This paper extends previous liquid film flow boiling studies by including the effect of an additional electrohydrodynamic (EHD) force, namely, the dielectrophoretic (DEP) force. Rather than using only EHD conduction pumping of the liquid film to electro-wet the heater surface, a localized nonuniform electric field above the heater surface is established to generate a DEP force for improved vapor bubble extraction during the nucleate boiling regime. The effects of liquid film height and applied potential are studied as a function of heater superheat and heat flux. A brief analytical study is also used to estimate the expected DEP force magnitude to explain the results. All of the above studies are also used to quantify the enhancement in heat transfer that can be achieved when heat transport systems are driven or augmented by these two EHD mechanisms. The results show remarkable enhancement of up to 1217% in boiling heat transfer coefficient at a given superheat when both mechanisms are used simultaneously. The experimental data are important for applications in thermal management in terrestrial and space conditions.
Electrohydrodynamics: EHD Conduction and Dielectrophoresis.
The first term in Eq. (1) represents the Coulomb force which acts on free charges within the fluid. The second and third terms represent the translational and distortional responses of polarized charges resulting from the imposed electric field and are known as the dielectrophoretic and electrostriction forces, respectively.
EHD conduction pumping is primarily driven by the Coulomb force acting on free space charges which are redistributed to the vicinity of the electrodes. Free charges are formed due to the imbalance in the dissociation and recombination of neutral electrolytic species in the dielectric fluid. Proper asymmetric design of the electrodes generates net axial flow motion, pumping the fluid . EHD conduction pumps can be used as the sole driving mechanism for small-scale heat transport systems and have a simple electrode design, which allows them to be fabricated in exceedingly compact form (down to microscale). EHD conduction is also an effective technique to pump a thin liquid film. It has been previously well studied, and detailed theoretical, numerical, and experimental work can be found in Refs. [2–7] and references therein.
In Eq. (2), particles are repelled from regions of stronger electric fields if their permittivity is less than that of suspension medium, ε2 < ε1. For the experiments in this work, the liquid medium is the working fluid hydrochlorofluorocarbon (HCFC)-123 and its permittivity is found in Table 1, i.e., ε1 = 42.43 × 10−12 F/m. For the vapor bubble, the permittivity of a vacuum is used, i.e., ε2 ≈ ε0 = 8.854 × 10−12 F/m. The DEP force is proportional to the gradient of the electric field squared. A strong nonuniform electric field results in a DEP force acting on individual vapor bubbles. Therefore, by designing the appropriate electrode geometry and applying a high enough potential, the DEP force magnitude can be made equal to or greater than the buoyancy force acting on a given vapor bubble (up to 2 orders of magnitude greater in this study, as will be shown below). Vapor bubbles which are departing from the heater surface during nucleate boiling can be removed at a much higher rate than that possible via buoyancy forces alone.
It is important to mention that in addition to bubble motion, the applied electric field can also deform liquid droplets or bubbles into prolate spheroids or elongate them in the direction of the electric field . This changes the dipole moment, and as a result, the net DEP force is changed as well. This also has a reciprocal effect of changing the electric field around the bubble. If the deformation is small, the motion of bubbles can be predicted with reasonable accuracy. However, if bubble deformation is significant, the effects must be included in the analysis. A pertinent example from the literature of previous studies in bubble deformation in a dielectric fluid in the presence of a nonuniform electric field was given by Pearson and Seyed-Yagoobi . They carried out a three-dimensional numerical study that modeled bubble deformation and calculated the net DEP force exerted by the electric field on the bubble. They found that deformation can be significant especially within small-scale devices where bubble size is on the order of channel size or electrode spacing.
The use of DEP forces to enhance boiling and evaporative heat transfer has been studied for some time, including earlier efforts by Ogata and Yabe , Seyed-Yagoobi et al. [12,13], and Darabi et al. . More recently, Kweon and Kim  studied the use of a nonuniform electric field to enhance nucleate boiling heat transfer. In their experimental study of saturated pool boiling in the presence of a nonuniform DC electric field, a plate-wire electrode configuration was used with Freon-113 as the working fluid. High-speed imaging was used to measure boiling parameters. The results showed that there was a shift in the boiling curve and a delay in the onset of nucleate boiling (ONB) and critical heat flux (CHF) to higher values. For a given heat flux, the relative heat transfer coefficient increased with increasing applied voltage. For example, at 15 kV DC voltage, the heat transfer coefficient was enhanced about 215% for a heat flux of 29 kW/m2. In addition to enhancement in the pool boiling curve, Kweon and Kim  also confirmed that the mechanism of EHD nucleate boiling was closely connected to the dynamic behavior of bubbles, such as bubble velocity, frequency, and diameter. The overall conclusions of the study were that the nonuniform electric field strongly affected bubble dynamics and was responsible for enhanced heat transfer.
Further research in the use of nonuniform electric fields for nucleate boiling and CHF enhancement was conducted by Hristov et al. . An experimental and theoretical study was performed in pool boiling of HCFC-123 on a horizontal surface with two electrode designs (parallel rods and wire mesh). Experimental data were compared to similar results by other researchers with differences in heater surface finishes and electrode design. The data indicated that heat transfer coefficient and CHF were enhanced by the DC electric field. The parallel rod electrodes created a more nonuniform electric field, while the mesh electrodes created a uniform electric field but obstructed vapor bubbles during nucleate boiling. At the highest electric field strength of 5 MV/m, there was a large nonlinear increase in the heat transfer coefficient for the rod electrode design and this was attributed to greater density in small nucleation sites on the smooth heater surface. A theoretical model was also developed for the growth of a single vapor bubble on a superheated wall in an electric field, which led to a numerical simulation based on the level-set method. The results of the numerical simulation provided preliminary solutions for bubble detachment and evolution of dry spots on the heater surface with and without the electric field.
More recently, Kano et al. [17,18] studied nucleate boiling enhanced by a local nonuniform electric field. In Ref. , the working fluid was hydrofluoroether (HFE)-7100, and the heater surface was made of copper. The microscale electrode was designed to allow for liquid convection and inflow at low superheat values, and attraction of bubbles (via dielectrophoresis) at high superheat values. The pool boiling experiments were conducted for electrode heights of 100, 200, and 300 μm above the heater surface. The maximum CHF value of all the experiments was 47 W/cm2 at electric field strength of −5 kV/mm and occurred at electrode height of 300 μm. The heat transfer coefficient was 14 kW/m2 K at these operating conditions. The CHF value was three times higher than the maximum CHF for the no-electric field case. In addition to the pool boiling curves, bubble behavior was also observed above the electrode and heater surface using a transparent indium tin oxide (ITO)-coated electrode. The imaging results suggested that the electric field effects induced Kelvin–Helmholtz type instabilities which divided larger bubbles into smaller ones. The visualizations were also used to make the argument that the increased heat fluxes were due to periodic thin film creation by the electric field at the bubble lower interfaces which strongly enhanced the heat transfer. In addition to the experimental work, Kano et al.  also considered the classical Kelvin–Helmholtz instability analysis on the liquid–vapor interface by modifying it to include EHD effects. The ratio of CHF with and without electric field was predicted by the frequency ratio (of oscillation of liquid–vapor interface) of the periodic thin film in the gap between the boiling surface and electrode; details of the analysis can be found in Ref. .
The research presented in this paper is a combination of EHD conduction pumping and DEP force. Experiments in liquid film flow boiling are conducted in the radial heat transport system configuration as done previously in Refs. [3,4]. EHD conduction pumping is used to generate liquid film flow from the surroundings for electro-wetting of the heater surface. Simultaneously, a strong nonuniform local electric field above the heater surface is also used to generate the DEP force for increased vapor bubble extraction during the nucleate boiling regime. The height of the liquid film and applied potentials for the EHD and DEP electrodes are varied to determine their effect on the entire liquid film flow boiling regime. The understanding gained from these experiments will allow for the development of electrically driven heat transport systems for a wide range of applications in different scales in terrestrial and especially space conditions where EHD conduction pumping of liquid film will make the boiling effectively feasible.
Concept and Experimental Setup
Liquid film flow boiling driven by electrohydrodynamic (EHD) conduction pumping has been experimentally studied previously in a terrestrial environment  (including studies of bare and nanofiber-enhanced heater surfaces ) as well as in a microgravity environment . The concept of liquid film flow boiling with combined EHD conduction pumping and dielectrophoretic (DEP) force is illustrated in Fig. 1. It consists of a heater installed in the center of a circular chamber. The heater is immersed in a film of liquid (with a thickness of 2.0 mm in this case). When heat is applied, the liquid on the heater surface boils. The vapor bubbles rise due to buoyancy and release vapor to the ambient, which moves to the periphery of the chamber where it condenses. An electrode installed above the heater surface is used to impose a local nonuniform electric field, which increases vapor bubble extraction via DEP force during the nucleate boiling regime. In addition, EHD conduction is used to pump liquid film radially inward from the heater surroundings to the heater surface. In this way, the freshly condensed liquid film continuously moves toward the heater to boil, forming a loop. Liquid film flow boiling is similar to the well-known pool boiling. However, classical pool boiling does not involve forced convection of fluid surrounding the heater surface (i.e., flow generated electrically or otherwise). It involves characteristic physical dimensions that are large compared to the typical bubble length scale. On the other hand, liquid film flow boiling does involve forced convection of liquid surrounding the heater surface, in this case due to the EHD conduction pumping mechanism. The thickness of the liquid film is similar to the typical bubble length scale. Liquid film flow boiling should not be confused with the so-called film boiling, which refers to vapor blanket formation over the heater surface at very high heat flux levels exceeding the critical heat flux (CHF) during pool boiling.
EHD Conduction Electrode Design.
The same liquid film flow boiling experimental setup from Ref.  was used in this study (described in detail below), with the exception of the EHD conduction pump electrode disk which had fewer electrode pairs (7 versus 14). The larger electrode sizes and spacing with seven pairs allowed for higher applied potential (up to 2.0 kV), greater pressure generation and flow rate in the liquid film during the experiments, despite less number of electrode pairs. The dimensions are shown in Fig. 2. The EHD conduction pump was fabricated by lithographically printing electrodes onto a substrate disk to pump liquid film, based on the original design of Pearson and Yagoobi . The substrate disk was made of 96% alumina with a diameter of 152.0 mm and thickness of 1.0 mm. Alumina was chosen because it had low electrical conductivity (<10−12 S/m) but relatively high thermal conductivity (25.0 W/m K). Electrode traces were made of Palladium–Silver (Pd–Ag) and printed onto the surface of the substrate in pairs. Each pair consisted of a narrow electrode (connected to ground) and wide electrode (connected to high voltage) with a space in between. A total of seven electrode pairs were printed on the substrate, with each pair decreasing in diameter near the center of the disk, where a heater was installed. Bus lines for electrical connections to the electrodes were also printed on the disk. The dimensions and spacing between electrodes and electrode pairs were based on detailed numerical solutions of the governing differential equations for the electrical field, charge conservation, and fluid flow [6,7]. The EHD conduction pump was designed with seven electrode pairs to provide sufficient liquid flow to the heater at the maximum heat flux.
DEP Electrode Design.
The high-voltage DEP electrode was a square stainless steel plate with sides of 22.6 mm and thickness of 0.381 mm, installed directly above the heater at a fixed height. It was designed such that it would be larger than the heater (which had a diameter of 18.0 mm) and could be installed in the existing experimental setup without having to make significant modifications. A total of 17 slots of 0.51 mm width were laser-cut into the electrode. This type of geometry was chosen for two reasons: (i) it allowed for nonuniformity of the electric field and required for the generation of the DEP force (as shown in Eq. (2)) and (ii) since the electrode would be directly above the heater surface where bubbles nucleated and departed, slots were necessary to allow extracted bubbles to escape. The DEP electrode dimensions are shown in Fig. 3.
Four threaded holes were made at the corners for Nylon screws to support the DEP electrode above the heater surface. Nylon was chosen because it was electrically insulating and compatible with the working fluid. The height of the DEP electrode could be easily adjusted by turning the screws with a screwdriver. The screw pitch was known from manufacturer data. This information was used to determine the vertical movement of the electrode based on the number of turns of the screw. Each complete rotation of a screw caused a height change of 0.32 mm. For applied potential of 2.5 kV, the nominal electric field strength changed by 7.8 kV/mm for each complete rotation of the screws. Therefore, the height of the DEP electrode was unchanged for all the experiments (it was set to ∼1.0 mm to ensure that the DEP electrode would remain submerged in the 2.0 mm thick liquid film). A copper rod was soldered to the outer top surface of the DEP electrode and this acted as an additional structural support but also served as the connection to the high-voltage feedthrough installed in the periphery of the experiment housing. In this way, potential could be applied to the DEP electrode separately from the EHD electrodes. The corresponding ground electrode of DEP force was the heater itself, described in the Heater Design section.
The heater was fabricated using 32-gage nichrome resistance wire (with a resistance of 34 Ω/m at 25 °C) wrapped around a machined copper piece which had a thermal conductivity of 390 W/m K. The resistance wire had a thin layer of polyimide electrical insulation, and the outer diameter of the wire (including the insulation layer) was 0.241 mm. The cylindrical copper piece was machined with a metal lathe, and the top surface was faced to make it smooth. The diameter of the top surface (where boiling occurred) was 18.0 mm, which gave a surface area of 254 mm2 or 2.54 cm2. The bare heater surface was polished successively with 240-grit and 600-grit sandpaper for a smooth finish. A 36-gage T-Type wire thermocouple was soldered to the copper piece; a hole with a depth of 3.0 mm was drilled into the side of the copper piece, and the tip of the thermocouple (where the temperature was measured) was inserted in the hole and soldered. The tip was 1.5 mm below the top surface where the working fluid was boiled. The thermocouple gave the measurement for Tsurface as shown in the Experimental Results and Discussion section. A 2D axisymmetric numerical simulation of steady-state heat conduction within the copper piece at all the expected heat loads was performed. The results of the simulation confirmed a uniform heat flux on the top surface of the copper piece. A convection boundary condition with a constant high heat transfer coefficient (HTC) was used for the top surface, based on a maximum expected heat flux of 30 W/cm2 and corresponding ΔT from previous experimental data. Although the constant HTC assumption along the heater surface was approximate, heat flux uniformity was not expected to be affected appreciably because of the high thermal conductivity and small mass and area of the copper heater. The simulation results also showed that the maximum difference in temperature at the location of the thermocouple (as illustrated in Fig. 4) and corresponding temperature on the top surface of the heater was 0.9 °C. It is important to note that this only occurred for heat fluxes greater than 20.0 W/cm2. Therefore, for the majority of heat loads, the top heater surface temperature measurement via embedded thermocouple was justified. The copper piece wrapped with resistance wire was inserted into a cylindrical Delrin insulator as shown in Fig. 4. Epoxy was applied around the edge of the heater to ensure that working fluid did not infiltrate into the Delrin insulator.
Combined EHD and DEP Electrode Installation in Experiment Housing.
The experiment housing was a cylindrical tank made of aluminum, with a high-strength glass lid and two chambers. The chambers were separated by a removable aluminum interface plate which was sealed with o-rings. The disk with imprinted EHD conduction pump electrodes was fixed by epoxy on the interface plate (illustrated in Fig. 5) and installed into the tank. The top chamber contained the working fluid, refrigerant HCFC-123 (properties are given in Table 1). The working fluid was boiled on the heater surface and condensed on the outer periphery of the electrode disk surface, where EHD conduction pumping was used to drive it toward the heater at the center. Heat was dissipated through the electrode disk and interface plate to the bottom chamber of the tank where cooling water flowed from a recirculating chiller. Figure 5 shows a cross section view of the experiment housing illustrating the two chambers for refrigerant and cooling water.
The high-voltage and ground feedthroughs were used to connect the EHD conduction pump electrodes (on the disk surface) and the DEP electrode to the separate high-voltage power supplies. High current-carrying wires were used for the heater power connections, and this wire pair also had a separate feedthrough. A thermocouple probe was inserted through a port in the side wall of the housing to measure vapor temperature of the refrigerant (saturation temperature was elucidated from this) just above the heater surface. This is the Tsat measurement in the Experimental Results and Discussion section. The tip of this thermocouple probe was approximately 12 mm above the heater surface. An absolute pressure transducer was used to measure vapor pressure of the refrigerant via another port in the experiment housing. These two measurements confirmed matching of the saturation pressure and saturation temperature in the vapor phase. Two thermocouples were also inserted prior to the recirculating chiller connections to measure the cooling water temperature at the inlet and outlet. The cooling water flow rate was known from the readout on the recirculating chiller.
The EHD conduction pump electrode disk, DEP electrode, and heater assembly described above were installed into the experiment housing. The DEP electrode was installed directly above the heater at a height of 1.0 mm. An additional wire was also soldered to the side of the heater and connected to the common ground bus line of the EHD conduction pump electrodes. The entire assembly is shown in Fig. 6. The experimental uncertainty in all the measurements and propagation of error analysis are given in Table 2.
Experimental Results and Discussion
The experiment procedure is as follows: the experiment chamber was first evacuated down to 500 mTorr and charged with a fixed amount of refrigerant HCFC-123. Depending on the experiment, refrigerant charge resulted in either a liquid film 2.0 ± 0.3 mm thick or a liquid pool 10.0 ± 0.3 mm deep above the electrode disk and heater surface. The electrodes in this study were originally designed for a 2.0 mm liquid film ; for any other film thickness, the electrode design needs to be optimized (e.g., for thicker films, electrodes should penetrate into the liquid film in order for pumping to be more effective). The recirculating chiller was set to a fixed temperature, and the system was allowed to reach steady-state (this was the point at which the saturation temperature and heater surface temperature did not fluctuate by more than 0.1 °C/min about the mean value). The temperature difference of the cooling water was found to be minimal for the given high water flow rate from the recirculating chiller. The chiller set point was adjusted to maintain constant saturation conditions in the boiling chamber. Once the saturation temperature and pressure matched values from thermodynamic tables for pure HCFC-123, a potential of 1.5 kV was applied to the high-voltage EHD electrodes. At the same time, a potential of 2.5 kV was applied to the high-voltage DEP electrode. Next, power was applied to the electric heater. Applied voltage and the wire resistance were measured to calculate heater power which was divided by the heater surface area to give heat flux. The following liquid film flow boiling and pool boiling experiments listed in Table 3 were performed using the combination of EHD conduction pumping and DEP force. The limits of applied DEP potential in all the cases were considered from an electrical breakdown perspective only. Although there are additional considerations such as reaching the limit of bubble extraction rate upon application of DEP forces, the DEP potential will be varied in future detailed parametric studies to examine these.
Heat flux was incremented initially by 0.25 W/cm2 until 2.50 W/cm2 was reached. After this point, it was incremented by 0.50 W/cm2 until the dryout condition was reached. This was the point at which the vapor generation rate exceeded the liquid flow rate to the heater and was signified by the rapid and sustained increase in superheat (>10 °C/s) for a small increase in heat flux (0.25 W/cm2).The time between heat flux increments was 300 s, which allowed the surface temperature to reach steady-state (defined above). The results of all the experiments are shown in Fig. 7 (correlation predictions shown are discussed in the Numerical Simulation of Nonuniform Electric Field in Dielectric Liquid section). Heat flux, q″, was plotted against the superheat, ΔT = (Tsurface − Tsat). The low heat flux data for all the cases from Fig. 7 are shown in Fig. 8. The onsets of nucleate boiling for all the cases are labeled as ONB1–ONB5 (for clarity, ONB1 is shown in Fig. 7 and ONB2–ONB5 are shown in Fig. 8). The error bars show the measurement uncertainty in ΔT (note that the error bars for ΔT include the minor contributions of random error. However, the systematic error inherent in the thermocouples has a major contribution to the overall error, giving the error bars the appearance of constant values of ∼ ±0.7 °C). Since uncertainties in heat flux (which have a maximum of ±3.9%) are too low to be visible as vertical error bars, they are not included. For clarity, uncertainty bars in Fig. 8 have been removed.
Case 1 represents the experimental data for liquid film flow boiling in the absence of any applied electric field (with the DEP electrode removed). They show that the superheat increased steadily with increasing heat flux. The results for case 1 shown in Fig. 8 appear to have fewer data points for the given range of ΔT; however, this is due to the low initial slope of the boiling curve. The onset of nucleate boiling (ONB) occurred at 1.10 W/cm2, labeled in Fig. 7 as ONB1. As heat flux was increased beyond 5.00 W/cm2, the high rate of vaporization due to rapid bubble formation was accounted for by incoming liquid from the surroundings, and liquid film flow was driven exclusively by hydrostatic pressure (maximum of 30 Pa based on liquid film height). The maximum heat flux (which occurred at heater dryout as described above) for case 1 was 20.14 W/cm2 at ΔT of 29.9 °C. The dryout was determined based on the rapid and sustained increase in superheat (>10 °C/s) for a small increase in heat flux (0.25 W/cm2).
In case 2, the applied potential to the DEP electrode was set to 2.5 kV (potential was not applied to the EHD pumping electrodes for this case). At low heat fluxes, liquid circulation was observed above the heater/ground electrode. Therefore, although the purpose of the DEP electrode was to increase the rate of vapor bubble extraction via the DEP force acting on the bubbles during nucleate boiling, at low heat flux in the presence of abundant liquid, it also generated EHD-driven circulation due to the presence of electric permittivity gradient within the liquid film above the heater caused by the temperature gradient. This strong local liquid circulation caused the heater superheat to be significantly lower in case 2 than case 1 at lower heat fluxes. For example, at a heat flux of 2.00 W/cm2, the heater superheat in case 2 was 3.25 °C versus 14.4 °C in case 1. The ONB was signified by an increase in the slope of the boiling curve as shown in Fig. 7. For case 2, this occurred at a heat flux of 2.25 W/cm2, and of course, bubble nucleation was observed on the heater surface as well. As the heat flux was increased further to 10.0 W/cm2, superheat remained low in case 2 (11.4 °C) compared to case 1 (21.7 °C). Bubble nucleation occurred on the whole heater surface, and the fraction of vapor covering the heater surface compared to liquid was increased. The continued enhancement suggests that the mechanism of DEP force that initially caused liquid circulation acted directly on polarized bubbles. The higher rate of vapor bubble extraction allowed for increased inflow of liquid from the surroundings, maintaining a low superheat in case 2 compared to case 1 for a given heat flux. The ONB for case 2 was a useful indicator of when the DEP force began to influence vapor bubble motion. In addition to the generated DEP force being larger than the buoyancy force (discussed further below), it also exceeded the three-phase contact-line tension force. This was clear from the experimental data as well as direct observation of the bubbles extracted when DEP electrode was activated. However, it is important to note that the three-phase contact-line was present mainly when dryout was reached.
In case 3, 1.5 kV was applied to the EHD pumping electrodes, and 2.5 kV was applied to the DEP electrode. The flow rate of liquid from the heater surroundings was increased as a result, since in addition to the hydrostatic pressure (≤30 Pa) in the liquid film, the pressure generated by the EHD electrodes at applied potential of 1.5 kV was ∼150 Pa (which produced local velocities in the liquid film on the order of ∼3 cm/s as approximated from experimental measurements ). The increased incoming flow, as well as local liquid circulation directly above the heater surface due to the DEP electrode, caused the ONB to be increased from 1.10 W/cm2 in case 1 and 2.25 W/cm2 in case 2, respectively, to 6.25 W/cm2 in case 3. Despite the reduction in superheat already present in case 2 compared to case 1, the activation of the EHD conduction pump in case 3 reduced it even further for heat fluxes greater than 10.0 W/cm2. For example, at 14.5 W/cm2, superheat in case 3 was 12.8 °C versus 15.5 °C in case 2 and 26.1 °C in case 1. Alternatively, the enhancements in heat flux for a given superheat were quite remarkable. The enhancements in heat flux for ΔT = 14.1 °C for all the cases are given in Table 4. The comparison of boiling heat transfer coefficient, h, is also given in Table 4 (h = q″/ΔT). Up to 834 ± 53% enhancement in heat flux (and boiling heat transfer coefficient) was possible for case 3 compared to case 1.
In case 4, the applied EHD potential was increased to 2.0 kV, and applied DEP potential was kept at 2.5 kV. Case 4 resulted in the highest enhancement in heat flux among all the cases. As shown in Table 4, up to 1217 ± 53% enhancement was made possible by application of both EHD pumping (at higher potential) and DEP techniques. The heater power (based on heater surface area of 2.54 cm2) and combined power input for both EHD and DEP electrodes (based on applied potential and current measurements) for all the cases are also shown in Table 4. The largest increase in heater power among all the cases was 56.6 W and occurred between cases 1 and 4, for the given ΔT. This enhancement required only 0.39 W power input to the EHD and DEP electrodes to achieve. The ratio of electric power input for the combined techniques was 0.7% of the corresponding heater power increase for this level of enhancement.
In case 5, the applied EHD pumping potential was set to 0 kV, but applied DEP potential was 2.5 kV and the height of the liquid–vapor interface above the heater surface was also changed from 2.0 mm to 10.0 mm. This increased the hydrostatic pressure in the liquid from ≤30 Pa to ≤150 Pa. The results show that the pool boiling curve of case 5 initially had similar values of ΔT to that of case 2 up to a heat flux of 6.00 W/cm2. However, beyond this heat flux, the two curves crossed and the pool boiling (with DEP) results of case 5 showed lower ΔT values for all the heat fluxes compared to liquid film flow boiling (with DEP) of case 2. They also fell in between the curves for cases 3 and 4. For a given heat flux (above 10.0 W/cm2), the ΔT values followed the following trend: case 4 < case 5 < case 3. This suggests that the increase in hydrostatic pressure in pool boiling was equivalent to increasing the applied EHD conduction pumping potential in liquid film flow boiling to a value between 1.5 and 2.0 kV. As mentioned above, the EHD conduction pumping electrode design can be changed to allow pumping to give further enhancements, by using electrodes inserted into the liquid film. The above results also show that EHD conduction pumping will allow for liquid film flow boiling as well as typical pool boiling in the absence of gravity.
For all the liquid film flow boiling experiments, the maximum heat fluxes that were reached corresponded to the dryout condition, where vapor generation rate exceeded the liquid flow rate to the heater. They were similar in magnitude to the critical heat flux, which is relevant in classical pool boiling when the vapor layer forms over the heater surface, with a pool of liquid above it. Therefore, although the two phenomena are distinct, these maximum heat flux values at dryout were similar to the CHF value of the working fluid under pool boiling condition, as determined in previous liquid film flow boiling studies . Although the use of EHD and DEP resulted in only minor increases in the maximum heat flux at dryout, they occurred at much lower ΔT than the corresponding no-EHD/DEP condition of case 1, as shown in Fig. 7.
Numerical Simulation of Nonuniform Electric Field in Dielectric Liquid.
Other forces acting on a bubble as it moves through a liquid medium include viscous drag. Additional inertia generated by the EHD conduction pumping also influences the bubble removal. However, this analysis was simply a direct comparison between the DEP and buoyancy forces. This was done in order to gain a quantitative understanding of the forces involved; more detailed work would include, among other things, bubble motion and deformation effects which are beyond the scope of this study. To determine the DEP force on a bubble of radius a, the electric potential and electric field intensity were numerically calculated as a function of the spatial variables for the geometry considered, as shown in Fig. 9.
The overall domain was the dielectric liquid medium. The charge at each boundary (far from the electrodes) in the overall domain was set to zero. The numerical simulation was performed in comsol multiphysics. The origin of the coordinate system coincided with the center of the heater/ground electrode in the experiment, i.e., x = 0, y = 0, and z = 0 (directions of axes are as shown in Fig. 6). To determine the DEP force in the y-direction (although the DEP force could be relevant in all the directions, only the component of the DEP force in the y-direction was considered because the buoyancy force acts in the y-direction), the electric field needed to be squared and then differentiated with respect to the y-coordinate, i.e., . This was done at the four x-locations (x = 0.0 mm, 0.2 mm, 0.22 mm, and 0.5 mm) illustrated in Fig. 10 (which shows the side view of the DEP and ground electrodes). The variation of E2 along the y-axis at these locations is shown in Fig. 11.
where fluid properties of HCFC-123 are given in Table 1, and acceleration due to gravity was g = 9.81 m/s2. Values for the superheat and heat flux were chosen to be ΔT = 4 °C and q″ = 2.25 W/cm2, respectively. This was in the vicinity of the ONB2 point for case 2 shown in Fig. 8 and was considered the isolated bubble regime; it most closely represented the single-bubble assumption made above. With the parameters input into Eq. (7), the correlation predicted a departure diameter of 0.45 mm, giving a radius of 0.225 mm. For the purposes of this study, a departure radius of 0.25 mm was chosen. Finally, with all the quantities in Eq. (2) set, the dielectrophoretic force acting on a bubble of radius 0.25 mm was calculated as a function of the y-coordinate (since the interest was to calculate the DEP force in the y-direction, the opposite of g, as indicated previously). The expected buoyancy force on a bubble of radius 0.25 mm was also determined using Eq. (3), where values of liquid and vapor density are given in Table 1. The results are shown in Fig. 12.
The results of the estimation in Fig. 12 show that the DEP force at x = 0.20 mm and x = 0.22 mm suddenly increases as the high-voltage electrode is approached at y = 1.0 mm. However, these are only included to illustrate sudden changes in electric field gradient due to the effect of the electrode corners on the electric field distribution. The large surges in DEP force for these locations are not considered for the analysis since the area of effect is only localized to a small region in the electrode slot near the corners. At x = 0.00 mm, the DEP force increases along the y-axis up to a maximum value of 0.021 mN at y = 1.0 mm. Compared to the buoyancy force of 0.00093 mN, the ratio of maximum DEP force to buoyancy force is 22 to 1. At x = 0.50 mm, the DEP force decreases along the y-axis and the lowest value is −0.0083 mN. This indicates that the vapor bubbles present between the DEP electrode, and the heated surface would be repelled away from the high-voltage electrode back toward the heated surface.
where Csf, r, and s are the system-specific constants, and the original equation from Ref.  has been rearranged to solve for the superheat, ΔT. Fluid properties from Table 1 were substituted into Eq. (8) along with prescribed heat fluxes and constants (Csf = 0.0065, r = 0.33, and s = 1.7 were found in the literature from the experimental results  of nucleate boiling of HCFC-123 on a polished copper surface) to give values of the superheat. The expected effect of the DEP force was estimated by using the ratio FDEP/Fbuoyancy = 22 from the above analysis as a multiplication factor for the gravitational acceleration, g, in Eq. (8). Therefore, ΔT values were found at 1 g (which represented nucleate boiling in the absence of electric field) and compared to the ΔT values at 22 g (which represented nucleate boiling enhanced by DEP force). The 1 g and 22 g predictions were compared to the experimental data of cases 1 and 2, respectively, and the comparisons are shown in Fig. 7.
The prediction of the Rohsenow correlation (at 1 g) showed good agreement with the experimental data for case 1 in the absence of electric field. However, the correlation prediction at 22 g showed significantly higher superheat values for a given heat flux compared to the experimental data for case 2, at heat fluxes below 10.0 W/cm2. The primary reasons for this substantial deviation were the underlying assumptions made during the analysis, i.e., the DEP force calculation was very approximate since it was assumed that there was no vapor phase. It was based on an electrostatic field which did not account for fluid and bubble motion/deformation, and the effect of shear forces from EHD conduction pumping on bubble removal was not accounted for. The bubble departure diameter was fixed, and the Rohsenow correlation was not intended to be used for g > 1. As the heat flux was increased to 15.0 W/cm2, superheat values between the correlation prediction at 22 g and experimental data of case 2 appeared to become close but began to diverge immediately with further increase in heat flux. The discrepancies between experimental data and correlation predictions demonstrate that the above methodology is only useful as an order-of-magnitude analysis. Accurate numerical prediction of liquid film flow boiling and pool boiling in the presence of DEP force and EHD conduction pumping of liquid film which takes into account all the physical phenomena occurring are beyond the scope of the current work.
The experimental data and simplified analysis presented in this work suggest that under the operating conditions and electrode design considered in this study, there is an optimal range of heat fluxes where the DEP force dominates and EHD conduction effects become smaller, due to the increased presence of vapor bubbles above the heater surface. Despite these results, the role of EHD conduction pumping is vital in reduced or in the absence of gravity.
Liquid film flow boiling and pool boiling in the presence of combined EHD conduction pumping and DEP force were successfully studied. The results showed significant enhancement in heat flux and heat transfer coefficient up to 1217% for a given superheat value when both mechanisms were used. The ratio of electric power input for the combined techniques was only 0.7% of the corresponding heater power increase for this level of enhancement. The results also provided new physical insights into the dominant mechanisms of heat transfer enhancement during liquid film flow boiling and pool boiling in the presence and absence of electric fields. For example, they showed that at low heat flux, the EHD conduction-generated liquid film flow allowed for increased forced convection and delayed the ONB. It was found that increasing the height of the liquid pool was equivalent to increasing the applied EHD potential, since both resulted in higher static pressure within the liquid which resulted in higher flow rate and lower ΔT. The estimation of the DEP force magnitude (via numerical simulation of electric field) in comparison to the buoyancy force revealed insights to the expected enhancement in the liquid film flow boiling curve when the results were applied to a basic heat transport model. Beyond the enhancement of heat flux and heat transfer coefficient possible with EHD conduction and DEP force, their roles are vital in space applications. They will allow for boiling heat transfer in the absence of or in reduced gravity.
This project was financially supported by the National Aeronautics and Space Administration (NASA) Headquarters Microgravity Fluid Physics Program.
- a =
bubble radius, m
- cp =
specific heat, kJ/kg K
- Csf =
- Dd =
bubble departure diameter from Zuber 
- E =
electric field intensity, V/m
- E =
electric field vector, V/m
- F =
force vector, N
- fe =
electric body force density, N/m3
- g =
gravitational acceleration vector, m/s2
- h =
boiling heat transfer coefficient, W/m2 K
- hfg =
latent heat of vaporization, kJ/kg
- k =
thermal conductivity, W/m K
- Lb =
bubble length scale from Rohsensow , m
- Nu =
- Pr =
- q″ =
heat flux, W/m2
- r =
- Re =
bubble Reynolds number from Rohsenow
- s =
- T =
- V =
applied voltage, V
- x =
- y =
- ΔT =
temperature difference, K