Dielectrophoretically-Assisted Electrohydrodynamic-Driven Liquid Film Flow Boiling in the Presence and Absence of Gravity

Electrohydrodynamics (EHDs) characterizes the interaction between electric fields and fluid flow. This phenomenon can induce fluid flows, create mixing, and enhance heat transfer. As a pumping mechanism, EHD has shown promise due to its low power consumption, rapid response, geometric simplicity, low weight, and heat transport capabilities. It also involves no mechanical parts, avoiding issues with vibration and fatigue, which is especially advantageous for space applications.

where E represents the electric field, ρ_e represents the net charge density, ρ is the fluid density, and ε is the fluid electrical permittivity. The first term in this expression represents the Coulomb force density, which exists when free charges are present in the fluid under an electric field. The second term in the expression represents the dielectrophoretic (DEP) force density, which exists, for example, when there is a liquid/vapor interface or a large temperature gradient corresponding to a gradient in the electrical permittivity of the medium. The third term in the expression is the electrostriction term, which is negligible when the working fluid is an incompressible liquid film. Both the Coulomb force density and DEP force density are the driving mechanisms in this study.

Electrohydrodynamic pumping can be separated into three main forms: ion drag pumping, induction pumping, and conduction pumping [2]. This study utilizes EHD conduction pumping, which uses ionic dissociation to generate free charges in the fluid [3]. In a dielectric fluid, the rate of dissociation and recombination of these free charges exists at an equilibrium. If acted upon by a strong enough electric field, the rate of dissociation exceeds the rate of recombination. Via this mechanism, nonequilibrium charge layers, comprised of these free charges, form near the electrodes, which are referred to as heterocharge layers. As charges are attracted to these layers, bulk fluid motion occurs. If the electrodes are designed with an asymmetrical geometry, a net Coulomb force is induced in the desired direction, and therefore, a fluid net flow can be produced. Figure 1 [4] shows these heterocharge layers along with the induced net fluid flow direction. The smaller arrows in Fig. 1 near the heterocharge layers represent the attraction of charges. Further analysis into the physical fundamentals of EHD conduction phenomenon can be found from the efforts of Vázquez et al. [5], Yazdani et al. [6], and Talmor et al. [7].

EHD conduction pumping has been explored in macro-and meso scales as well as microscale [8]. Additionally, pumps in both rigid and flexible configurations have been explored, with the inclusion of particle image velocimetry and particle tracking [9–12]. The results of these studies have shown that EHD conduction pumping, in both rigid and flexible configurations, can generate strong net flows upwards of 20 cm/s of dielectric fluids in the presence of electric fields.

The use of DEP forces as a method to enhance boiling heat transfer has been studied previously through the efforts of Ogata and Yabe [13], Yagoobi et al. [14,15], and Darabi et al. [16]. Additional studies on enhancing nucleate boiling via a nonuniform electrical field were conducted by Kano and Takahashi [17], including a study using HFE 7100 [18]. Their work consisted of a microscale electrode design where heights from the surface of the heater ranged from 100 to 300 μm. It was found that the maximum critical heat flux (CHF) value was approximately three times higher than the observed CHF under the influence of no electric field. Recently, Garivalis et al. [19] explored the enhancement of critical heat flux in microgravity using microstructured surfaces and applied electric fields. The CHF in this study was found to increase by over 50% when utilizing the combination of electric fields with enhanced surfaces. Patel et al. [20] explored the impact of gravity on EHD conduction pumping and its effect on heat transfer enhancement. When activated, EHD pumping lowered the heater surface temperature at higher heat fluxes in microgravity. However, no DEP mechanism was involved in this study.

The coupling of the EHD conduction pumping mechanism and the DEP extraction force on boiling heat transfer enhancement in the absence of gravity is explored for the first time in this work. It is important to note that liquid pool boiling has been successfully explored in the absence of gravity by Stephan et al. [21] and Grassi et al. [22], the latter of which used an electric field to reduce bubble diameter and enhance heat transfer in pool boiling conditions. Despite this, it is still considered impractical, especially at higher heat fluxes. This has been confirmed by studies from Henry and Kim [23] and Dhir et al. [24], which showed that under microgravity conditions, pool boiling is dominated by a large primary vapor bubble formation, causing dryout. Additionally, previous studies [21–24] focused on pool boiling, and this study explores liquid film flow boiling. The working fluid in this study is Novec 7100 (C₄F₉OCH₃). This fluid, also known as HFE 7100, was selected for its favorable dielectric properties, and its thermophysical and electric properties are tabulated in Table 1 [25,26].

This work is an extension of a previous study carried out by Patel and Yagoobi [27], which explored the boiling heat transfer enhancement of EHD conduction and DEP mechanism together in a terrestrial environment only using HCFC-123 as the working fluid. The main difference between the previous study and the current study is that the sole and combined DEP and EHD mechanisms and their effects on liquid film flow boiling are investigated in different gravity conditions. Additional differences between these studies include the designs of the DEP electrode, EHD conduction pump, and heater, as well as the working fluid. Similar to the previous experiment, a radial EHD conduction pump drives dielectric fluid inward toward the center as a way to electrowet a heater. This heater generates vapor bubbles at the center of the experiment. A DEP electrode is installed 1.6 mm above the heater surface to provide a local nonuniform electric field, which enhances vapor bubble extraction during liquid film flow boiling via the DEP force. As the vapor is extracted from the heater surface by the DEP electrode, it travels to the periphery of the experimental chamber and condenses back onto the EHD conduction pump, where it travels as liquid back to the heater.

The boiling phenomenon of this study is explored in terrestrial and microgravity flight environments, and the results are compared. Combining DEP and EHD forces, this study explores enhanced liquid film flow boiling as a way of removing heat in space. DEP and EHD conduction mechanisms are enabling technologies for the next-generation cooling of high-powered electronics and thermal management in space.

The experiment consists of several main components including a radial EHD conduction pump, a DEP electrode, and a resistance heater. The design of the radial EHD conduction pump used in this study is shown in Fig. 2. The characteristic length, denoted as d, represents the spacing between the high voltage and ground electrode of a selected pair. Yazdani and Yagoobi [6] determined the electrode sizing ratio and spacing between the neighboring pairs to be the ideal dimensions for EHD conduction via numerical optimization. The main difference between the previous EHD conduction pump design [20,27] and the one used in this study is the material of the substrate and electrodes. Here, the substrate material of the pump is silicon, and the electrodes are platinum. The DEP electrode design, shown in Fig. 3, is made from stainless steel and exhibits grate-like spacing, similar to the DEP electrode from [27], to produce a nonuniform diverging electric field. The design imposes a DEP force on the bubbles that form on the heater surface and allows the bubbles to pass through the spaces within the electrode. In this configuration, the heater surface acts as the ground electrode to the DEP electrode. Constructed via platinum vapor deposition, the 2.25 cm² heater is located in the center of the chamber on an Ultem 1000 pedestal, which thermally isolates it. This heater is different from the design used in Patel [27], which used a circular copper heater encased in a Delrin housing. Finally, a ThermoCube recirculating chiller utilizes chilled water to provide a constant temperature of 15 °C below the EHD conduction pump disk. The EHD disk acts as the condenser in the system, allowing for the vapor generated by boiling to condense on the disk to subsequently be pumped back to the heater. A diagram showing top-down and cross-sectional views of this system is shown in Fig. 4.

The experimental chamber utilizes an aluminum circular housing with NPT and Yor-Lok fittings for filling, vapor pressure measurement, electrical connections, and supplying chilled water. Additionally, two Stanford Research Systems PS350 high voltage power supplies are used to power the conduction pump and the DEP electrode, and an Agilent 6634B DC power supply is used to control power the heater. The complete flight rack with the experimental chamber and all associated equipment is shown in Fig. 5.

An Agilent 34970A data acquisition system is used to collect data during the experiment. Applied voltage is monitored along with the corresponding current for the EHD pump, DEP electrode, and heater. Temperatures in the experiment are monitored in multiple locations. The heater has a platinum resistance temperature detector (RTD) embedded on its surface, as well as a thermistor for redundancy. The surface temperatures of the EHD conduction pump disk are also monitored with platinum resistance thermometers (PRTs) at five locations labeled in Fig. 2. These PRTs are covered in epoxy to prevent electrical interference due to proximity to the EHD electrodes. Another RTD probe is used to measure the vapor temperature. The ambient temperature in the aircraft and in the lab, depending on the gravitational scenario, as well as the chamber outer wall and experiment housing base plate temperatures, are recorded. The base plate houses the majority of the sensors and the experiment itself. In order to capture the gravitational aspects of the experiment, an accelerometer is installed on the baseplate. LabVIEW is used to control and monitor the experiment and has an automatic experiment shut down procedure, should the heater temperature exceed 70 °C. Visualization data at 1080p/60fps were obtained with a camcorder mounted directly above the experiment overlooking the glass window installed on the top of the test chamber.

Prior to charging, the chamber is vacuumed and then filled with a liquid film of HFE 7100 up to a height of 2 mm. The chamber is then degassed using a vacuum pump to the saturation pressure that corresponds to the operating temperature of the experiment. This was done to remove any noncondensable gasses that may enter when charging with fluid. The system loop is as follows; the working fluid is boiled at the heater surface. The DEP electrode extracts the vapor from the heater surface. The vapor condenses on the chilled silicon EHD conduction pump disk. The EHD conduction pump then drives the condensed liquid film back to the heater. In a typical thin-film boiling system, buoyancy/gravity drives the wetting of the heater and removal of vapor bubbles. The addition of EHD and DEP forces allows the loop to be sustained in the absence of gravity, where such a buoyancy force/gravity is negligible or not present.

The electric potential applied to the EHD pump was ramped up from 0 to 1500 V in 500 V increments. The incremental increase in voltage is required due to the sensitivity of forming the heterocharge layers on the conduction pump electrodes. Based on the spacing between electrodes, the voltage was limited to 1500 V to avoid dielectric breakdown of the fluid. The DEP electrode was either kept at 0 V or energized at 2000 V. Due to the nature of the parabolic microgravity flight, voltages of the EHD conduction pump and the DEP electrode were changed only during longer segments where the plane was leveled out. This is due to electrical steady-state taking several minutes to be reached. The microgravity flight consists of a series of parabolic maneuvers in which those onboard experience accelerations ranging from hypergravity (1.6 g to 1.8 g) on the lower vertex, to microgravity (≈0 g) at the higher vertex. The microgravity increments typically last between 15-20 s, and the hypergravity increments typically lasted 20-30 s. The flight campaign for this study consisted of a total of 120 flight parabolas conducted over 4 consecutive days. During the microgravity flights, the heater power was operated from 0 W/cm² to around 7 W/cm². The heater power was changed between parabolas to develop boiling curves from 0 W/cm² to dryout values for various cases of EHD and DEP voltages.

In addition to the microgravity flight, the experiment was further tested terrestrially on the ground using an updated heater design, which has an area of 1.0 cm², as well as a smaller DEP electrode to accommodate the heater. The purpose of this testing was to obtain full boiling curves and determine CHF with the enhancement of the EHD conduction pump and DEP mechanism in a 1 g environment. CHF for this ground testing occurred when the applied heat flux caused the heater surface temperature to rise very rapidly over the course of a few seconds. This rapid rise in temperature is caused by the boiling over the heater being strong enough to overcome the replenishment of cooler liquid HFE 7100. The CHF was increased from 9.76 W/cm² under no electric fields to 15.63 W/cm² with the application of electric fields.

Figure 6 shows the heat flux as a function of temperature difference between the heater surface and vapor for the cases of baseline (no EHD/DEP), EHD only, DEP only, and combined EHD and DEP cases for data taken on the ground. The ground data show that EHD conduction pumping enhances heat transfer by providing an electrically-driven forced convection over the heater surface. This is attributed to an increased flowrate of liquid over the heater and local liquid circulation near the heater due to the EHD conduction pumping. This is confirmed by video taken during testing. This also results in an increased critical heat flux. However, the enhancements are not significant because the pressure generated by the EHD conduction pump is only slightly higher than that already provided by hydrostatic pressure at 15 °C. This is expected since the hydrostatic pressure provided by the 2 mm fluid film is approximately 30 Pa, while the EHD pump is able to provide pressure generation of approximately 50 Pa at 1.5 kV. Therefore, naturally, in microgravity, the pump has more impact, as there is no hydrostatic pressure in the fluid. It is important to recognize that the role of the EHD conduction pumping is essential in the absence of gravity to electrowet the heater surface to maintain a fluid film for boiling.

The DEP extraction mechanism significantly enhances the heat transfer. Higher heat fluxes are reached with lower heater surface superheat. For example, at the heat flux of 9.76 W/cm², the heater surface temperature is lowered by 18.65 °C compared to the baseline case. The case of EHD and DEP mechanisms combined further enhance heat transfer as shown in Fig. 6. This is clear as the CHF reaches its maximum value of 15.63 W/cm² compared to only 9.76 W/cm² for the baseline case. Considering the combined power consumption (maximum of 400 mW) of the DEP electrode and EHD conduction pump, this result demonstrates a significant improvement in heat removal at the cost of low power. For qualitative comparison, the Rohsenow correlation for boiling is estimated below and presented in Fig. 6.

Here, C_sf and r are constants that are specific to the system and the working fluid properties. Equation (2) has been rearranged from the original equation given by Ref. [28] to solve for ΔT as a function of heat flux, q″. Fluid properties from Ref. [25] along with the constants (C_sf = 0.0036, r = 0.33) [29] were used to find these values of ΔT. These temperature values were calculated for the case of a terrestrial environment (i.e., 1 g = 9.81 m/s²). The 1 g prediction based on this correlation is compared to the experimental ground data and is plotted in Fig. 6.

The trend qualitatively agrees with the data in the baseline case. Patel et al. [27] conducted a similar Rohsenow analysis and also found that the correlation qualitatively aligned with their baseline (no electric field present) data. Comparing the data obtained in [27] with this study reveals similar trends, but a direct comparison is not practical, as the fluids used were different in each study (HFE 7100 versus HCFC-123). Again, this comparison is qualitative, as Rohsenow is used for pool boiling, and this study evaluates liquid film flow boiling.

Figure 7 shows the resultant heat transfer coefficient as a function of temperature difference between the heater surface and vapor for the same cases on the ground given in Fig. 6. Activating the DEP electrode significantly raises the heat transfer coefficient, by as much as three times when compared to the case of no EHD or DEP influence. The enhanced heat transfer coefficient with the DEP mechanism activated remains constant at lower ΔT values below the ONB. At these values, the DEP force stirs the liquid film (in the absence of vapor bubbles). This is due to the electric permittivity gradient that is expected to be present within the liquid film height because of the presence of a temperature gradient. Further enhancement is observed with the combined operation of EHD pumping and DEP extraction force.

Figure 8 illustrates the impact of presence of EHD conduction pumping and DEP vapor extraction mechanism on hysteresis, on the ground. As seen in the figure, in the absence of EHD pumping and DEP mechanism, there is a clear hysteresis present when comparing increasing versus decreasing heat flux curves. Furthermore, the onset of nucleate boiling (ONB) occurs at a ΔT of 16.6 °C, corresponding to 1.75 W/cm².

In the presence of EHD conduction pumping or DEP mechanism, as depicted in Fig. 8, the hysteresis almost gets eliminated. This is primarily due to the fact that EHD conduction pumping effectively wets the heater surface as it provides forced convection, and the DEP mechanism extracts bubbles as they get formed. The DEP mechanism also raises the ONB from 1.75 W/cm² to 2.95 W/cm², which was visually observed during testing. This delay in the ONB with the DEP mechanism activated can be attributed to additional heat transfer taking place before boiling. As mentioned before, the DEP force stirs the liquid film due to the presence of an electric permittivity gradient in the liquid film height.

The compiled flight results are shown in Figs. 9–11(d). Due to the nature of parabolic flights and the short time allocated between changes in gravity conditions, inertial forces result in fluid avalanching between transitions. Therefore, the results correspond to unsteady state situations. One the other hand, the ground data were obtained under steady-state. For reference, the data show the time required to reach steady-state on the ground was approximately 10-15 s. The data from the parabolic flights were taken over different, but consecutive days, which could also contribute to challenges in comparing data points. Despite the above issues with testing in parabolic flights, the results show that the EHD conduction pumping, and, to much extent, the DEP mechanism enhanced the heat transfer. To obtain full boiling curves and determine the true impact of these mechanisms in the absence of gravity at steady-state, a steady microgravity environment, such as the International Space Station, is needed.

Figure 9 presents the results of the microgravity sections of the parabolic flights. The most important trend to notice in this plot is the effect of the DEP electrode on the liquid film flow boiling heat transfer. The DEP electrode's capability to extract vapor raises the heat flux to its highest value of 7 W/cm² before dryout. This value is considered the dryout point since the heater surface temperature rises very rapidly over a few seconds. It should be noted that dryout is not necessarily the same as CHF, as the experiment is not at steady-state, and the nature of the microgravity flight is not controllable. This increase in heat flux is 1.5 W/cm² or a 27.3% increase compared to the dryout point of the baseline case. Furthermore, this trend exists for lower ranges of heat flux (0–4 W/cm²), indicating that high heat flux values are not necessary to capture the heat transfer enhancement that these EHD mechanisms can provide in microgravity. Additionally, combining the EHD conduction pump with the DEP electrode provides further enhancement. The combined effect of these mechanisms reached higher heat fluxes for a given temperature difference compared to baseline and EHD pumping-only cases. This is shown and labeled in Fig. 9 as a difference of 15 °C exists for the same heat flux value between the combined EHD/DEP case and the baseline case. This result demonstrates that using EHD and DEP together under unsteady state, a heated surface experiencing liquid film flow boiling in the absence of gravity can reach higher heat flux values and still maintain a lower surface temperature when compared to traditional baseline cases where EHD and DEP are not present. Without gravity, the role of EHD conduction pumping is critical in providing the liquid to the heater surface. Regardless of the transient environment of the flights, the DEP mechanism shows significant enhancement of heat transfer raising the CHF to 7 W/cm².

Similar to the microgravity heat flux results, a set of results in 1.6 g to 1.8 g ranges was also plotted in the same fashion. Figure 10 highlights these results and shows that the DEP electrode continues to dominate the heat transfer enhancement, especially toward dryout values. The combined effect of the EHD conduction pump and DEP electrode also provides enhancement, especially at lower heat flux values, and results in a 9 °C drop in temperature for the same heat flux value when compared to the baseline test case. This result indicates that these mechanisms could provide heat transfer enhancement, even under harsh conditions associated with parabolic flights.

Figures 11(a)–11(d) directly compare the ground, microgravity, and 1.8 g data for different test cases of baseline, EHD, DEP, and combined EHD with DEP. These figures demonstrate that these mechanisms provide very similar enhancement in microgravity as compared to the ground, indicating that they could be effective not only for terrestrial applications, but also in space. It should be noted that the ground data reach significantly higher than the microgravity or 1.8 g data as a result of the updated hardware mentioned earlier. The heat flux values in the microgravity data are observed to plateau as this is associated with the dryout point. To elaborate, nearing dryout, the heat flux remains constant, while the superheat (ΔT) increases rapidly. Thus, a plateau is observed in these plots. Also indicated by these plots is the significance of the DEP electrode as a method of thermal management, reaching higher heat fluxes than those of EHD pumping only or baseline. Additionally, for a given value of heat flux, the heater surface temperature is decreased the most under the influence of the DEP electrode in all gravitational conditions (unsteady state) as compared to the baseline and EHD pumping only cases, up to a difference of 12 °C.

This results in a buoyancy force of F_buoyancy = 6.02 × 10⁻⁸ N. The maximum DEP force on a vapor bubble was calculated to reach maximum force of 55.0 × 10⁻⁸ N, resulting in a ratio of DEP force to buoyancy force of 9.14. This indicates that the DEP mechanism can effectively extract bubbles away from the heater surface. In addition to providing vapor extraction in the absence of gravity, this also indicates that on the ground, the DEP electrode will still be a superior vapor extraction method compared to the natural buoyancy forces induced by gravity as illustrated in Fig. 6.

Experimental uncertainty in all measurements and the derived values are compiled and represented in Table 2. The horizontal and vertical error bars depicted in the data graphs correspond to two standard deviations. Overall, the derived error contributions come from the ΔT values (±0.7 °C), the heat flux values (±3.1%), and the heat transfer coefficient values (±14%).

This study investigated the effect of EHD conduction pumping and the DEP mechanism under various gravitational conditions. The testing conditions aboard the parabolic flight corresponded to unsteady state. Regardless of this, both mechanisms illustrated that they enhance heat transfer, even during harsh conditions associated with parabolic flights, especially when combined. Additionally, they also allow for sustainable liquid film boiling in the absence of gravity. It was also observed that the presence of electric fields from the EHD and DEP mechanisms eliminated boiling hysteresis. Throughout all operating conditions, the maximum current drawn by the EHD and DEP was less than 0.3 mA with the average being substantially lower. This resulted in less than at most 600 mW of power drawn, with the average being much lower, highlighting this technology's advantage of low power consumption while enabling two-phase heat transfer in microgravity. This study paves the way for future implementation of DEP/EHD-driven two-phase heat transport devices into space and aeronautical applications.

The work was supported by the Biological and Physical Sciences Division in the Science Mission Directorate at NASA HQ under NASA Grant NNX16AT09G. The work of the first author was supported by the NASA Space Technology Research Fellowship NSTRF Grant 80NSSC19K1170.

• National Aeronautics and Space Administration (NASA) (Funder ID: 10.13039/100000104).

a =

bubble radius (m)

c_p =

specific heat (kJ/kg K)

C_sf =

surface-fluid constant for Rohsenow correlation

d =

characteristic length (m)

E =

electric field (V/m)

E_e =

electric field vector (V/m)

F_buoyancy =

buoyancy force (N)

F_DEP =

DEP force (N)

f_EHD =

electrohydrodynamic body force (N)

g =

gravity (9.81 m/s²)

h_fg =

heat of vaporization (kJ/kg)

k_l =

liquid thermal conductivity (W/m K)

Pr_l =

liquid Prandtl number

q″ =

heat flux (W/m²)

r =

system-specific constant for Rohsenow correlation

T =

temperature (K or °C)

V =

electric potential (V)

ΔT =

temperature difference (K or °C)

ε =

electric permittivity (F/m)

μ =

dynamic viscosity (kg/m s)

ρ_l =

liquid density (kg/m³)

ρ_v =

vapor density (kg/m³)

σ =

surface tension (N/m)