim Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01178 • Publication Date (Web): 01 Jun 2016 Downloaded from http://pubs.acs.org on June 10, 2016

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A Pseudo 1-D Micro/nanofluidic Device for Exact Electrokinetic Responses Junsuk Kim1, Ho-Young Kim2,3,4, Hyomin Lee1,3† and Sung Jae Kim1,4,5†

1

Department of Electrical and Computer Engineering,

Seoul National University, Seoul 151-744, Republic of Korea 2

Department of Mechanical and Aerospace Engineering,


Institute of Advanced Machines and Design,


Big Data Institute, Seoul National University, Seoul 151-742, Republic of Korea 5

Inter-university Semiconductor Research Center,

Seoul National University, Seoul 151-744, Republic of Korea

†

Correspondence should be addressed to Dr. Hyomin Lee and Prof. Sung Jae Kim E-mail: (HLee) [email protected], (SJKim) [email protected]

ACS Paragon Plus Environment

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ABSTRACT Conventionally, a 1-dimensional micro/nanofluidic device, whose nanochannel bridged two microchannels, was widely chosen in the fundamental electrokinetic studies. However, the configuration had intrinsic limitations of the time-consuming and labor intensive tasks of filling and flushing the microchannel due to the high fluidic resistance of the nanochannel bridge. In this work, a pseudo 1-D micro/nanofluidic device incorporating with air valves at each microchannel was proposed for mitigating these limitations. High Laplace pressure formed at liquid/air interface inside the microchannels played as a virtual valve only when the electrokinetic operations were conducted. The identical electrokinetic behaviors of the propagation of ion concentration polarization layer and current-voltage responses were obtained in comparison with the conventional 1-D micro/nanofluidic device by both experiments

and

numerical

simulations.

Therefore,

the

suggested

pseudo

1-D

micro/nanofluidic device owned not only experimental conveniences but also exact electrokinetic responses.


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1. Introduction Over the past decades, electrokinetic micro/nanofluidic devices combined with a permselective nanoporous membrane have drawn significant attentions in the field of not only biomedical1-7 and environmental applications8-13 but also the fundamental researches of electrokinetic theory14-24. Among several new cutting-edge findings, an ion concentration polarization (ICP) was considered as one of the most unique phenomena, since it had numerous exciting features in terms of nanoscale electrokinetics and the great applicability for the engineering fields that required the proficient manipulation of ions. ICP is the generation of a steep concentration gradient between the anodic/cathodic side of a nanoporous membrane (or nanochannel) under dc bias25. While the original ICP device consisted of the 1-dimensional serial connections of microchannel-nanochannel-microchannel19, 23, 26, the engineering applications of it required the intensive modification of the original device for the desirable performances or functions, such as the 2-dimensional connections for applying a tangential electric (or pressure) field1, 27, the bifurcation of either or both microchannel for fractionating samples11, 28 and the parallel connections of them for high-throughput multiplexing schemes29, 30. However, the original 1D ICP device was still broadly chosen in fundamental electrokinetic researches, because the device had various advantages such as no uncontrollable pressure gradient across a whole domain and the convenience of tuning transport mechanisms, etc. Nevertheless, the original 1-D ICP device had intrinsic limitations: the labor-intensive and time-consuming tasks of (1) filling samples and (2) flushing the device for initializing the electrolyte concentration. In usual, samples for the original device were filled before or after vacuuming process for the building block of silicon/glass or poly-dimenthylsiloxane (PDMS), respectively31. A natural diffusion should be chosen as a mechanism for the flushing a sample


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through the microchannels, waiting more than several hours to re-use the device. One possible solution had been reported that thin side-microchannels were connected adjacent to the nanoporous membrane for the convenience handling of the samples32, but the I-V responses were inconsistent to that of the original device due to the residual flow through the side-microchannels. While the amplified electrokinetic flow pumped by the local high electric field33 should be balanced with a backflow in the original 1-D ICP device34, the amplified flows leaked through the side-microchannels in the device with the sidemicrochannels. Thus, the convective ion transportation was changed. In this work, a new 1-D ICP device was proposed to resolve the limitations. We fabricated a pseudo 1-D ICP device by incorporating an air valve structure that utilized high Laplace pressure at the interface of liquid/air/(hydrophobic)solid as shown in Figure 1(a) and 1(b). The in situ propagations of ICP layer and its I-V responses were tracked in the original device, the pseudo 1-D device with and without the valve operation by both experimental and theoretical manners. Conclusively, all of electrokinetic responses in the original 1-D and the proposed pseudo 1-D ICP device (in the case of closing the air valve) were identical within experimental error bounds so that one would retain both experimental conveniences and exact electrokinetic responses with the pseudo 1-D device, promoting the researches for both fundamental nano-electrokinetics and its engineering applications.


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2. The operation principle of the air valve The 1-D ICP device incorporating with the side-microchannels near the nanojunction at the main microchannel had been utilized for easy-filling (or flushing) of samples32. However, uncontrollable leakage through the side-microchannels due to an amplified electrokinetic flow inside ICP layer hindered an exact measurement of electrokinetic fields. Here we added an air valve structure at both side-microchannels. As denoted in Figure 1(a), the device contained three electrolyte reservoirs and four air reservoirs. Main (red) and buffer (blue) microchannels were connected with a permselective nanojunction in Figure 1(b). Along the side-microchannels, there was a bifurcation of narrow and wide channels (the dotted square). The air valve based on a high Laplace pressure prevented the fluid leakages through the sidemicrochannels during ICP operations. The air valves were open/closed as following steps. Step 1. Fill the samples from the main microchannel to the entire side-microchannels as shown in Figure 1(c). This was an “opening”-state of the air valve. Step 2. By filling air from the air reservoir 1 (a narrow bifurcation), the samples along the narrow and wide microchannel would flow out toward the air reservoir 2 as shown in Figure 1(d). Due to the difference of the hydrodynamic resistance between the narrow and wide portion of microchannel, the fluid swept out as indicated as the magnitude of arrows. This was a “close”-state of the air valve. This step 2 was performed for both side-microchannels. The supporting video was provided for the sequences of the operations. Note that the air filling (or applied pressure) was stopped once the meniscus was formed. The meniscus was theoretically able to endure the pressure more than 4000 Pa (approximately 40 cm of water column) with the given geometrical parameters based on the Young-Laplace equation, leading to a complete blocking of the leakage under a regular applied voltage.


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When the liquid meniscus was formed in the side-microchannel, the withstanding pressure of the meniscus between the inside and the outside of the liquid can be calculated by the YoungLaplace equation as following: ∆P = Pliquid − Pair = −σ (

cos θ T + cos θ B cos θ L + cos θ R + ) ds ws

(1)

where Pliquid and Pair are the pressure at the interface of liquid and air, respectively and σ is the surface tension of water. θ indicates the advance contact angle of the water and the subscripts of T, B, L, R indicates the top, bottom, left, right surface of the side-microchannel, respectively. ds and ws are the depth and the width of the side-microchannel. Since water was chosen as the solvent and the microchannel was made of PDMS and glass substrate, we used values35 of σ = 74 mN/m, ds = ws = 15 um, θT = θL = θR = 118o, θB = 54o. When the meniscus was formed at the middle of the side-microchannel, the theoretical value of ∆P was calculated as 4048 Pa (40cm height of water column), which was large enough to withstand the pressure (Pind) due to the amplified electrokinetic pumping. As shown in Figure 1(e) and 1(f), the meniscus was able to resist the electric body force with the applied voltage of 100 V which was much larger than the conventional driving voltage of ICP operation. In this work,

θ1 is almost the same as θ2 and they should bigger than π – advance contact angle for stop the movement of meniscus. We experimentally confirmed that they were bigger than 62o as shown in Figure 1(e) and 1(f). If the meniscus fail to stop at the middle of the sidemicrochannel, it advanced to the bifurcated point of the side-microchannel. In such case, the contact angle of the left and right side of the meniscus were reduced due to a diverging section. In other words, the meniscus was able to withstand higher pressure based on the new advanced contact angle35. The maximum pressure difference was obtained by substituting θL and θR with 180o in equation (1) resulting the new pressure difference as 9283 Pa (93cm height of water column).


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3. Materials and methods 3.1 Experimental setups General PDMS fabrication steps were used to fabricate microchannel structure (the mainand buffer-microchannel: 200 um width X 15 um depth, the side-microchannel of narrow region: 15 um width X 15 um depth and the side-microchannel of wide region: 100 um width X 15 um depth)36. The Nafion (Sigma Aldrich, USA) nanoporous membrane was patterned on the glass substrate based on surface patterning method32, 37. On top of Nafion-patterned substrate, prepared PDMS molding block was irreversibly bonded to a designated position. A mixture of 1 mM KCl solution (Sigma Aldrich, USA) with sulforhodamine B (SRB) (25 nM, Sigma Aldrich, USA) as a fluorescent tracer and fluorescent micro-particles (diameter = 2 um, Invitrogen, USA) were injected. The propagations of ICP layer were imaged by an inverted fluorescent microscope (IX53, Olympus) and CellSens program. Using Ag/AgCl electrodes, current-voltage responses were obtained by a source measure unit (Keithley 236, USA) and Labview program. The voltage sweep rate was 0.2 V/30 sec from 0 V to 10 V. 3.2 Numerical methods Numerical simulations were conducted by COMSOL 4.4 as commercial FEM software under a 2-dimensional domain and a steady state. Usually 2-d model is valid only if the geometrical dimension of a system along the eliminated direction is much larger than along the others. However, if the length scale in z-direction is large enough to capture the twodimensionality, the overlimiting current regime in ICP theory jumps to the electroosmotic instability regime. According the ICP theory, the dominant overlimiting current regimes were divided into (1) surface conduction regime if the minimum characteristic length scale < 2 um, (2) the electroosmotic mixing regime if the minimum characteristic length scale was between 2 um and 20 um and (3) the electroosmotic instability regime if the minimum characteristic


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length scale > 20 um17, 34. Therefore, we employed the imaginary 2-d numerical domain that possessed only the electroosmotic mixing effect, since actual dimensions in our device laid in regime (2). This was the best way not to lose the important characteristics of ICP phenomenon. The convergence and consistency of the numerical simulation would not be guaranteed in 3-d simulation of ICP in any regime, because of the low concentration inside the ICP layer. This method was conventionally adapted in a number of previous publications 27, 38-42

.

Under a steady state, mass conservations for cations (c+) and anions (c-) were described by the Nernst-Planck equations as following. FD   ∇ ⋅  − D ∇ c+ − c+∇ψ + c+u  = 0 RT  

(2)

FD   ∇ ⋅  − D ∇ c− + c− ∇ ψ + c− u  = 0 RT  

(3)

and

for a 1:1 symmetric electrolyte with the same diffusivity (e.g. KCl solution). Conventional simulation usually treated the diffusivity of K+ and Cl- as the same, since K+ diffusion coefficient and Cl- diffusion coefficient were 1.96 x 10-9 m2/s and 2.03 x 10-9 m2/s, respectively25, 43, 44. We adapted the diffusion coefficients of each ionic species as 2 x 10-9 m2/s for numerical convenience. In the above equations, D is the diffusivity, F is the Faradaic constant, R is the gas constant, T is the absolute temperature, ψ is the electric potential, and u are the velocity fields. In the case of 1 mM electrolyte solution, the thickness of electric double layer (~ 10 nm) was much smaller than the length scales of the main microchannel (15 µm depth and 200 µm width) and side microchannels (15 µm depth and 15 µm width) so that the local electroneutrality (the cation concentration is equal to the anion concentration in the


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whole domain, i.e. c+ = c- = c) and thin double layer approximation were adopted to reduce the computational cost. Adding equation (3) to equation (2) with the local electroneutrality assumption gave,

∇ ⋅ (− 2 D∇c + 2cu ) = 0

(4)

which is the diffusion-convection equation. Substituting equation (3) from equation (2) provided,  2 FD  ∇ ⋅− c∇ ψ  = 0  RT 

(5)

which is the current conservation. Using equation (4) and (5) as the governing equations instead of equation (2) and (3), the electromigration was able to be decoupled from the diffusion and the convection so that the computational cost was further reduced. Under the assumptions of thin double layer and local electroneutrality, the local electric potential would be determined by the current conservation (equation (5)) rather than the Poisson equation. This approach was able to resolve the numerical stability because the thin electrical double layer which is the cause of the “stiff” Poisson equation was eliminated by theoretical manner so that numerous publications adopt the current conservation equation to calculate the local electric field near the permselective nanoporous membrane 15, 34, 45-47. The flow fields (u) were described by the continuity equation and the Stokes equations. ∇ ⋅u = 0 − ∇ P + µ∇ 2u = 0

(6) (7)

where P is the hydrodynamic pressure and µ is the dynamic viscosity of water. Under 2dimensional domain as denoted in Figure 1(g), equations (4) ~ (7) were solved numerically


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with appropriate boundary conditions. The length of main microchannel (2000 um) was chosen based on the experimental observation that the depletion boundary was not exceed 2000 um at the applied voltage less than 10 V. Thus, we choose 2000 um as a minimum length for saving computational cost. The length of side-microchannel was selected as 1000 um as similar as the actual device. The real dimensions in experimental device were 6500 um and 1000 um for the main microchannel and the side-microchannel, respectively. At the bulk reservoir, the following boundary conditions should be satisfied.

ψ = Vapp , c = c 0 , and P = 0

(8)

where Vapp is the applied voltage at the bulk reservoir and c0 is the bulk concentration. P = 0 means that the pressure at the bulk reservoir was identical to the atmospheric pressure in terms of the gauge pressure. At the ideally cation-selective nanojunction, anion flux was equal to zero so that the condition relating to the electric potential was F   n ⋅  − ∇c + c∇ ψ  = 0 RT  

(9)

where n is the outward normal unit vector on the surface of whole boundary. Since the electrochemical potential for cationic species at the ideally permselective surface was the same with the value of the buffer microchannel48, the condition about cationic species was

ln

c Fψ + =0 c0 RT

(10)

when the electrochemical potential at the buffer microchannel was set to be zero. Meanwhile, the electrical boundary condition at the membrane was determined by the zero-anion flux condition (equation (9)) instead of specified potential or electric field. If the cation


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concentration is determined by the diffusion-convection equation (equation (4)), the anion concentration is automatically determined by the local electroneutral assumption. Thus, the zero-anion flux condition would impose the electric field on the membrane surface15, 34, 45-47. The flow on the nanojunction surface was u=0

(11)

which implied that zero flow rate through the membrane and the no-slip condition. On microchannel walls, no penetration conditions for the ionic current and the ionic flux were imposed as following.

n ⋅ ∇ψ = 0

(12)

n ⋅ ∇c = 0 .

(13)

and

Since the thin double layer approximation was chosen in the domain, the tangential velocity on the walls was described by the Smoluchowski slip velocity

t ⋅u = −

εζ t ⋅ ∇ψ and n ⋅ u = 0 µ

(14)

where t is the tangential unit vector of which direction was from the reservoir to the nanojunction (x-direction), ε is the electrical permittivity, ζ is the zeta potential of the walls and µ is the dynamic viscosity of water. When the side microchannels were connected with the main microchannel, additional constraints should be applied. Without the air valve operation, the induced pressure near the membrane would lead to the residual flows through the side microchannel. The effect of the pressure was simply modeled by the leakage flow rate. Thus, at the ends of each side microchannel, following constraints were imposed.


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ψ = float ,

(15)

c = 0,

(16)

Q = γQEOF

(17)

and

where Q is the flow rate through arbitrary cross section, γ is the leakage parameter in the range from 0 to 0.5, and QEOF is the inward electroosmotic flow rate evaluated from the bulk reservoir surface. If γ was non-zero value, there was non-zero residual flow through the side microchannels. The residual flow caused by the induced pressure inside ICP layer was modeled as an effective flow rate through the side-microchannel. The inward electroosmotic flow rate (QEOF) was expressed as Q EOF = ∫

S

εζ ∇ ψ ⋅ ndS µ

(18)

where S is the cross sectional area on the inlet and n are the outward normal unit vector on surface S. The zeta potential on PDMS surface was set to be -100 mV at 1 mM KCl solution49, . The flow rate through the side-microchannels (Q) was modeled by equation (17) where γ

50

was set to be zero and 0.2 for pseudo 1-D ICP device with closing and opening the air valve, respectively. 0.2 means that the 20 % of inward flow rate leaked through the each sidemicrochannel and 60 % of the flow rate turned into the back flow because of the low permeability of the nanoporous membrane. This value was chosen based on the experimental results shown in Figure 2. A Lagrangian multiplier was used for calculating the ionic current in accordance with an applied voltage.


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4. Results and discussion 4.1 The flow tracking with opening and closing the air valve In order to confirm whether the fluid was leaked through the side-microchannels, the generations of ICP layer were tracked in situ with opening and closing the air valve. As shown in Figure 2 (a), the polystyrene beads as a flow indicator exited along the sidemicrochannels (indicated by yellow arrows) and the fluorescent intensity at the sidemicrochannel was diminished due to the leakage flow induced by ICP layer. Note that the leakage flow had a minimal amount of fluorescent dye, because most of dye would be filtered at the boundary of ICP layer. The air valve was opened and the applied voltage was 10 V in this demonstration. It had been reported that the electric field inside ICP layer was significantly amplified, leading ICP layer to strongly pump the fluid toward the nanojunction33. Since there were the side-microchannels near the nanojunction, the portion of the amplified flow would be leaked through the side-microchannels and the other turned back toward to the main-microchannel. In contrast, the particles were frozen inside the sidemicrochannels with closing the air valve as shown in Figure 2(b). Also the fluorescent intensity inside the side-microchannels was maintained, reflecting there was no leakage through the side-microchannel. These results strongly supported that there was no flow through the side-microchannel if the air valve closed. Consequently, the propagation of the depletion boundary (indicated by white arrows in each figure) was faster with closing the air valve than opening the valve. See supporting videos for each case. 4.2 The formations of the depletion boundary with opening and closing the air valve The detailed formations of the depletion boundary for three distinct cases were shown in Figure 3. The external voltage was swept from 0 V to 10 V at the sweeping rate of 0.2 V per 30 s. Comparing three types of devices which were an original 1-D ICP device (the first


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column), a pseudo 1-D ICP device with closing the air valve (the second column) and a pseudo 1-D ICP device with opening the air valve (the last column), the original 1-D ICP device and the pseudo 1-D ICP device with closing the air valve had the identical propagation length of the depletion zone. On the other hand, opening the air valve would show much smaller propagation of the depletion zone than other cases. This was because the leakage was completely prevented by the air valve. See the supporting video for these experiments. The results of the propagations were well-matched with the numerical simulations shown in Figure 3(c). Instead of considering the surface tension and Laplace pressure boundary condition in the simulation, the no flow condition was adapted from the fact that the high Laplace pressure can stop the flow through the side-microchannel. Thus, the main objective of the simulation was that the electrokinetic response of the pseudo device with open the air valve was completely different from either the original or pseudo device with close the air valve. In the meantime, the another main objective of the simulation was to confirm how another electrokinetic fields such as concentration distributions, electric fields, and slip velocity in the original and the pseudo device with open air valve were different, since we cannot visualize the detailed distributions (The length of the ion depletion zone was the only observable data that we can experimentally measure). While the air-valve effectively stopped the flow through the side-microchannel as we demonstrated in Figure 2, we had to prove the “no leakage” condition was the only main reason to provide the identical electrokinetic responses. Other possible reasons could be the alteration of the electric field and flow motions due to the side-microchannel. The numerical simulation should be perform to confirm that the electric, flow and concentration fields were the same as well in the original and the pseudo device with close air valve. As shown in Figure 3(d), all of simulated electrokinetic fields (concentration, electric field strength and slip velocity) along the depletion zone were also


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identical at both case of the original and the pseudo 1-D ICP device with closing the air valve. Since the ion depletion zone acts as a dominant electrical resistance once the zone reaches the steady state, the electrical field in both simulation and experiment had to be similar. A small deviation was caused by the numerical domain containing only the main microchannel, while the electric field in the actual device was applied through the main microchannel – nanojunction – the buffer microchannel. Therefore, the air valve enabled the pseudo 1-D ICP device to substitute the original 1-D ICP device. 4.3 Current-voltage responses with opening and closing the air valve The I-V responses were considered the most important characteristics of a system comprising a perm-selective nanoporous membrane. Under dc bias, a linear I-V relationship called Ohmic region was appeared and the plateau was followed due to the limitation of ionic carriers51, 52. This limiting current behavior was a nuisance in terms of an electrical power efficiency, since the current was saturated at the limiting value. Further application of voltage would lead to an overlimiting current behavior which was affected by various constraints such as a surface conduction17, 34, an electroosmotic flow16, 24, 34, 39 and an electroosmotic instability15,

53

. These particular behaviors would imprint the signature of the system.

Therefore, the I-V responses would be a fingerprint to identify the system. As shown in Figure 4, the I-V curve of the pseudo 1-D ICP device with closing the air valve (green) coincided with that of the original 1-D ICP device (blue). Since the measurements were repeated more than 20 times, the deviation of each plot were within the error bars. In contrast, the pseudo 1-D ICP device with opening the air valve had higher overlimiting conductance than others due to the suppressed depletion zone32, while the Ohmic conductance were the same. This was because the most of leakage flow would initiate after the limiting current was reached and the suppressed ICP layer would result in the increase of conductivity inside the


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ion depletion zone32.


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5. Conclusions In this work, a new structural component for a fast and convenient experiment of a 1-D micro/nanofluidic device was proposed. The pseudo 1-D micro/nanofluidic device combined with the air valve not only reduced the total time of experiment but also provided the identical electrokinetic response with the original ICP device. The total time that took for one experiment include pre-process and run. The run times with the original and the pseudo device until the ICP reached steady state were identical (~40 minutes). However, the preprocess for resetting the electrolyte concentration inside microchannels took much shorter with the pseudo device than with the original device, because the reset only relied on a diffusion process with the original device. Thus, the time comparison for one experiment between the two devices was as follows. The original 1-D device; pre-process (100 minute) + run time (~40 min) = ~140 minutes. The pseudo 1-D device; pre-process (1~2 minute) + run time (~40 min) = ~45 minutes. Therefore, if 10 data points are needed, it takes 1 day with original device and 7 hours 30 minutes with pseudo device. We confirmed that there were no leakages at the interface of air-stop along the sidemicrochannel as long as the induced pressure × surface area on the meniscus was smaller than the surface tension × perimeter of the meniscus. In addition, the original 1-D ICP device and the pseudo 1-D ICP device with closing the air valve showed the identical formation of ICP layer and I-V responses, while the opening the air valve lead to the distorted results. These demonstrations were well-matched with numerical simulations. Therefore, the presented method would provide an effective platform in the fundamental research of electrokinetic phenomenon by eliminating the time-consuming and labor intensive tasks.


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Acknowledgements This work was supported by National Research Foundation of Korea (CISS-2011-0031870, 2012-0009563, 2014-048162, 2013R1A1A1008125) and Korean Health Technology RND Project (HI13C1468 and HI14C0559). All authors acknowledge the support from BK21+ program of Creative Research Engineer Development IT, SNU.


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Figure captions Figure 1 (a) Snapshot and (b) microscopic view of the fabricated pseudo 1-D ICP device. The sequences of operating air valve structures (c) Step 1: Flushing and (d) Step 2: Air cutting. The microscopic images of the meniscus at the air valve and its force balances (e) with and (f) without applied voltage. Here θ1 and θ2 were π – (meniscus contact angle at the side PDMS wall without applied voltage) and π – (meniscus contact angle at the side PDMS wall with 100 V applied voltage), respectively. (g) The schematic representation of 2dimensional numerical domain (not to scale) Figure 2 The movement of fluorescent microparticles and dyes at the applied voltage of 10 V with (a) the opening the air valve and (b) closing the air valve. In each figure, the depletion boundaries were denoted as two opposite white arrows. Figure 3 The propagation of the ion depletion zone in three different types of device. (a) Schematic diagrams of each device, (b) experiments and (c) numerical simulations. The calculated ionic concentration distributions, electric field strength and slip velocity inside the ICP layer were plotted in (d). Figure 4 The current-voltage responses measured by experiments for three different types of device.


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Nanofluidic Device for Exact Electrokinetic

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