Study of Electrohydrodynamic Micropumping through Conduction Phenomenon

2224 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 5, SEPTEMBER/OCTOBER 2011 Study of Electrohydrodynamic Micropumping Through Conduction Phenomenon Seyed Reza Mahmoudi, Kazimierz Adamiak, Fellow, IEEE, G. S. Peter Castle, Life Fellow, IEEE, and Mehdi Ashjaee Abstract—In the present paper, a single-stage axisymmetric conduction micropump in the vertical configuration has been proposed. This micropump consists of four components: highvoltage ring electrode, grounded disk-shaped electrode, insulator spacer, and inlet/outlet ports. The high-voltage electrode and grounded electrode of the device were patterned on the two separate commercial LCP substrates with 30 µm copper cladding using standard lithographic techniques. The final spacing between two electrodes and the overall size of the device were measured to be 286 µm and 50 mm × 70 mm × 5 mm, respectively. The static pressure generation of the micropump was measured at different applied voltage using three different dielectric liquids, 10-GBN Nynas and Shell Diala AX transformer oils, and N-hexane. The range of applied voltages was between 300 and 1500 VDC, and maximum pressure generation up to 100 Pa was achieved at 1500 VDC applied voltage. To further verify the experimental results, a numerical simulation was also performed. The pressure head generation was predicted numerically and compared with experimental results at different applied voltages. Index Terms—Dielectric liquids, electrohydrodynamics, finite element method, micropumps, space charge. I. I NTRODUCTION HE OPERATION of electrohydrodynamic (EHD) micropumps is based on the interaction between electric fields and electric charges in a dielectric fluid. The electric body force f in a dielectric liquid, which results from an imposed electric  can be expressed as [1] field, E, T     1 2 ∂ε 1 2    f = ρc E − E ∇ε + ∇ E ρ 2 2 ∂ρ T (1) where ρc is volume charge density, ε is the fluid permittivity, and ρ is the fluid density, T is the fluid temperature. Manuscript received November 8, 2010; revised April 29, 2011; accepted May 17, 2011. Date of publication July 14, 2011; date of current version September 21, 2011. Paper 2010-EPC-450.R1, presented at the 2010 Industry Applications Society Annual Meeting, Houston, TX, October 3–7, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Electrostatic Processes Committee of the IEEE Industry Applications Society. S. R. Mahmoudi, K. Adamiak, and G. S. Peter Castle are with the Department of Electrical and Computer Engineering, University of Western Ontario, London, ON N6A 5B9, Canada (e-mail: smahmou3@uwo.ca; kadamiak@eng.uwo.ca; pcastle@eng.uwo.ca). M. Ashjaee is with the Department of Mechanical Engineering, Faculty of Engineering, University of Tehran, 14174 Tehran, Iran (e-mail: Ashjaee@ut.ac.ir). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2011.2161970 The first term on the right-hand side of (1) is the electrophoretic, or Coulombic, force that results from the net free space charges in the fluid. The second term, known as the dielectrophoretic force, arises from the permittivity gradient. The last term, called the electrostrictive force, is important only for compressible fluids. Free space charges in dielectric liquids can be generated by three different mechanisms: I) Induction: occurs in dielectric liquid with variable electrical conductivity, which can be caused due to the presence of a thermal gradient, or in two or multiphase flows; II) Conduction: through imbalanced dissociation–recombination reactions in the areas adjacent to the electrodes; III) Injection: by direct charge injection from the solid/liquid interface. These three distinctive mechanisms for free space charge generation can be exploited to create induction, conduction, and injection EHD pumping effects [4]. For an isothermal single-phase dielectric liquid, the last two terms of (1) vanish and EHD pumping operation require the existence of net space charge in the presence of an electric field to produce a net Coulombic force. Because the induction EHD pumps require a fluid nonhomogeneity for its operation, it cannot be utilized for isothermal single phase liquid pumping purposes. Therefore, there are only two possibilities to produce free space charge: ion injection and dissociation mechanisms. Ion drag pumps are based on direct ion injection from a charged electrode surface to the liquid. As a main disadvantage, these pumps cause degeneration of the working fluid and its electrical properties; thus, they are not reliable for long-term operation [2]. The typical electrode life time in ion injection pump was reported to be less than 1 h [3]. The chemical reactions cause serious electrode damages which affect the static head generation produced by the micropump. In contrast, conduction pumping is based on interaction between the electric field and charge carriers, which result from the imbalance rate of dissociation– recombination reactions around the electrodes submerged in a low conductivity dielectric liquid. A similar effect in liquids with high electrical conductivity, such as electrolytes, is called electroosmosis. The feasibility of conduction pumps has been proven for nonisothermal liquids and two phase flow applications [4]. Elimination of the direct ion injection and their operation in both isothermal and nonisothermal dielectric liquids makes them potentially attractive in many applications. The conduction mechanism in weakly conductive dielectric liquids is a complicated phenomenon. When a relatively small electric field (below 0.1 V/μm) is established between a low potential and a high potential electrodes immersed in a dielectric liquid, the ion injection is negligible, but the liquid impurities adjacent to the electrodes may begin to dissociate. 0093-9994/$26.00 © 2011 IEEE MAHMOUDI et al.: STUDY OF ELECTROHYDRODYNAMIC MICROPUMPING THROUGH CONDUCTION PHENOMENON The process of dissociation of the neutral species and recombination of the created ion pairs can be schematically written as follows [5]: Kd −→ + A + B−. A B ←− Kr + − (2) By increasing the applied voltage, but before reaching some threshold value of electric field (approximately 0.1 V/μm), the rate of neutral species dissociation and the rate of generated ions recombination are in equilibrium everywhere. By increasing the electric field above this threshold, depending on the liquid properties, the rate of dissociation in the vicinity of the electrodes exceeds that of recombination. The nonequilibrium dissociation–recombination process near the electrodes creates a layer with charges, having polarity opposite to the electrode voltage, in which the dissociation is dominant over recombination and is called the heterocharge layer. The attraction between the electrodes and the charges results in a net fluid flow from the blunt electrode toward the electrode having smaller radii of curvature. The conduction mechanism in this regime is mainly due to the ionic dissociation and is referred to as EHD conduction pumping. Further increasing of the electric field (in the order of 10 V/μm, depending on the liquid characteristics and impurity concentration), results in ion injection from the liquid/metal interface and produces a reverse pressure. Beyond this threshold, the ion-injection pumping mechanism will be dominant [6], and the pumping direction is reversed. The concept of the charge generation through the dissociation phenomenon has been known for long time [1], but the idea of using this phenomenon for pumping dielectric liquids is comparatively new [20]. Several theoretical [6], [17], numerical [12], [15], [18], [19] and experimental works [5], [13], [16], [21] were carried out to determine the feasibility of EHD pumping through the conduction phenomenon. In all of the previous studies, commercial refrigerants R-123, R-134a, and N-Hexane were introduced as working fluids to a single or multistage pump with the electrode spacing in the order of millimeter and the steady-state static pressure generation of the pump was determined. Furthermore, several geometries for highvoltage electrodes were investigated to increase pressure generation [21]. The initiation of a typical macroscale conduction pumping for R-123 was observed for voltages in the order of 5 kV DC. The main motivation in miniaturization of the EHD pumps is to shrink the separation between the electrodes to generate an intense electric field over a small volume of the working fluid even with reduced applied voltage for lab-on-a-chip applications. In this article, an EHD micropump is referred to a device with an electrode spacing d in the order of d ≤ 10−4 m. Typically, scaling down an EHD pump electrode spacing from macro- to microscale reduces the level of applied voltage required for the operation as much as one or even two orders of magnitude. This significant change in the operating voltage eliminates the need for a bulky high-voltage power supply. 2225 Moreover, EHD pumping of the dielectric liquids used for heat transfer, such as high Prandtl number liquids (transformer oils), fluorinert dielectric liquids [10] with low boiling temperature, and high latent heat of vaporization, cryogenic liquids [32] and other commercial refrigerants, shows promising performance in recent advanced cooling systems. Accordingly, scaling of the EHD pumps to smaller sizes can be potentially attractive in microfluidic devices. A survey of the literature for microscale EHD pumps shows that the miniaturization of ion drag pumps has been the subject of many investigations [28], [33]. Bart et al. [7] and Richter et al. [8] proposed preliminary designs for an ion injection micropump. Ahn [9] studied an ion drag micropump with 30-mm channel length and a planar electrode pair on glass substrate. Two different design with emitter-collector spacing of 100 and 200 μm were fabricated. The device was operated in the range of applied voltages between 20 and 130 V DC. Static pressure heads up to 200 Pa at 110 V applied voltage was achieved with 100 μm gap spacing using ethylene glycol. Darabi et al. [10] developed an ion drag pump consisting of 50–90 pumping stages with 100 μm electrode gaps fabricated on an alumina substrate. They used HFE-7100 (3M Co.) as a dielectric working fluid and obtained static pressure heads up to 700 Pa at 300 V applied voltage. Recently, several attempts were carried out to find a suitable high resistivity material to protect the electrodes and working fluid against oxidation and aging due to the ion injection at the solid–liquid interface. Yang et al. [3] fabricated an ion drag micropump with indiumtin oxide (ITO) as a material resistant against corrosion for the electrodes instead of using conventional electrode materials such as evaporated Cr/Au [10]. More stable operation of the micropump without visible damages of the ITO electrodes was initially observed and looked promising. However, in subsequent tests, the lifetime of the electrodes at 15 V DC applied voltage was only 6 min. This short lifetime of the electrodes and deterioration of the thermophysical properties of the working fluid due to the significant electrochemical effects during the operation [2] are the main disadvantages of the ion drag micropumps, and recently fewer investigations have been carried out to improve such designs. Although there have been these several attempts to scale down the ion injection pumps and decrease the operating voltage level, there were no similar attempts to miniaturize the conduction pumps mainly because they have been proposed just recently. Also, to the best of the authors’ knowledge, few investigations have been carried out to match the experimental results and the numerical simulations for the conduction pumping [14]. Moreover, in all of the numerical and experimental studies, the effect of conduction pumping has been reported with only three dielectric liquids, R-123, R-134a, and N-Hexane, as working fluid [15]–[21]. In the present work, an axisymmetric single-stage microscale conduction pump in the vertical configuration was designed, fabricated, and tested using three different working fluids: 10-GBN Nynas and Shell Diala AX transformer oils, and N-hexane. At steady-state operation and in the absence of the fluid flow, the static generated pressure and electric current of the device were measured at different applied voltages. To find an estimate for the charge density 2226 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 5, SEPTEMBER/OCTOBER 2011 Fig. 1. Qualitative description of electrode design. distribution and the electric field variation in the micropump, and further verify the experimental results, a numerical study based on the double-species bipolar conduction model was performed. The pressure generation was predicted numerically and compared with experimental results at different applied voltages. II. E LECTRODE D ESIGN FOR A C ONDUCTION M ICROPUMP To exploit charge carriers generated by the conduction mechanism for pumping purposes, the electrode geometry should be designed properly to form an effective heterocharge layer. For conduction pumping, high-voltage electrodes are needed to provide large projected area perpendicular to the flow direction or pressure gradient [21]. Moreover, to mitigate the ion injection effect at the metal/liquid interface, sharp edges should be avoided. If an imposed electric field is applied to a pair of parallel plates, a heterocharge layer is formed adjacent to both electrodes. The Coulombic forces exerted on the heterocharge layers near both electrodes are balanced. Therefore, net flow cannot be produced in this geometry [6]. However, by implementing some small changes in the configuration of the electrodes, one may increase the projected area and achieve a conduction pumping effect. For example, the high-voltage electrode may have the form of a series of concentric annuli, fixed parallel to the planar grounded electrode, which is immersed in a dielectric liquid, as shown in Fig. 1. Heterocharge layers, adjacent to each electrode, are formed, and the nonuniform field distribution near the high-voltage electrode creates an attraction toward the upper electrode. In this particular configuration, the radial component of the electric force exerted on the heterocharge layer is balanced, and the axial component of the electric force generates a pressure gradient, eventually causing a net flow in the axial direction. Since the electric field is more intense near the edges of the annuli, the thickness of the corresponding heterocharge layer will be larger, and the static pressure across it will be high. Therefore, the flow direction in the micropump is from the grounded electrode toward highvoltage electrode. In this study, the proposed conduction micropump consists of four components: high-voltage electrode, grounded electrode, insulator spacer, and inlet/outlet ports. The printed circuit board technology (PCB) was adapted to pattern the electrode geometries for the micropump. The PCB technology was recently Fig. 2. Top view of (a) high-voltage annulus electrodes and (b) grounded electrode patterned on two separate substrates. (Not scaled). implemented to fabricate several devices such as a magnetic fluxgate sensor [23], RF switch [35], and microfluidic devices [22], [34]. The schematic configuration of the high-voltage electrode and grounded electrode of the micropump patterned on the two substrates are presented in Fig. 2. The high-voltage electrode, shown in Fig. 2(a), consists of a series of concentric annulus rings patterned on a commercial liquid crystal polymer (LCP) substrate coated with copper cladding using standard lithographic techniques. A total of 75 concentric annuli each 25 μm wide and spaced 75 μm apart were electrically connected together. Considering the 75 ring structures with a thickness of 30 μm as a high-voltage electrode provides the projected area perpendicular to the axial direction in the order of 1 cm2 . Furthermore, this radial symmetric electrode design helps to minimize the number of sharp points and edges, which are usually encountered in a rectangular planar electrode design, thus minimizing any undesired ion injection. A disc-shaped grounded electrode was patterned on another piece of LCP substrate with the cladding using the same technique. A 230 μm thick annulus LCP spacer was utilized to position the two substrates parallel to each other. To seal the micropump, a layer of resin epoxy was used on both sides of the spacer. The final spacing between the two electrodes and the total volume of the fluid in the micropump was measured to be d = 286 μm and 0.8 μL, respectively. Comparing the electrode separation of this device (d < 0.3 mm) with previous macroscale design (d ∼ 2 mm), the current device is expected to operate at one order of magnitude smaller applied voltage. Two identical holes on both substrates, 2 mm in diameter, serve as inlet/outlet ports. The details of the geometry and dimensions are shown in Fig. 3. The MAHMOUDI et al.: STUDY OF ELECTROHYDRODYNAMIC MICROPUMPING THROUGH CONDUCTION PHENOMENON Fig. 3. Details of packaged conduction micropump. performance of EHD micropumps is temperature dependent. Temperature rise in pumping volume can be induced by Joule heating of working fluid particularly at higher applied voltages. Therefore, one should be cautious about the thermal effects which may significantly affect the performance of EHD pump. For the presented packaged device, since the total surface area of the pump is comparatively large (∼60 cm2 ) with respect to the total volume of the micropump, the temperature rise in working fluid is expected to be small. Therefore, in the present work, the variation of ion mobility, permittivity, and electrical conductivity of the working fluid due to thermal effects was assumed to be negligible. III. E XPERIMENTAL A PPARATUS AND P ROCEDURE The packaged micropump was investigated using three different working fluids. The two transformer oils mentioned earlier were selected due to their low electrical conductivity. Commercial grade normal hexane (N-hexane) was also used, and it was chosen because it showed no significant pumping effect in the previous macroscale studies. The V –I characteristics and the magnitude of generated pressure for this micropump were obtained for each of the different working fluids. The electrical and thermophysical properties of the fluids are tabulated in Table I. The charge relaxation time of the dielectric liquids used in this study is typically long. Therefore, the mobility of ions [11], charge density distribution, electric field variation, and resultant 2227 pressure of the device may be affected by even a weak stream of the fluid. The vertical positioning of the micropump enabled us to minimize the impact of disturbance and to measure the static pressure generation in the absence of fluid flow. The grounded side of the micropump was positioned at the bottom of a bath of working fluid, and the HV side of the pump with the patterned ring structures was positioned at the top. The micropump was completely submerged in the bath of working fluid, and a hypodermic syringe was used to fill it. A variable 0–3600 V DC power supply with a resolution of 10 V was connected to the upper electrode to provide the necessary voltage for the operation of the micropump. A microammeter was connected between the lower electrode and ground to measure the electric current. In the present work, only the static operation of the micropump at steady-state condition has been investigated; therefore, no mass flow rate measurement was carried out. To measure the generated static pressure at different values of applied voltage, a transparent tube 2 mm in diameter and 20 mm long was perpendicularly connected to the pump outlet. After reaching the steady-state condition, the column of working fluid is at a position where the electric body force is balanced with the weight of the column. Both the column rise due to the capillary action and conduction pumping were measured for different working fluids at different applied voltages with a CCD camera. Before starting the image processing, the measurement system was calibrated using an external object with known sizes. Its size in pixels, both in vertical and horizontal directions, was obtained at a specific focal length. To minimize the optical aberration, the liquid column is adjusted to be at the center of the image. A MATLAB code was used to convert the number of pixels directly to the liquid height and static pressure. To find the net liquid column rise due to EHD conduction pumping, the experimental column rise due to the capillary action was subtracted from the generated head (H = hgenerated − hc ). The total static pressure generation was calculated from the equation P = ρgH. The measured column rise due to the capillary action was approximately 2 mm, 3 mm, and 3.5 mm for N-hexane, Shell Diala AX, and 10-GBN Nynas, respectively. To verify the experimental observation of liquid column rise due to the capillary forces, the height of liquid was calculated for a narrow tube from the relation hc = 2γ/ρgr, where γ is the surface tension and r is radius of the tube. The comparison showed consistency between experimental observation and the formula with ±0.5 mm difference. The experimental uncertainty of the calculated pressure generation was mainly due to the column level measurement. Although the conduction pressure generation relies on the electrical and thermophysical properties of the working fluid which may vary significantly with small changes in concentration of contaminants, in the present study, the numerical values of these properties were obtained from the literature (Table I). The uncertainties associated with the measured parameters are summarized in Table II. The electrical permittivity of other materials used in this study is presented in Table III. Each experiment was repeated three times to ensure the repeatability of experiments, and error bars are affixed to all the data in the graphs presented. 2228 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 5, SEPTEMBER/OCTOBER 2011 TABLE I E LECTRICAL AND T HERMOPHYSICAL P ROPERTIES OF THE W ORKING F LUIDS U SED IN T HIS S TUDY AT 296.7 K TABLE II U NCERTAINTY OF E ACH Q UANTITY W HICH WAS M EASURED IN THE P RESENT W ORK dicates thermal equilibrium condition. The momentum balance equation can be expressed as − → − → (7) −∇∗ P ∗ + Co ρ∗c E ∗ + ρ∗ g ∗ = 0 where ρ∗ and P ∗ are dimensionless mass density and the generated pressure, respectively. The definition of dimensionless parameters appearing in the above equations are z z∗ = , d p∗ = TABLE III E LECTRICAL P ERMITTIVITY OF M ATERIALS n n∗ = neq IV. N UMERICAL A NALYSIS A. Governing Equations In this study, the system of governing equations is formulated − → based on the previous assumptions [12]. The electric field E ∗ around the electrodes, which is responsible for the charge generation, is distorted by the net free charges ρ∗c in the dielectric liquid and is governed by Poisson’s equation − → ∇∗ · E ∗ = Co ρ∗c (3)  ∗ = −∇∗ ϕ∗ ρ∗c = p∗ − n∗ and E (4) where where p∗ and n∗ are positive and negative charge densities, respectively. The charge transport equations of positive and negative charge carriers for the simplest conduction model [5] are − → ∇∗ · (p∗ E ∗ − α∇∗ p∗ ) = 2Co (1 − p∗ n∗ ) − → −∇∗ · (n∗ E ∗ + α∇∗ n∗ ) = 2Co (1 − p∗ n∗ ). p , neq (5) (6) Co in (5) and (6) is a nondimensional conduction parameter which can be interpreted as ratio of charge relaxation time, τT = ε/σ, to charge transit time, τ = d/bE, Co = (τT /2τ ) ≈ (neq d2 )/(εV ) = (σeq d2 )/(2bεV )(τT /2τ . The subscript eq in- E∗ = E V d P∗ = ρ∗ g ∗ = , r∗ = ε· P  V 2 , ε· r , d ϕ∗ = ϕ V d ρg  V 2  1  . d (8) d The diffusion coefficient α in (5) and (6) is equal to D/bV = (kT /eV ) ≈ (1/40 V). The order of magnitude analysis shows that the contribution of the hydrodynamic convection and diffusion terms are negligible comparing with that of the electric body force at steady-state condition and static operation of the device. This assumption is consistent with the previous numerical model proposed by Atten and Yagoobi [5], and Jeong et al. [12]. Therefore, the charge convection terms in (5) and (6) can be neglected. The applied boundary conditions are summarized in Table IV. An unstructured triangular mesh with increased mesh density in the area of the intense electric field around the highvoltage electrodes and in the heterocharge layer region around the grounded electrodes was applied. To ensure that the numerical results are independent of the computational grid, a grid sensitivity analysis was performed for different working fluids at different applied voltages. The criterion for the grid independency analysis was that the total pressure generation calculations were to be constant to the second decimal. V. R ESULTS AND D ISCUSSION Fig. 4 shows a photograph of the micropump submerged in a bath of 10-GBN Nynas transformer oil during its operation. By increasing the applied voltage and before reaching the steady-state conditions, the electric current passing through the micropump increases and a liquid column rise is generated in the vertical direction. In all experiments before reaching steadystate conditions, the direction of the net flow in this particular design of the micropump was from the grounded side (blunt MAHMOUDI et al.: STUDY OF ELECTROHYDRODYNAMIC MICROPUMPING THROUGH CONDUCTION PHENOMENON 2229 TABLE IV S UMMARY OF B OUNDARY C ONDITIONS Fig. 4. Demonstration of the column rise for a conduction micropump in a bath of 10-GBN Nynas transformer oil at (a) V = 0 and (b) V = 1500 VDC applied voltages. electrode) toward the high-voltage electrode. The direction of the net flow from blunt electrode toward high-voltage electrode which is a visible feature of the conduction pumping effect confirms that the current micropump predominantly operates based on conduction phenomenon. It takes a few seconds, depending on the magnitude of applied voltage, to reach the steady-state conditions. At the steady-state condition, the electric current of the micropump shows no measurable fluctuation and the liquid column rise in the capillary tube remains static. Both the electric current and static pressure generation measurements presented in this paper were performed at the steady-state conditions. The presented device was tested at 1500 VDC for a 14-h continuous operation, and the static generated pressure and electric current were monitored frequently. No appreciable change was observed in the pressure and electric current during the time. This suggests that the chemical reaction in the electrode/liquid interface due to the direct ion injection is not appreciable, and the electrodes remain relatively unchanged during this period. Comparing the direct ion injection micropump and conduction pumping, one can conclude that the conduction micropumps are remarkably reliable and suitable for long-term operations. By increasing the applied voltage, the current through the conduction micropump increases. Fig. 5 shows V –I characteristics for the micropump with 10-GBN Nynas and Shell Diala AX transformer oils. At the fixed gap spacing between the electrodes of 286 μm, the level of applied voltage for initiation of the conduction pumping is reduced to a few hundred volts. Changing the working fluid results in only small variations in the V –I characteristics, because the electrical properties of these two fluids are very similar. Fig. 5. V –I characteristic for conduction micropump measured for two different working fluids. Fig. 6. Distribution of equipotential lines for microscale conduction pumping for 10-GBN Nynas at 1500 VDC applied voltage. Potential difference between two adjacent lines is 50 V. The numerically calculated equipotential lines for the conduction micropump submerged in the bath of 10-GBN Nynas transformer oil are depicted in Fig. 6. Potential difference 2230 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 5, SEPTEMBER/OCTOBER 2011 Fig. 7. Calculated positive and negative charge densities in microscale conduction pump with 10-GBN Nynas oil transformer. Fig. 8. Axial electric field in microscale conduction pump calculated for different working fluids. between two adjacent lines is 50 V. The equipotential lines are distorted by the charge distribution near to the electrodes, and they are closer to each other adjacent to the high-voltage and grounded electrodes. The solution of the charge transport equations yields the spatial variation of charge carriers. Fig. 7 shows the numerical results for the concentration of positive and negative charges at 300 and 1500 VDC applied voltage with 10-GBN Nynas transformer oil as the working fluid. Because the thermophysical properties of the two transformer oils are very similar, the distribution of charges for Shell Diala AX is not presented. It can be seen that the heterocharge layers extend into entire the gap spacing at both lowest and highest applied voltages. Fig. 8 shows the electric field distribution between the electrodes for 10-GBN and N-hexane. The integration of electric field along a given path between the two electrodes should be Fig. 9. Comparison of calculated and experimental static pressures for conduction micropump using 10-GBN Nynas oil transformer. equal to the electric potential difference V because the applied voltage is constant. Therefore, the model predicts electric field enhancement in the whole space over the electrode gap particularly adjacent to the electrodes due to the existence of charge excluding a depression in a narrow band in the equilibrium region. A much smaller enhancement of the electric field near both electrodes can be observed for N-hexane due to its lower concentration of heterocharges. The comparison between the numerical results and experimental pressure generation for 10-GBN Nynas as the working fluid is presented in Fig. 9. The conduction pumping effect was started at the average field strength of 1 V/μm, and a maximum 101 Pa pressure generation was achieved at the average field strength of 5.24 V/μm. The comparison between numerical prediction and experimental results for pressure generation shows a good agreement with an average 8% deviation. The numerical results fall in the band of experimental uncertainty except at highest applied voltage. It is of interest to note that at 1500 VDC, the pressure generation of the device is overestimated. This corresponds to the average field strength of 5.24 V/μm, a condition where the ion injection phenomenon may produce a back pressure, reducing the pressure generated by the conduction micropump. This interpretation is confirmed when it is realized that the local field strength around the highvoltage electrode is approximately twice as that of the average value of field strength and is in the order of the theoretical threshold, 10 V/μm, where ion injection can occur. Fig. 10 shows the comparison between the experimental and numerical results for the pressure generation of the micropump using Shell Diala AX indicating a good agreement with an average deviation of 12%. Similar to the 10-GBN Nynas, the numerical model overestimates the pressure generation. Comparing the numerical results of the pressure generation in microscale for 10-GBN Nynas and Shell Diala AX shows that there is a small difference between the experimental and numerical results. The main reason for this difference is believed to be the uncertainty associated with the ion mobility calculation. In MAHMOUDI et al.: STUDY OF ELECTROHYDRODYNAMIC MICROPUMPING THROUGH CONDUCTION PHENOMENON 2231 Fig. 10. Comparison of calculated and experimental static pressures for conduction micropump using Shell Diala AX oil transformer. this study, the ion mobilities of negative and positive charges were assumed to be identical and calculated based on Walden’s rule, which relates the ion mobility to dynamic viscosity. Referring to the thermophysical and electrical properties of these two working fluids shows that the electrical properties of the fluids are very similar, whereas there is appreciable difference between their dynamic viscosities and ion mobilities. It should be noted that the dynamic viscosity of both transformer oils are exponential function of temperature and small changes in temperature may significantly change their viscosity and ion mobility [24], [26]. It should be noted that in the present numerical analysis, the field enhancement coefficient was assumed to be negligible. This assumption is particularly valid at low-field regimes (E < 4 V/μm). However, it was shown that neglecting the field enhancement coefficient for even moderate electric fields (4–6 V/μm) still provides good agreements between experimental and numerical pressure generation [6]. By submerging the micropump in the bath of N-hexane and applying the voltage, an electric current was measured, but no appreciable pressure generation was produced. A similar effect has been reported in the literature for a macroscale conduction pump with N-hexane as working fluid using various configurations of the electrodes [5]. Because of its shorter relaxation time, thicker heterocharge layer, and the associated enhancement of the electric field in the gap, one should expect higher numerical pressure generation for N-hexane based on the thermophysical properties tabulated in Table I. However, N-hexane is proven to be particularly sensitive to the effect of contaminations, and the electrical conductivity of values on the order of 10−8 to 10−17 (nine orders of magnitude difference) can be found throughout the literature [5], [25], [31]. Implementing the tabulated value of conductivity, σ = 63.9 × 10−12 S/m, agreement between experimental and numerical pressure generation cannot be achieved. To obtain agreement, a numerical value of σ = 1 × 10−12 S/m for electrical conductivity of N-hexane must be assumed. The dimensionless positive and negative charge densities and the electric field Fig. 11. Distribution of positive and negative charge densities in microscale conduction pump calculated for N-hexane. were calculated and shown in Fig. 11. The charge distribution is very similar to that of 10-GBN Nynas, but N-hexane charge distribution profile is more diffusive due to its two order of magnitude higher ion mobility. Assuming the numerical value for electrical conductivity σ = 1 × 10−12 S/m, the thermal equilibrium charge density for N-hexane, neq = 4.17 × 10−5 C/m3 , becomes two order of magnitude lower than neq = 1.91 × 10−4 C/m3 for 10-GBN Nynas. With this assumed value of electrical conductivity for N-hexane, the numerical solution predicts pressure generations about 10−1 Pa at applied voltages up to 1500 kV, which is consistent with the experimental observations of negligible column rise. A typical distribution of charge density over the microscale gap for a given dielectric fluid spacing slightly differs from that of macroscale spacing. By increasing the applied voltage, the weakly conductive liquid around the electrodes experiences the bipolar ionization, and heterocharge layers develop. By further increasing the electric field strength, the heterocharge layers extend over the entire gap spacing. Generally, at macroscale, the gap is larger than the thickness of the heterocharge layer. The conduction parameter Co determines the regime of charge concentration distribution. The different regimes of heterocharge layer distribution are demonstrated in Fig. 12. To show the impact of Co on the charge distribution patterns, the growth of the heterocharge layer is qualitatively demonstrated at different scales of Co for macroscale gap spacing [Fig. 12(a) and (b)] and for microscale gap spacing [Fig. 12(c) and (d)]. The conduction parameter is a function of the electric field strength, thermophysical properties of dielectric fluid, and the square of electrode spacing. By decreasing the gap space from order of centimeters to micrometers, Co becomes very small. Thus, depending on the dielectric fluid properties, the heterocharge layers around the opposite polarity electrodes extend to the gap spacing, and no definitive equilibrium region 2232 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 5, SEPTEMBER/OCTOBER 2011 Fig. 12. Space charge density and electric field in macro- and microgaps. (a) and (b). Impact of space averaged conduction parameter on formation of heterocharge layers in parallel plate geometry filled with a low conductive dielectric liquid. (c) Extension of heterocharge to the length of gap spacing for microscale gap spacing in parallel plate geometry filled with low conductive electrodes at comparatively lower applied voltages. (d) Heterocharge extension for microscale gap spacing in parallel plate geometry filled with low conductive electrodes at comparatively higher applied voltages. can be identified. For the operating voltage of 300–1500 VD, the Co varies between 10−4 < Co < 10−3 for transformer oils and 1 × 10−2 < Co < 5 × 10−2 for N-hexane. Therefore, the operation of the device falls in the regime depicted in Fig. 12(d). Moreover, by shrinking the distance between the electrodes, the required voltage to initiation of the conduction pumping effect decreases. Because the diffusion coefficient is inversely proportional to the applied voltage, it becomes one or two order of magnitude higher for the microscale device. It should be noted that the theoretical static pressure generation obtained for macroscale conduction pump overestimates the resulted static pressure generation of the micropump. The quadratic relation between the pressure generation and the electric field P = 0.85εV 2 /d2 was derived by Feng and Yagoobi [6] for a conduction pump with macrospace separation between the electrodes, where λ ≪ d. This cannot be applied for the device tested here with microscale gap spacing, where λ is in the order of ∼d. This equation can be applied only for the conduction macropump, where the thickness of the heterocharge layer near the electrode is smaller (or much smaller) than the electrode spacing [see Fig. 12(a)]. In the present conduction micropump with an electrode gap spacing in the order of few hundreds micrometers, the heterocharge layers, formed around two opposite charged electrodes, extend to the entire gap spacing [compare Fig. 12(a) and (d)]. Therefore, the theoretical analysis based on the simplifications due to the small heterocharge layer thickness is not applicable to the present study. Furthermore, in the previous theoretical model, it has been assumed that ion diffusion has a negligible contribution in the carrier transport process. According to the discussion given by Atten and Yagoobi [5], the ion diffusion term should be taken into account for V < 2500 VDC. Therefore, P = 0.85εV 2 /d2 cannot describe the static pressure generation at microscale gap spacing with heterocharge layers extended to the length of electrode separation. VI. C ONCLUSION In this paper, an axisymmetric EHD conduction micropump with 286 μm gap spacing between electrodes was proposed. The micropump was tested in the vertical configuration with three different working fluids: two transformer oils and N-hexane. The static pressure generation due to the conduction pumping was measured at different applied voltages. As an important result, the initiation of conduction pumping was reduced to 300 VDC applied voltage, which is one order of magnitude lower than that of the typical macroscale conduction pumps. To verify the experimental results, the 2-D axisymmetric model of the micropump was developed based on a double species conduction model. The static pressure generations were calculated and compared with the experimental results in steady-state static operation at different applied voltages. The numerical static pressure generations of the device are generally in a good agreement with the experimental data except for an overestimation at 10 V/μm local field strength (1500 VDC). 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Bryan, “Electrohydrodynamic conduction pump,” U.S. Patent 6 932 580, Aug. 23, 2005. [21] S. I. Jeong and J. Seyed-Yagoobi, “Innovative electrode designs for electrohydrodynamic conduction pumping,” IEEE Trans. Ind. Appl., vol. 40, no. 3, pp. 900–904, May/Jun. 2004. [22] L. Pagel and S. Gabmann, “Microfluidic systems in PCB technology,” in Proc. 31st IEEE IECON, 2005, pp. 2368–2371. [23] O. Dezuari, E. Belloy, S. E. Gilbert, and M. A. M. Gijs, “Printed circuit board integrated fluxgate sensor,” Sens. Actuators A, Phys., vol. 81, no. 1–3, pp. 200–203, Apr. 2000. [24] C. Yeckel, R. D. Curry, and P. Norgard, “A comparison of the AC breakdown strength of new and used poly-α Olefin coolant,” IEEE Trans. Dielectr. Elect. Insul., vol. 14, no. 4, pp. 820–824, Aug. 2007. 2233 [25] J. M. Crowley, G. S. Wright, and J. C. Chato, “Selecting a working fluid to increase the efficiency and flow rate of an EHD pump,” IEEE Trans. Ind. Appl., vol. 26, no. 1, pp. 42–49, Jan./Feb. 1990. [26] K. M. 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Maryland, College Park, MD, 2008. [33] B. D. Iverson and S. V. Garimella, “Recent advances in microscale pumping technologies: A review and evaluation,” Microfluid. Nanofluid., vol. 5, no. 2, pp. 145–174, Aug. 2008. [34] A. Wego and L. Pagel, “A self-filling micropump based on PCB technology,” Sens. Actuators A, Phys., vol. 88, no. 3, pp. 220–226, Jan. 2001. [35] B. A. Centiner, J. Y. Qian, H. P. Chang, M. Bachman, G. P. Li, and F. De Flaviis, “Monolithic integration of RF MEMS switches with a diversity antenna on PCB substrate,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 332–335, Jan. 2003. [36] P. Langevin, “Recombmaison et mobilites des ions dans les gag,” Ann. Chim. Phys., vol. 28, p. 433, 1903. Seyed Reza Mahmoudi is currently working toward the Ph.D. degree in the Department of Electrical and Computer Engineering at the University of Western Ontario (UWO), London, ON, Canada. From 2003 to 2008, he was with the Laser Diagnostics Research Laboratories in the Department of Mechanical Engineering, University of Tehran, Tehran, Iran, working on visualization of electrohydrodynamic natural convection heat transfer enhancement using a Mach-Zehnder interferometer and also investigating conduction pumping effect in dielectric liquids. In 2009, he joined the UWO Applied Electrostatics Research Center where his current research focuses on liquid/vapor phase change phenomenon in the presence of corona discharge. He has coauthored about 15 peer-reviewed conference and journal publications. Kazimierz Adamiak (M’87–SM’06–F’09) was born in Poland in 1951. He received the M.Sc. and Ph.D. degrees in electrical engineering from Szczecin University of Technology, Szczecin, Poland, and the D.Sc. degree (habilitation) from Gdansk University of Technology, Gdansk, Poland, in 1974, 1976, and 1983, respectively. From 1984 to 1986, he was an Assistant Professor in the Department of Electrical Engineering, Kielce University of Technology, Kielce, Poland. He was then a Visiting Professor at Queen’s University, Kingston, ON, Canada, the University of Minnesota, Minneapolis, and the University of Wisconsin, Madison. During 1989–1990, he was associated with Quantic Laboratories Inc., Winnipeg, MB, Canada. In 1990, he joined the Department of Electrical and Computer Engineering, University of Western Ontario, London, ON, Canada, where he is currently a Professor and a member of the Applied Electrostatics Research Centre. His research interests include applied electrostatics, electrohydrodynamics, and computational electromagnetics. He is the author or coauthor of numerous published technical papers. Dr. Adamiak is a Registered Professional Engineer in the Province of Ontario, Canada. 2234 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 5, SEPTEMBER/OCTOBER 2011 G. S. Peter Castle (S’61–M’68–SM’77–F’92– LF’05) received the B.E.Sc. and Ph.D. degrees in electrical engineering from the University of Western Ontario, London, ON, Canada, in 1961 and 1969, respectively, and the M.Sc. (Eng) degree and DIC from Imperial College, University of London, London, U.K., in 1963. He is Professor Emeritus and Adjunct Research Professor in the Department of Electrical and Computer Engineering, University of Western Ontario, London, ON, Canada. He has been active in research in the field of applied electrostatics for over 45 years, having published extensively in the areas of electrostatic precipitation, electrostatic painting and coating, electrophotography, and electrostatic separation. Mehdi Ashjaee received the Ph.D. degree from the University of Wisconsin, Madison, in 1986. He is a Professor of thermal-fluid science at the University of Tehran, Tehran, Iran. His main research interest is visualization of transport phenomena through optical techniques such as interferometry and holography. He has also contributed to the field of spray and atomization. He has published more than 100 articles in well-recognized journals and proceedings.