Experimental Study of EHD Flows in Symmetric Electrode Systemin Wide Range of Low-voltage Conductivities

I. Ashikhmin, Y. K. Stishkov, and Y. DonskovREC “Electrophysics”, Department of Physics, St. Petersburg State University, Russia

Abstract—The paper presents the results of an experimental study of electrohydrodynamic flows in the symmetric wire-wireelectrode system placed in a cell with polydimethylsiloxane (PDMS). PDMS was doped with butanol, which causes the originalconductivity of the fluid to grow by five orders of magnitude. The effects of impurities on the structure of emerging flows and thecurrent-voltage characteristics are described. There exists a range of butanol concentration in the system, where the through flowoccurs, which can be used for pumping a liquid. At lower values of admixture concentration, the arising EHD flows are highlyunstable. At higher concentrations, the EHD flows become symmetric, so the through flow weakens and symmetric 4-vortex flowstructure emerges.

Keywords—EHD flow, PIV, EHD pump, injection charge formation

I. INTRODUCTION

It is well-known that high electric fields can cause chargeformation in fluids, which in turn leads to emergence of theso-called EHD flows. The most interesting among differenttypes of EHD flows are those that create the one-directional orthrough flow, because such flow can be used to pump liquids.Stuetzer [1] was among the first to make a device that createsexcessive pressure in an open hydraulic circuit, and he showedthat we can use it to pump liquid. In 1960, he built [2] anEHD pump that worked in a closed circuit filled with variousliquid dielectrics. His works featured an asymmetric electrodeconfiguration of the needle-ring type. Such electrode systemswere chosen by analogy with those used to create ionic wind inthe air. The main problem of asymmetric electrode systems inliquids is that, in contrast to the air, the volume electric chargefails here to become neutralized on the collector electrode dueto high values of electric Reynolds number (ReE). It meansthat ions in liquids move predominantly along streamlines,whereas they move in the air along the electric field lines.Therefore, the high ReE value in liquids leads to the bulkcharge being carried out from the inter-electrode gap to outerregion.

To reduce the amount of bulk charge in the outer region,some authors [3], [4] used grids for the collector electrode,but these as any obstructions lower the efficiency of pumpingliquid. Another way to solve the problem is to use a systemof electrodes where bipolar injection takes place, i.e. bothelectrodes can produce ions of different signs that recombineafterwards. The electrode system that implements this mecha-nism of charge formation was proposed Stishkov et al. [5] andit consisted of two symmetrical parallel wire electrodes. It hasbeen shown that the flow structure in this system depends onthe concentration of admixture. Among others, the through

Corresponding author: Ilya Ashikhmine-mail address: ashikhmin.ilya@gmail.com

Presented at the 2014 International Symposium on Electrohydrodynamics(ISEHD 2014), in June 2014

(one-directional) flow without vortices emerges, so the systemis capable of pumping liquids.

The variety of flow patterns in the symmetric electrode sys-tem was examined through computer simulation of the modelthat takes into account Nernst-Planck equations for transportof positive and negative ions, Poisson equation for electricpotential and that of Navier-Stokes for the hydrodynamics [6].It has been shown that the equal injection currents lead toformation of symmetrical closed four-vortex flow structure,unipolar injection leads to an asymmetrical two-vortex flowwith a small through flow. Between these two cases, there is arange of injection current ratios where through flow emerges.

The ratio of injection currents depends on properties of themetal-liquid interface. The easiest way to change the propertyis through doping of dielectric liquid with impurities. Forexample, it has been shown that doping transformer oil withvarious concentration of butyl alcohol results in changing theflow pattern from the through flow to a symmetric recirculationpattern [5]. It raises the question, how the concentrations ofimpurities change injection currents and affect the conductivityof liquid. In order to account for this, the EHD flow model wasrefined by adding specific initial values for concentrations [7].The simulation showed the increasing the conductivity to resultin a consistent increase of the injection current. Since thereis yet no theoretical description of dependency of injectioncurrent on the concentration, one way to obtain the relation itis to compare experimental data with simulation.

Thus, the main goal of this work is to obtain velocitydistribution at various values of applied voltage with differentlevels of butanol concentration in PDMS.

II. METHODOLOGY

Fig. 1 shows the schematic drawing of the electrode system.It consists of two identical parallel horizontal copper elec-trodes with radii 250 µm and 1 cm distance between them.The bottom electrode is at a high voltage of negative polarity,which varies from zero to 20 kV. The top electrode is groundedthrough a resistor that is used to measure the current by an

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Fig. 1. The cuvette and electrode system, in which the experiments wereconducted.

analog-digital converter. The electrodes are placed into theplexiglass cuvette filled with PDMS doped with butyl alcoholof various concentrations.

The speed was measured on the FlowMaster equipment ofLaVision Inc. by applying PIV method. The setup consists ofdouble-pulsed Nd:YAG laser, CCD camera and synchroniza-tion unit. To visualize the EHD flow, the working liquid wasseeded with tracer particles. They were illuminated with a lightsheet, formed by passing double pulsed laser beam throughoptical arrangement with cylindrical lenses. The energy perlaser pulse was 50 mJ. The light sheet was 0.5-1 mm wide.A CCD camera (Image proX) positioned at a perpendicularto the light sheet plane is shuttered to capture an imageof tracer synchronously with laser flashes. The CCD matrixhas resolution 1600×1200 and 14 bit dynamic A/D range.A pair of recorded images was divided into correspondinginterrogation windows of size 48×48 for the first pass andof 24×24 for the second one. The separation time betweenlaser flashes was chosen so that the displacement of tracerparticles in interrogation window obeyed the inequality 0.1 px< ds < 1/4 dintWin. The resulting velocity field was obtainedby adaptive PIV algorithm with 50% window overlap. Then,a median filter was applied to the data. The measurementseries were averaged. The rms deviation of velocities is used tocalculate the observation error that proved to be about 5-15%.

One of the major concerns when employing PIV method isthe selection of tracer particles. The particles should be insol-uble, have relative permittivity close to that of the liquid and,of course, they should follow the flow. The authors [8] havetested SiO2 as seeding particles for visualization of EHD flow.They concluded that concentration of SiO2 less than 0.1 g/lhas no effect on the fluid conductivity, hence it can be suitablefor measurement. Our experiment used hollow borosilicateglass spheres. They have density 1.10±0.05 g/cm3, averagesize 9-13 µm. The seeding concentration was 0.2 g/l. It hasbeen tested that such tracer concentration changes the systemcurrent less than the observation error. So it can be used forvisualization of EHD flow.

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Fig. 2. Dependences of conductivity on concentration of butyl alcohol.

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Fig. 3. Dimensionless CVCs at different values of doping admixture.

As mentioned, PDMS was chosen as working liquid forthe experiment. It has the following properties: kinematicviscosity 5 cSt, density 950 kg/m3, relative permittivity 2.4,pure liquid conductivity 10−13 S/m. It has been doped withbutyl alcohol from 1% up to 17% in increments of 2%. Foreach concentration, the conductivity of solution was measured.The dependences of conductivity on concentration are givenin Fig. 2.

III. RESULTS

The current-voltage characteristics (CVCs) at various con-centrations of butanol are shown in Fig. 3. Since the conduc-tivity of the solution changes by several orders of magnitude,it is reasonable to plot the CVCs in dimensionless form, i.e.divide the value of the current by σ0E, where σ0 is the low-voltage conductivity of the fluid. In other words, the values ofthe current are divided by extrapolated initial linear section ofthe CVC.

The CVCs run from unity (Fig. 3) because the startingvalues of the current are determined by the low-voltageconductivity. At low concentrations of butanol, we can seethe current to grow considerably and in a linear manner. It

2 International Journal of Plasma Environmental Science & Technology, Vol.10, No.1, MARCH 2016

0 5 10 15 20 25

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PMS + 3% butanol. Contours of velocity (cm/s) at U=1.0 kV.

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PMS + 3% butanol. Contours of velocity (cm/s) at U=11.0 kV.

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Fig. 4. The EHD flow velocity distribution at 1 kV (top) and 10 kV (bottom).

can be inferred that when the conductivity of liquid is low,the convective charge transport after emerging of EHD flowprevails over the migration. The linear shape of current isdue to parabolic shape of original non-dimensionless current(DLC). The maximum value of DLC is attained at the 1%concentration and is as high as to 7 (the plot is not presentedin the figure).

With the increasing admixture concentration, the deviationof the current from unity decreases. At the concentrationvalue of 17%, we can see DLC even decrease with increasingvoltage. It infers that in this case there is an indication oflimiting current in the system [9].

Consider typical distributions of speed obtained in theexperiment. It is worth noting that the value of charge decaytime in pure liquid is about 100 seconds. Therefore, this leadsto very unstable chaotic flows. The first stable flow patternscan be obtained at concentration of butanol about 3% (Fig. 4).

A. 3% concentration of butanol

Fig. 4 shows the distribution of velocities at different valuesof applied voltage. The top plot presents the so called unde-veloped EHD flow. Such velocity distribution is typical forvoltage in the range from the threshold to about 1-1.5 kV. It isshaped as an asymmetrical counter flow with the average speedof several millimeters per second. The velocity maximums arelocated near electrodes.

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PMS + 9% butanol. Contours of velocity (cm/s) at U=1.5 kV.

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PMS + 9% butanol. Contours of velocity (cm/s) at U=5.5 kV.

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Fig. 5. The EHD flow velocity distribution at 1.5 kV (top) and 5.5 kV(bottom).

With increasing voltage, the through unidirectional flow isgenerated and, we can see another acceleration zone near thepassive electrode. The velocity maximum is located in IEGand in the outer region. Thus, such type of flow can be usedin pumping.

Thess flow structures are similar to those obtained forconcentrations of butanol up to 9%.

B. 9% concentration of butanol

With the impurity concentration increasing to 9%, the flowstructure changes. The undeveloped EHD flow becomes moresymmetrical, and the velocity profiles near electrodes are widerthan those presented earlier, but the velocity maximum is stilllocated near the electrodes.

The major difference appears at higher voltages. As in theearlier case, the acceleration of fluid occurs in IEG, but thestructure of flow beyond the passive electrode is different.The flow splits into two plumes that diverge from the axis ofsymmetry. So the flow in the outer region becomes divergentbut it, if put in a channel, still can be used for pumpingliquid. The absence of the second acceleration zone beyondthe passive electrode suggests that the injection currents fromit are eliminated.

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mPMS + 15% butanol. Contours of velocity (cm/s) at U=1.5 kV.

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PMS + 15% butanol. Contours of velocity (cm/s) at U=9.0 kV.

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9

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Fig. 6. The EHD flow velocity distribution at 1.5 kV (top) and 9 kV (bottom).

C. 15% concentration of butanol

With further increase of the concentration of butanol in theelectrode gap, closed four-cell counter vortices appear (Fig. 6).The undeveloped EHD flow widens and the velocity maximummoves away from the axis of symmetry.

Flow structure at high voltages is symmetrically shaped, i.e.the acceleration region shifted under each of the electrodes andcounter-jet acceleration occurs along the axis towards eachother.

With further increase in the concentration of butanol, theflow retains its counter-symmetric shape up to quite highconductivity of the liquid when the injected charge recombineswith the current of counterions coming from the bulk of theliquid and does not penetrate into the IEG. This results in thedecreasing maximum velocity value.

Fig. 7 shows the dependency of maximum speed of EHDflows on the applied voltage and with different impurity con-centration of butanol, hence different low-voltage conductivity.

Voltage increases along the y-axis, low-voltage conductiv-ity increases from left to right along the x-axis. For eachconductivity, there is a linear dependence of the maximumspeed of the flow on applied voltage, and such dependenceshave different inclinations. It can be noted that the thresholdvoltage of EHD flows with increasing conductivity increasesfrom about 0.4 kV for the 1% concentration to 1.5 kV for the17% concentration.

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Fig. 7. Dependence of the velocity maximum on conductance and voltage.

If we view the dependence of the maximum speed on theconductivity at a fixed voltage, we can see an extremum. At thestart, the increasing conductivity causes the maximum speed toincrease up to concentration values of 15%, which correspondsto the conductivity of 10−7 S/m. A further increase in theconcentration leads to a decrease in the speed of EHD flows.

IV. CONCLUSION

Let us highlight the main results:• At low concentrations of butanol (up to 9%) in PDMS

using symmetric wire-wire electrode system, the EHDthrough flow is realized, which can be used for pumpingthe liquid. At 9%, there is a change in the structure ofthe flow, it widens.

• With further concentration increase, there is a change ofshape from the through flow to counter symmetric flows.

• The dependence of the velocity maximum on conduc-tance at a fixed voltage was found to have an extremumat the conductivity of 10−7 S/m.

ACKNOWLEDGMENT

The research was carried out at the Geomodel ResearchCenter of the St. Petersburg State University.

REFERENCES

[1] O. Stuetzer, “Ion drag pressure generation,” Journal of Applied Physics,vol. 30, pp. 984–994, 1959.

[2] O. Stuetzer, “Ion drag pumps,” Journal of Applied Physics, vol. 31, pp.136–146, 1960.

[3] A. Richter and H. Sandmaier, “An electrohydrodynamic micropump,” inMicro Electro Mechanical Systems, 1990. Proceedings, An Investigationof Micro Structures, Sensors, Actuators, Machines and Robots. IEEE, Feb1990, pp. 99–104.

[4] M. K. Bologa, F. P. Grosu, and I. V. Kozhevnikov, “Features of electrohy-drodynamic flows in a multielectrode system,” Surface Engineering andApplied Electrochemistry, vol. 43, 2007.

[5] Y. K. Stishkov, A. A. Ostapenko, and Y. M. Rychkov, “Space chargeand EHD flows in symmetric electrode systems,” Elektron Obrab Mater,vol. 43, 1982.

[6] I. Ashikhmin and Y. Stishkov, “Electrohydrodynamic injection convert-ers,” Surface Engineering and Applied Electrochemistry, vol. 48, pp. 268–275, 2012.

4 International Journal of Plasma Environmental Science & Technology, Vol.10, No.1, MARCH 2016

[7] I. A. Ashikhmin and Y. K. Stishkov, “Influence of the level of the low-voltage conduction on the structure of the through electrohydrodynamicflow in a symmetric electrode system,” Surface Engineering and AppliedElectrochemistry, vol. 50, pp. 52–58, 2014.

[8] M. Daaboul, C. Louste, and H. Romat, “PIV measurements on chargedplumes-influence of SiO2 seeding particles on the electrical behavior,”IEEE Transactions on Dielectrics and Electrical Insulation, vol. 16, pp.335–342, 2009.

[9] A. Castellanos and A. Perez, “Electrohydrodynamic systems,” in SpringerHandbook of Experimental Fluid Mechanics. Springer-Verlag BerlinHeidelberg, 2007, ch. 21, pp. 1317–1333.

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