Journal of Chromatography A, 1344 (2014) 99–108

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Effect of insulating posts geometry on particle manipulation in insulator based dielectrophoretic devices夽 Alexandra LaLonde, Aytug Gencoglu, Maria F. Romero-Creel, Karuna S. Koppula, Blanca H. Lapizco-Encinas ∗ Microscale Bioseparations Laboratory and Biomedical Engineering Department, Rochester Institute of Technology, Rochester, NY, USA

a r t i c l e

i n f o

Article history: Received 26 December 2013 Received in revised form 25 March 2014 Accepted 30 March 2014 Available online 8 April 2014 Keywords: Dielectrophoresis Electric field Electrokinetics Microfluidics Microparticles

a b s t r a c t In this study, the effect of the geometry of insulating posts on microparticle trapping in insulator based dielectrophoresis (iDEP) was analyzed. The motivation for this research was to study how to improve particle trapping and enrichment by modifying the shape of insulating posts used in iDEP microdevices, while keeping post spacing constant. Mixtures of inert polystyrene particles were employed for demonstrating the effects of insulator shape on particle capture and enrichment. A series of experiments were carried out using an array of devices with different insulating post shapes. All the different post shapes employed had a width of 200 ␮m and were arranged in a square array of 250 ␮m center-to-center, thus, the spacing between posts was 50 ␮m in all cases. Mathematical modeling with COMSOL Multiphysics was employed to assess the magnitude of electric field gradients achieved with each one of the geometries tested. The results showed that the electric potential required to obtain effective particle trapping and enrichment can be significantly reduced by modifying the geometry of the insulating posts, without having to modify the separation distance between posts, thus, preserving the porosity of the microchannels. The separation of a mixture of 1-␮m and 2-␮m diameter particles was achieved in the form of dielectropherograms employing two different insulating post geometries (circle and diamond). Concentrated particles were released as peaks from the insulating post arrays where higher peak resolution separation was obtained with the sharper diamond geometry. Concentration enrichment above one order or magnitude was obtained for both particle types in both dielectropherograms. The results demonstrate that more efficient iDEP separations can be achieved at lower applied electric potentials by carefully selecting the geometry of the insulating structures. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Microfluidic systems offer attractive characteristics for applications involving biological particles such as macromolecules and cells. Working on the microscale allows for rapid response time, increased resolution and sensitivity, low sample consumption and increases the potential for portability. Additionally, the recent developments in microfabrication methods have significantly reduced the cost of miniaturized systems; opening the

夽 Presented at the 20th International Symposium on Electro- and Liquid PhaseSeparaton Techniques (ITP 2013), 6–9 October 2013, Puerto de la Cruz, Tenerife, Canary Islands, Spain. ∗ Corresponding author at: Biomedical Engineering Program, Rochester Institute of Technology, Institute Hall (Bldg. 73), Room 3103, 160 Lomb Memorial Drive, Rochester, NY 14623-5604, USA. Tel.: +1 585 475 2773. E-mail addresses: [email protected], [email protected] (B.H. Lapizco-Encinas). http://dx.doi.org/10.1016/j.chroma.2014.03.083 0021-9673/© 2014 Elsevier B.V. All rights reserved.

possibility for single use disposable devices, which are of particular importance in biomedical and clinical applications [1]. Electrokinetic (EK) methods are one of the leading trends in microfluidics, especially for the manipulation of bioparticles. Electrokinetic techniques offer great flexibility, simplicity, ease of integration with other processes within the same device, since electric fields can be used to simultaneously manipulate the suspending medium and the particles. Electrokinetic methods also offer the possibility of probing and assessing bioparticles by exploiting differences in dielectric properties, offering additional parameters to achieve a desired separation or sorting process. Dielectrophoresis (DEP), an EK mechanism, is the motion of particles caused by polarization effects when particles are exposed to a nonuniform electric field. In uniform electric fields, the Coulombic attractions between particle electrical charges and the electric field are balanced and therefore, no movement is produced in the case of neutral particles, only particles with a net charge (positive or negative) will move. In contrast, in the presence of nonuniform electric fields, as a particle becomes polarized, one side of the dipole

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will be exposed to slightly higher intensity electric field, producing net particle movement, regardless of the presence of net particle charge [2,3]. Dielectrophoresis provides high flexibility, since it can be used to manipulate charged and neutral particles with alternating current (AC) and/or direct current (DC) electric potentials. Dielectrophoresis also offers the capability for significant particle enrichment, up to three orders of magnitude [4], and a means for effective continuous particle sorting [5]. The two main approaches used for producing nonuniform electric fields are employing arrays of electrodes or arrays of insulating structures. Electrode-based DEP (eDEP) is the more traditional method; DEP was discovered employing a rudimentary electrode-based system [6]. There have been significant developments on microfabrication techniques, which have made possible new and novel electrode designs employed in many successful eDEP studies [7–9]. Microelectrodes for eDEP can be fabricated from a variety of materials, and due to the small dimensions high electric fields can be achieved by applying low voltages. However, eDEP has important drawbacks to consider: Microelectrodes may require expensive and complex fabrication methods; planar electrodes cannot be utilized for high throughput operations; and fouling, which is common when handling bioparticles, can significantly affect electrode performance. In contrast, iDEP offers an alternative by employing 3dimensional (3D) insulating structures located between two external electrodes to produce non-uniform electric fields [8,10,11]. Among the attractive advantages offered by iDEP is the feasibility of high throughput operations; deep channels can be used in iDEP devices since high electric field gradients are not confined to the bottom surface of the channel, as is the case with planar electrodes in eDEP [12]. Additionally, fouling does not affect the performance of iDEP devices, since an insulator will work despite fouling. Since majority of iDEP systems have been used with DC electric fields, electroosmotic flow (EOF) can be used to pump the liquid and particles through microchannels, making systems much simpler and more portable than electrode-based devices. Insulators are simpler to fabricate and can be made from polymeric materials such as plastic, leading to more economical systems than embedded electrode devices, opening the possibility for disposable single-use iDEP devices for diagnostic and clinical applications [13–15]. Additionally, iDEP devices offer great flexibility; depending on the relative magnitude of DEP and other EK forces (EP and EOF), different regimes of DEP can be used. Streaming iDEP, where particles are governed by both DEP and EK, allows for continuous and effective particle sorting [5,13,15,16]. Trapping iDEP, which reversibly captures particles between the insulating posts, can achieve significant particle enrichment, and has been used to successfully concentrate a wide array of biological particles, from macromolecules to cells [17–19]. Although the geometry of insulating structures is one of the main parameters that influences the performance of iDEP devices, there are not many studies focused on this topic. Besides insulating posts, other device configurations have been successfully employed for iDEP: oil menisci as insulators [20], nanopipettes [21], trapping at the reservoirs [22], insulating hurdles [15,16], microchannels with sawtooth [23], curved [24] and spiral [25] walls. Cummings and Singh reported the first application of arrays of insulating posts to produce iDEP [10], where an electric field across a microchannel was made nonuniform by the presence of insulating posts that “pinch” the channel cross-section “concentrating” the electric field at the constrictions between posts. In that report, circular and diamond shaped insulating posts were studied by varying the angle at which the posts were aligned with respect to the electric field [10]. Barbulovic-Nad et al. made an early attempt to manipulate constriction size in an iDEP device by actuating an oil droplet that acted

as an adjustable insulating post. In this device, constriction size was varied to change the magnitude of the DEP force [26]. Nakano et al. used triangle and ellipse shaped posts for streaming iDEP of proteins, focusing on characterizing the behavior of single protein particles as well as protein aggregates. Their study presented computational estimates of electric field and electric field gradient values at the tips of the insulating posts, but did not focus on comparing the performance obtained with the two post geometries [27]. The same research group later studied DEP effects by adding nano-sized insulating posts inside the constriction between a pair of triangular insulating posts [28]. Kwon et al. reported a study focused on the improvement of the arrangement of the insulating posts in iDEP channels. Only circular insulating posts were studied, where the longitudinal spacing between the posts was varied using mathematical models. It was found that a spacing between posts of 0.6 times the post radius produced the largest DEP to EK force ratio to enhance particle trapping. This is perhaps the only report focused on varying geometrical parameters to improve the performance of an iDEP channel with an array of insulating posts [29]. To date, insulating post shapes have been selected intuitively. Computational estimates of electric fields and electric field gradient values are often made, but their purpose is to determine whether particles will experience trapping or streaming iDEP in a given insulating post array, and they seldom guide device design efforts. The present study suggests that iDEP device design can include informed choices about insulating post geometry, and by selecting optimal post geometries which maximize the electric field gradients under a given set of conditions, the voltages required to achieve trapping or streaming iDEP of a certain particle can be reduced, leading to lower power requirements and less sample degradation. The present work investigated the effect of the geometry of the insulating posts on particle trapping with iDEP. Mathematical modeling with COMSOL Multiphysics and a series of experiments were performed to study the effect of post shape and post tapering on particle trapping. Modeling demonstrated that significant differences in the distribution of electric field and electric field gradients are obtained by varying post geometry. An array of iDEP microchannels containing different shapes of insulating posts were fabricated. The posts were 200 ␮m wide and were arranged in a square array of 250 ␮m center-to-center, thus, the spacing between posts was 50 ␮m in all cases. Two different geometries were analyzed, circular and diamond-shaped posts. The “tapering” of the posts was also studied by varying the length (not the width) of the posts. All devices were made from polydimethylsiloxane (PDMS) employing standard soft lithography techniques. Experiments were carried out with 1-␮m and 2-␮m diameter fluorescent polystyrene particles by applying DC electric potentials across the iDEP microchannels. It was found that particle trapping can be achieved at lower applied potentials by selecting geometries that had sharper angles (circles vs. diamonds) and more pronounced tapering (short vs. long posts). Dielectropherograms illustrating the enrichment and separation of a 1-␮m and 2-␮m diameter particle mixture showed that effective separations can be achieved at lower applied voltages (i.e., less energy consumption) than in previous studies by employing shorter posts with higher “tapering.” The geometry of insulating structures is an additional parameter that can be used to significantly enhance particle separation and enrichment in iDEP systems. 2. Theoretical background and mathematical model DEP is an EK mechanism caused by polarization effects, producing net particle motion under nonuniform electric fields. The DEP force exerted on a spherical particle is defined as [3]:  FDEP = 2εm rp 3 Re(fCM )∇ (E · E)

(1)

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fCM =

ε∗p − ε∗m

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(2)

ε∗p + 2ε∗m

where εm is the real permittivity of the suspending medium, rp is the particle radius, E is the local electric field, and Re(fCM ) is the real part of the Clausius–Mossotti (CM) factor, which accounts for particle polarizability. The CM factor involves εp * and εm * , which are the complex permittivities of the particle and the suspending medium, respectively. The complex permittivity is defined as: ε* = ε − (j/ω), where  and ω are the suspending medium conductivity and angufrequency of the applied electric potential, respectively; and lar √ j = −1. As seen in Eq. (2) the DEP force can be positive or negative, resulting in positive DEP or negative DEP, respectively, since in the case of spherical particles Re(fCM ) ranges from −0.5 to 1. Positive DEP behavior is when particles are attracted to the regions with higher electric field gradient, and negative DEP is when particles are repelled from those regions [3]. In the present study, only DC potentials were applied, under these conditions fCM can be expressed in terms of the real conductivities of the particle and the suspending medium [30] as: fCM =

p − m p + 2m

(3)

Polystyrene particles are less conductive than the surrounding medium, therefore, under a DC electric field fCM is always negative for these particles and only negative DEP (repulsion) is observed. For the mathematical model it was assumed fCM = −0.5 [31]. Particle motion with DEP is defined by the DEP velocity (vDEP ) and mobility (DEP ) [32]:

vDEP = DEP ∇ E 2 DEP =

(4)

rp 2 εm Re[fCM ] 3

(5)

where  is the viscosity of the suspending medium. The microdevices employed in this study were made from PDMS, which has a negative zeta potential of −13.3 mV, as measured in our laboratory with PIV with the suspending medium employed in this study. Due to these characteristics, PDMS is suitable for EOF, which was employed for pumping the liquid and particles through the microchannels, from the positive electrode to the negative electrode (left to right, see Fig. 1a). Additionally, since the polystyrene particles possess a net negative charge, they may experience EP. Both of these forces are considered linear EK, and their velocities are defined as follows, respectively [33]:

vEOF = EOF E = vEP = EP E =

−w εm  E 

p εm  E 

vEK = EK E = (EOF + EP )E

where D is the diffusion coefficient, c is particle concentration and vBulk is the fluid’s bulk motion due to pressure-driven flow (non-EK component of the velocity). It can be considered that particle trapping is achieved when j · E = 0 is satisfied, i.e., where the particle velocity along the field lines is zero. Particle trapping occurs is in locations where DEP force dominates and DEP velocity is greater than EK velocity; this can be expressed in terms of the EK and DEP mobilities: (EK E + DEP ∇ E 2 ) · E > 0

(10)

(6)

Rearranged as a ratio, Eq. (10) gives the condition that has to be satisfied for dielectrophoretic trapping of particles as [31]:

(7)

−

(8)

2.1. COMSOL mathematical model

where vEOF , vEP , and vEK are the EOF, EP and EK velocities, respectively; and EOF , EP , and EK are the EOF, EP, and EK mobilities, respectively; and  w and  p are the zeta potentials of the microchannel wall and the particle, respectively. In order to achieve particle capture, DEP must overcome the other transport mechanisms present in the system (linear EK effects, advection and diffusion). In this study, due the large size of the particles employed, diffusion contributions to particle movement can be neglected. Care was taken in each experiment to eliminate pressure-driven flow, eliminating advection effects. Therefore, neglecting diffusion and advection effects, and assuming that flow of particles j along the microchannel is mainly controlled by EK and DEP effects [13,29]: j = D∇ c + c(v EK + vDEP ) ≈ c(vEK + vDEP ) Bulk + v

Fig. 1. (a) Schematic representation of one of the iDEP devices employed for experimentation depicting the dimensions of the channel and the insulating posts and the interrogation window used for fluorescence measurements. (b) Illustration of the six different geometries of insulating post employed in this study. (c) Representation of the coordinate system and dimensions used in Section 4.2, where y refers to the channel width and x refers to the channel length.

(9)

DEP ∇ E 2  ·E >1 EK E 2

(11)

Microchannels containing arrays of circular and diamond shaped insulating posts with different post lengths and constant post width were used in this study (Fig. 1). Since the insulating posts transverse the entire depth of the microchannels, they create a distortion on the electric field over the entire volume of the channel. A schematic representation of one of the microchannels employed in this study is included in Fig. 1a, a list of the six geometries employed is depicted in Fig. 1b, and a representation of the coordinate system used to interpret post tapering is shown in Fig. 1c. COMSOL Multiphysics 4.3b (COMSOL, Inc., Newton, MA) with the AC/DC module was used to estimate the distribution of the electric field, gradient of the square of the electric field, and particle DEP mobilities. The model used a mesh of 373,392 elements for a channel with circular posts and a mesh of 1,160,020 elements for a channel with

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diamond shaped posts, considering a two dimensional model; depth effects were not considered, since previous reports demonstrated that changes in electric field along the channel depth are negligible [31]. The same element size parameters were used for both meshes. It was considered that the particles in this study exhibited negative DEP, and a value of Re(fCM ) = −0.5 was used for simulations. Medium permittivity of 6.94 × 10−10 F/m and medium viscosity of 8.91 × 10−4 kg m−1 s−1 were assumed. Electrokinetic flow velocity was estimated for a zeta potential for the microchannel wall of −13.3 mV. These measurements were obtained from PIV experiments carried in PDMS channels with no insulating posts and using the same suspending medium (data not shown). A brief description of the mathematical model is included below. Laplace equation was employed to describe the distribution of the electric potential in the microchannel:

∇2 = 0

(12)

where is the electric potential. The following boundary conditions were considered:  · J = 0 at the boundaries n

(13)

= Vinlet at the inlet of the microchannel

(14)

= Voutlet at the outlet of the microchannel

(15)

3.2. Microparticles Fluorescent polystyrene microspheres of two different sizes were employed: 1-␮m diameter green and 2-␮m diameter red (ex/em 505/515 nm and 580/605 nm, respectively, Invitrogen, Eugene, OR). Microparticle stock suspensions were sonicated for 10 min to break aggregates, and diluted in deionized water with a pH of 8 and a conductivity of 20 ␮S/cm; pH values were adjusted by adding 0.1 N KOH. These suspensions had concentrations of 7.28 × 108 and 7.28 × 107 particles/mL for 1-␮m and 2-␮m particles, respectively. Experiments for identifying minimum voltage required for particle trapping and comparison of particle trapping at different applied voltages were carried out with 1-␮m particles only. Experimentation for particle separation in the form of dielectropherograms employed a mixture of 1-␮m and 2 ␮m particles, 100 ␮L of this mixture were created by adding 2 ␮L of 1-␮m particle suspension and 20 ␮L of 2-␮m particles suspension to 78 ␮L of deionized water. The concentration of each particle type in this mixture was 1.46 × 107 particles/mL.

3.3. Equipment and software

 is the normal vector to the surface, J is the electrical curwhere n rent density and Vinlet and Voutlet are the electrical potentials at the microchannel inlet and outlet reservoirs, respectively. The boundaries considered are the microchannel walls and the surfaces of the insulating posts.

3. Materials and methods 3.1. Microdevice Microchannels made from PDMS (Dow Corning, Midland, MI) were fabricated using standard soft photolithography techniques [34]. Channels and insulating structures were defined in SU-8 3050 (MicroChem, Newton, MA) on 10 cm diameter Si wafers (Silicon Inc., Boise, ID). PDMS layers with an approximate thickness of 3 mm were cast onto this mold to produce the microchannels and insulating posts. The channel and post dimensions were verified with scanning electron microscope. The PDMS channels were then sealed onto 10 cm diameter circular glass wafers (Howard Glass, Worcester MA) that were previously spin-coated with PDMS. Thus, all interior channel surfaces were made of PDMS and had the same zeta potential. Both the PDMS channel layer containing the microchannels and the PDMS-coated glass substrate were activated using a plasma corona wand (Electro Technic Products, Chicago, IL) to promote sealing. All microchannels contained an inlet and an outlet liquid reservoir, and an array of circular or diamond shaped insulating structures embedded at the center of the channel. All channels were 10.16-mm long, 1mm wide, 40-␮m deep, and had and array of 32 insulating posts arranged in eight columns of four posts each. A schematic representation of one of the microchannels is shown in Fig. 1a. All insulating posts were 200 ␮m wide and long, spaced 250 ␮m center-to-center, thus, producing 50 ␮m openings between the posts across the microchannel width (Fig. 1a). The spacing between the channel wall and adjacent posts was 25 ␮m. For each geometry, three different post lengths were employed, in order to study the effect of post “tapering,” that produced a total of six different geometries tested in this study as listed in Fig. 1b.

A high voltage sequencer was used to apply DC electric potentials (Model HVS6000D, LabSmith, Livermore, CA) employing platinum wire electrodes. The voltage sequencer was manipulated with the software Sequence provided by the manufacturer. The particle response was recorded in the form of videos and pictures employing inverted microscopes equipped with video cameras. The iDEP experiments were carried out using a ZEISS Axiovert 40 CFL inverted microscope (Carl Zeiss Microscopy, Thornwood, NY). An Infinity 2 camera (Luminera, Ottawa, Canada) was used to capture microscopy images. To obtain particle dielectropherograms (Fig. 6), RGB color videos taken with the Axiovert 40 CFL microscope were analyzed using uScope software (LabSmith). Green and red fluorescence signal were split into two different videos to improve measurement accuracy. Particle fluorescence measurements were taken over an interrogation window located at the outlet of the post arrays as shown in Fig. 1a. A personal computer was required to operate the voltage sequencer and the two microscopes.

3.4. Experimental procedure Experiments started with a clean microchannel that was filled with deionized water adjusted to pH = 8 with 0.1 N KOH, reaching a final conductivity of  = 20 ␮S/cm. The channels were reversibly sealed to a vacuum chuck manifold (LabSmith, Livermore, CA) with a vacuum pump (Model 400-3910, Barnant Company, Barrington, IL). The manifold interfaces with slip tip syringes, which allowed simple filling of channels with the suspending medium using pressure. Then, 10 ␮L of sample containing 1-␮m microparticles was introduced at the inlet reservoir of the microchannel. For dielectropherograms, a sample of 5 ␮L of 1␮m and 2-␮m particle mixture was employed. Platinum wire electrodes were then placed at the channel reservoirs and a DC electric potential was applied across the length of the microchannel by employing the high voltage supply. The response of the particles was observed and recorded for each experiment in the form of videos and pictures. Between uses, it was necessary to re-condition the PDMS microchannel to ensure negative surface charge and stable EOF [34,35]; to do this, each channel was soaked for 2 h in 0.1 N KOH solution and then soaked for 1 h in DI water.

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4. Results and discussion 4.1. Modeling of the effect of insulator post geometry on (E2 ) COMSOL modeling was employed to study the effect of post shape on the distribution of the electric field and gradient of the square of the electric field (E2 ). Specific information on the dimensions and length to width ratios of the six geometries employed in this study is shown in Fig. 1b. Our previous experiments employing simple circular and diamond shaped posts demonstrated that the shape of the posts had a significant effect on the distribution and magnitude of the values of E2 in an iDEP microchannel [36]. Fig. 2 depicts the distribution of E2 in an array of circular (Fig. 2a) and in an array of diamond shaped (Fig. 2b) posts obtained by applying 800 V. The posts in both arrays have a diameter or width and length of 200 ␮m, and a spacing of 50 ␮m between posts. As it can be observed, higher values of E2 are reached with the diamond posts, and these higher values (as depicted by the darker red color) cover a much greater area than that obtained with the circular posts. It is important to note that higher gradients are obtained with the diamond geometry, even though for practical effects diamond shaped posts occupy less volume than circular posts. The sharp and angled diamond geometry creates a different distribution for E2 . For the diamond posts the maxima E2 region is mainly composed of two large regions with a tiny minima region at the center of the constriction; while the soft circular geometry produces four smaller maxima regions with a larger minima region at the center. The interesting results in Fig. 2 encouraged us to also analyze the “tapering” of the insulating posts, by adding to this study the “short” and “long” geometries illustrated in Fig. 1b, producing a total of six geometries to be tested. A mathematical derivation to analyze the effect of post geometry and post tapering on the distribution of E2 is included in section 4.2, supporting both the experimental and modeling results. The derivation used the coordinate system represented in Fig. 1c. Fig. 3 depicts the values of E2 obtained for the six geometries in this study, these values were calculated as an average of E2 over the entire channel, to avoid skewing of the data from single point values. The following expression was utilized for these estimations: 2 ∇ EAVG

  2 ∇ E  dA  = dA

(16)

As it can be seen from Fig. 3, according to the COMSOL simulations results, there are clear differences in the magnitude of E2 . The diamond shaped posts allowed obtaining higher average values of E2 that are 1.7–1.8 times greater than those obtained with circular posts; which in turn leads approximately double the magnitude of the DEP forces exerted on particles (Eq. (1)). Additionally, by comparing the results for the short vs. long geometries from Fig. 3, it is seen that the “tapering” of the posts also has a significant effect on E2 , which is discussed in Section 4.2.2. Post shape is a characteristic that can be very easily modified, providing an extra parameter to fine tune an iDEP system. Insulator post geometries can be chosen depending on the desired magnitude of DEP effect. These differences were also studied with experiments, and the results are included in the following sections. 4.2. Experimental assessment of the effect of insulator post geometry on particle trapping A series of experiments were carried out to identify the minimum voltage required to achieve the trapping of 1-␮m particles with negative DEP in each one of the six post geometries used in this study. These experiments were performed by slowly increasing the applied electric potential until observable trapping of 1-␮m

103

particles was achieved. Under DC electric fields particles exhibit negative DEP, thus, particles were expected to be repelled from the regions of higher electric field gradient, in this case, the constrictions between posts. Due to the balance between EK and DEP forces, particles were expected to be trapped just prior to the constrictions between posts, forming a band of concentrated particles [36]. The results obtained were in agreement with the modeling results (Fig. 3) as it is shown in Fig. 4. Two main observations can be made from Fig. 4: (i) particle capture with diamond geometries is achieved at voltages ∼60–130 V lower than those required with circle geometries; (ii) particle trapping with the “short” geometries is achieved with applied potentials that are ∼200 V lower than those required with the “long” geometries. It is important to highlight that Fig. 4 illustrates observed experimental results. In these experiments the short circle and diamond post geometries appear to have the same value for the minimum voltage required to obtain trapping. Since the difference in average E2 for these two geometries is not too large (1.13 × 1014 vs. 8.68 × 1013 V2 /m3 ), it is expected that the experiments may lead to similar observed behavior. The trends observed in this study regarding post shape and post tapering are more significant than individual results. These trends reveal that the diamond geometries produce higher DEP forces that lead to trapping at lower voltage than the circle geometries; and that short geometries also produce stronger trapping that normal or long geometries. 4.2.1. Post shape effects: circle vs. diamond The experimental results plotted in Fig. 4 clearly demonstrate that variations in post geometries can reduce the voltage required for achieving 1-␮m particle trapping by hundreds of Volts, without reducing device porosity, since the spacing between posts is not being altered. This allows maintaining the same throughput when analyzing a sample while enhancing DEP trapping. Fig. 4 clearly depicts that much lower applied voltages are required to trap particles when employing the diamond-shaped insulators. The effect of the post shape was also analyzed by comparing experimentally the magnitude of particle trapping obtained at three different voltages (200, 500 and 800 V), these results are shown in Fig. 5. From this figure it can be observed that at 200 V no trapping is observed for any of the circle geometries (Fig. 5a), while evident particle capture is obtained with the short-diamond geometry, as depicted by the multiple bands of concentrated particles shown in Fig. 5b. These results demonstrate how DEP trapping of particles is affected by the distribution of the gradient of the square of the electric field (E2 ), which depends on post shape, and it is not affected by the relative volume occupied by the posts. In this case, the diamond posts, which produce more particle trapping than the circle posts, occupy less volume than the circle posts. The sharpness of the post geometry (circle vs. diamond) has a significant effect on particle trapping by negative iDEP. 4.2.2. Post geometry tapering: short vs. long Post tapering is another important parameter that has an effect on the magnitude of particle trapping. The modeling results in Fig. 3 depict that higher gradients of the square of the electric field (E2 ) are obtained with the shorter geometries. The experimental results in Figs. 4 and 5 illustrate that higher E2 values and greater particle trapping is obtained at lower applied electric potentials with the shorter geometries. For example, as shown in Fig. 5a, weak particle trapping is obtained with the short circle, while “textbook” electrokinetic flow, where particles flow following electric field lines [13], is obtained with the long-circle posts. This “textbook” electrokinetic flow occurs when DEP is comparable to, but smaller than EK , which is expected with lower E2 values. The main difference between these systems is the “tapering” of the posts. To assess the effect of post tapering, an expression of the electric field gradient

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Fig. 2. Distribution of the gradient of the electric field (E2 ) in microchannels with (a) circular and (b) diamond shaped insulating posts obtained by applying 800 V. These COMSOL simulations clearly show that higher gradients and greater gradient regions are obtained with diamond shaped posts. (For interpretation of the references to color in the text, the reader is referred to the web version of this article.)

Fig. 3. Mathematical modeling with COMSOL of the average values of the gradient of the electric field (E2 ) for the six different insulating post geometries analyzed in this study.

Fig. 4. Experimental measurement of the minimum voltage required to achieve trapping of 1-␮m particles with iDEP with the six insulating post geometries used in this study.

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Fig. 5. Experimental trapping of 1-␮m particles obtained at 200, 500 and 800 V with (a) circular and (b) diamond shaped insulating posts. Locations of the insulating posts have been marked on the microscopy images.

in the x direction (see Fig. 1c) for the circle and diamond shaped posts was derived. In both cases, the magnitude of the electric field gradient is linearly correlated to the aspect ratio (length/width, see Fig. 1b) of the posts. The electric field is related to the current flux J as follows: J E = m

the y direction at any point be Y (see Fig. 1c). For a constant channel depth and assuming constant medium conductivity, the following expression is obtained for the average magnitude of the electric field (EAVG ): EAVG =

(17)

The product of cross-sectional area and the total current flux over the channel cross-section is equal to the electric current, and constant along the length of the channel. Thus, in a channel with a uniform depth Z, the current flux and the electric field are inversely proportional to the channel width at any point along the length of the channel, assuming electric field is applied across the channel length. Considering the constriction region between two circular or diamond shaped posts, let the distance between the posts along

i 1 Zm Y

(18)

where iis the current, and the average electric field is obtained as: EAVG = (E · dy)/Y . Thus, the average electric field gradient is:

∂EAVG i 1 =− Zm Y 2 ∂Y

(19)

Thus, ∂EAVG /∂x can be determined from the current, medium conductivity, channel depth, ∂EAVG /∂Y and ∂Y/∂x. The tapering of the insulating posts is described by ∂Y/∂x according to the coordinate system shown in Fig. 1c, where y refers to the width and x

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refers to the length of the channel. Eqs. (20) and (21) illustrate these relations for circular and diamond posts, respectively: ∂Y r = −2 b ra ∂x



ra − x 2ra x − x2

∂Y b = −2 a ∂x

field (∂EAVG /∂x) included in Eqs. (22) and (23) that demonstrate that sharper gradients are obtained for the short geometries.

(20)

4.3. Experimental dielectropherograms for the separation of a mixture of particles

(21)

To further assess and compare iDEP particle behavior with different insulating post geometries, the separation of a mixture of 1-␮m and 2-␮m diameter polystyrene particles was successfully carried out. The main parameter exploited to achieve this separation is particle size, which directly affects particle DEP mobility as depicted in Eq. (5). The values of DEP mobilities for 1-␮m and 2-␮m particles are −3.25 × 10−20 m4 /(V2 s) and −1.30 × 10−19 m4 /(V2 s), respectively. The negative sign of these values corresponds to the negative fCM of these particles under DC electric fields, which was assumed as −0.5 [31]. As it can be observed from these values, the DEP mobility for 2-␮m particles is four times larger than that of the 1-␮m particles. This difference is enough to allow for efficient particle separation. The separation experiments were carried out by introducing to the channel a sample consisting of a mixture of 1-␮m and 2-␮m particles, then applying a high DC signal of 800 V aimed to significantly concentrate particles at the post array. Then the signal was lowered in steps in order to selectively release the 1-␮m particles as a plug of concentrated particles, followed later by the release of the 2-␮m particles as a second plug of enriched particles. The fluorescence signals obtained from these plugs of particles were used to plot dielectropherograms of particle concentration vs. time (Fig. 6). These fluorescence signals were obtained at the outlet of the post array in the interrogation window illustrated in Fig. 1a. The concentration factor C/C0 was estimated by dividing the fluorescence intensity of the eluting particles measured at the interrogation window (C) at each time point by the initial fluorescence intensity of the feed concentration (C0 ). This was done separately for green and red fluorescence signals to estimate C/C0 for green 1-␮m and red 2-␮m particles, respectively. The efficiency of the separation of the particle mixture was measured in terms of the peak resolution (Rs) which was estimated as follows:

where ra and rb refer to the diameters of the circular posts, and a and b refer to half-width and half-length of the diamond shaped posts (see Fig. 1c). Applying the chain rule to Eqs. (19)–(21), the following expressions for the circular and the diamond shaped posts are obtained, respectively:

∂EAVG ra − x i 1 r for circular-shaped posts =2 b  2 ra Z ∂x 2 m Y 2ra x − x

(22)

b i 1 ∂EAVG for diamond-shaped posts =2 a Zm Y 2 ∂x

(23)

It can be seen that the average electric field distributions presented in Eqs. (22) and (23) for both geometries are position dependent (Y is a function of x), but circular posts have a nonlinear relationship between electric field and position along the constriction, while the diamond shaped posts have a linear relationship. This is also reflected in the DEP force distribution within the constriction. The ratios rb /ra and b/a clearly show why sharper tapering (present in the short geometries) leads to higher DEP force for a given applied voltage, which was predicted with the modeling results (Fig. 3) and observed in experiments for assessing minimum trapping voltages (Fig. 4) and particle trapping (Fig. 5). For example, by observing the circular geometry results (Fig. 5a), strong 1-␮m particle trapping is obtained at 500 V with the shortcircle as depicted by the convex curvature of the band of captured particles. Slightly weaker trapping is observed with the circular geometry (the band of particles is less convex), while no trapping of particles is detected with the long circular post shape. At 800 V, very strong trapping with a pronounced, broken convex curvature is reached with the short-circle; strong trapping is achieved with the circle, whereas the long-circle geometry showed slightly weaker trapping. A similar trend was observed for the diamond shaped posts, Experimental images obtained with the three diamond geometries were a bit harder to observe since the trapping was too strong at the employed electric potentials, these results obtained for 1-␮m particles are reported in Fig. 5b. At 200 V with the short-diamond, effective iDEP particle trapping is depicted by the convex bands of particles clearly observed in rows 3–6, these are bands with a welldefined curvature. A combination of trapping-streaming iDEP is observed at 200 V for the normal diamonds posts, while “textbook” EK flow (i.e., particles flowing in streamlines) is illustrated at this voltage for the long-diamond posts. At 500 V, very strong trapping, shown by a significantly curved band of particles at the first row of posts, is observed for the short-diamond geometry. Slightly weaker trapping is achieved for the diamond and long-diamond insulating posts. Trapping is significantly much stronger at 800 V for all diamond geometries. In particular, the image obtained at 800 V for the short-diamond depicts bands of trapped particle with a very strong convex curvature; this demonstrates the high intensity of the negative DEP effects can be obtained for this particular geometry that combines a sharp diamond shape with a strong tapering. These experimental results clearly display the dependence of particle trapping on the “tapering” of the insulating post geometry. Additionally, these results are in full agreement with the simulations shown in Fig. 3 and the experimental measurements in Fig. 4; and are supported by expressions for the average electric

Rs =

tr2 − tr1 W2 + W1

(24)

where tr refers the retention times and W refers to the peak width at the base, respectively. If a particular post geometry results in a higher peak resolution for the same processing time and same applied electric voltage, this means that better separations can be obtained with that given geometry at lower voltages than those required with other geometries. Furthermore, it is advantageous to reduce voltages requirements, since lower applied voltages mean lower undesired effects such as cell death, bioparticle denaturation and Joule heating. The results in Fig. 6 illustrate that by employing the diamond posts it is possible to obtain a better separation in terms of peak resolution. The dielectropherogram in Fig. 6a was obtained with the circular post geometry, it includes a peak for the 1-␮m green particles at time ∼25 s when the voltage was 400 V, followed by a peak of the red 2-␮m red particles at time ∼65 s when the voltage was 200 V. The resolution of this separation as calculated with Eq. (24) is Rs = 0.61. The video from which this dielectropherogram was obtained is available as the electronic Supplementary material file Video 1. These peaks clearly show that the particles were released at different times and that good particle enrichment was obtained, where the 1-␮m green particles had maximum concentration enrichment of ∼25 times the feed, while the 2-␮m red particles had a maxima concentration enrichment of ∼30 times the feed. Peak characteristics such as height and width depend on the force balance between EK and DEP, particles are released

A. LaLonde et al. / J. Chromatogr. A 1344 (2014) 99–108

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Fig. 6. Dielectropherograms demonstrating the concentration and separation of green 1-␮m and red 2-␮m particles. The plots show the concentration factor C/C0 , estimated as the ratio of the measured fluorescence signal to its initial value. Fluorescence signals were measured over the interrogation window depicted in Fig. 1a. Particles were initially concentrated by applying a potential of 800 V. The potential was consecutively dropped in order to release the particles as “peaks” of concentrated particles, where 1-␮m green particles were eluted first, followed by the 2-␮m red particles (a) Dielectropherogram obtained with circular geometry posts. (b) Dielectropherogram obtained with diamond geometry posts. (For interpretation of the references to color in the text, the reader is referred to the web version of this article.)

when EK contribution to particle movement is larger than that of DEP. The main parameters that affect this force balance are the  which directly affects EK velocity), electric field electric field (E, gradient (E2 , which is directly affected by post geometry) and particle properties, as well as the number of constrictions in the array of insulating posts. In particular, the width of the peaks depends on the magnitude of the EK velocity, particles that experience higher DEP forces will be released at lower applied voltages, when the EK velocity is also lower, leading to wider peaks. Fig. 6 clearly illustrates that broader peaks are obtained for the 2-␮m particles due to their higher DEP mobilities (higher retention). Wider peaks are also observed in the diamond dielectropherogram (Fig. 6b) since higher retention is obtained with the diamond shaped posts. The peaks in both dielectropherograms shown in Fig. 6 were obtained in less than 150 s, demonstrating that iDEP allows for fast separations. Fig. 6b shows the dielectropherogram obtained with the diamond shaped posts. The video from which this dielectropherogram was obtained is available as the electronic Supplementary material file Video 2. This separation has a resolution of Rs = 1.21 which is higher than the resolution obtained with the circle dielectropherogram (Rs = 0.61 for circle). As expected, the particle peaks in the diamond dielectropherogram have longer retention times,

this is due to the higher DEP forces obtained with the diamond posts; making it necessary to further decrease the applied potential to achieve particle release when compared to circles. This higher trapping capacity obtained with diamond posts is what produces better separations in terms of peak resolution. The peak for the 1-␮m green particles comes out at time ∼35 s at an applied voltage of 300 V, and the peak for the 2-␮m red particles peak comes out at time ∼110 s at a voltage of 100 V. Furthermore, besides the higher retention, the elution of the particles was achieved at voltages that were 100 V lower than those required with the circular posts; leading to wider peaks since EK velocities are lower at these lower potentials, taking longer for the peaks to come out. Particles were enriched during this separation process, where the average maximum enrichment for the green 1-␮m particles was ∼25 times the feed concentration, while the maximum enrichment for the red 2-␮m particles was ∼15 times C0 , this is lower value than the one obtained with the circular posts (C/C0 ∼ 30), but due to higher retention, this peak is wider which produces a shorter peak height. Comparing the resolution values obtained in these dielectropherograms, it is clear that this type of separations can be significantly enhanced by selecting the appropriate post geometry.

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5. Concluding remarks Insulator-based DEP (iDEP) relies on the ability of insulating posts to significantly distort the distribution of the local electric field in a microchannel, generating an electric field gradient. The geometry or shape of these insulating posts is one of the major parameters that affect particle trapping with iDEP. In this study, six different insulating post geometries were employed to trap 1-␮m polystyrene particles with negative DEP by applying direct current (DC) electric potentials to iDEP channels. The study included mathematical modeling and experimental work. First, electric field gradients were simulated employing a COMSOL Multiphysics model, showing that higher electric field gradient were obtained with diamond geometry than with circle geometries. The “tapering” of the post was also studied, and posts that had a shorter length, thus a sharper tapering, also produced greater electric field gradients. Experimental results were in agreement with the mathematical model, lower electric potentials were required to trap particles with diamond geometries and with shorter insulating post shapes. The results showed that the minimum electric potential required to achieve trapping could be decreased by more than 200 V, just by modifying the shape of the posts. This is an important improvement for a number of reasons: lower voltage requirements means lower power consumption, opening the possibility for portable and smaller devices. Portability considerations are crucial in microfluidic systems concerned with real life applications such as point of care sensors and diagnostics. Similarly, lower voltage requirements means longer battery life, which is essential in point of care applications in low resource or emergency settings. As a final part of this study, the separation of a mixture of 1␮m and 2-␮m diameter polystyrene particles was carried out with a circular and diamond posts. Particle separations were achieved in the form of dielectropherograms obtained by plotting fluorescence measurements vs. time of the particles being eluted from the post array. The peaks of concentrated particles illustrated that particle separation and enrichment above one order of magnitude was achieved in less than 150 s for both geometries. The diamond posts produced separations with higher peak resolution than those obtained with the circular posts. These results, supported by a COMSOL model and a series of experiments, clearly demonstrate that the shape of the insulating posts can be used to fine tune iDEP separations. Sharper geometries (e.g., diamond posts) and short geometries produce higher electric field gradient that enhance DEP effects leading to particle trapping at lower applied voltages; decreasing energy consumption and improving potential for portable devices. However, there is a cost for this improvement in performance; the higher electric field gradients generated by the sharper and shorter geometries can produce higher Joule heating and less stable systems. Joule heating in particular is an important concern when handling biological particles. The results of this study illustrate that specific arrays of posts of different geometries can be selected to obtain a desired DEP effect, allowing for simultaneous particle enrichment and separation, with high resolution and short processing times. One possibility is the combination of different geometries within the same system, which can produce gradients in the desired DEP effects to achieve more complex separations.

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