The formation of a vapor layer at the solid-liquid interface at high temperatures (Leidenfrost phenomenon) degrades heat transfer substantially. Application of an electric field in this vapor layer can fundamentally eliminate the Leidenfrost state by electrostatically attracting liquid towards the surface. This study analyzes the influence of AC electric fields on electrostatic suppression of the Leidenfrost state; previous studies have only utilized DC electric fields. In particular, the influence of the frequency of the AC waveform on Leidenfrost state suppression is analyzed using high speed visualization of liquid-vapor instabilities and heat transfer measurements of evaporating droplets. It is seen that the extent of suppression is reduced with increasing AC frequency. At sufficiently high frequencies, the influence of an applied voltage is completely negated, and electrostatic suppression of the Leidenfrost state can be completely eliminated. A first-order electromechanical model is used to explain the frequency-dependent reduction in the electrostatic attraction force on the Leidenfrost droplet. Overall, this work highlights the importance of AC frequency as a tool to control the extent of suppression and the boiling heat transfer rate.
Boiling can enable ultrahigh heat flux dissipation due to the large latent heat of vaporization1–4 of typical working fluids and bubble-related convection. However, heat transfer degrades significantly at high temperatures due to the formation of an insulating vapor layer at the solid-liquid interface. This vapor layer fundamentally limits heat dissipation and the operating temperatures of industrial equipment which operate under boiling conditions. This vapor layer buildup was first discussed in 17565 and is known as the Leidenfrost effect. Numerous studies6–14 have analyzed the role of surface engineering (chemistry and texture) to delay vapor layer formation and increase the Leidenfrost temperature.
Recent studies15–20 have shown that an externally applied electric field in the vapor layer can fundamentally eliminate the Leidenfrost state, by electrostatically attracting liquid to the surface. Takano et al.15 showed that the boiling rate of R113 and ethanol droplets can be enhanced significantly under a DC electric field. Celestini and Kirstetter16 demonstrated electric field-induced suppression of the Leidenfrost state with water droplets. Shahriari et al.17 showed Leidenfrost state suppression of multiple liquids at temperatures as high as 550 °C. In a later study, Shahriari et al.20 analyzed the fundamental instabilities responsible for electrostatic suppression. The practical application of this concept was highlighted in a recent study18 on electrically tunable quenching of metal spheres. It was reported18 that electrostatic elimination of the Leidenfrost state can fundamentally alter the boiling patterns and the cooling curve. Key benefits18 of this concept include the opportunity for dynamic control of boiling, lack of need for surface modifications, and low electrical power consumption.
Previous studies15–20 on electrostatic suppression utilized DC fields. Since the liquid droplet was equipotential, the entire voltage difference was expressed across the vapor layer, resulting in a high electric field in the vapor layer. This work is a fundamental study on the influence of AC electric fields on Leidenfrost state suppression. In particular, the role of the frequency of the AC waveform is expected to be significant and is presently studied. This observation stems from studies on AC electrowetting-induced droplet motion21–24 on flat surfaces. The frequency of the AC waveform influences droplet motion significantly. Multiple studies25–28 show that the actuation force is AC frequency dependent and that the force decreases drastically above a threshold frequency. This observation has important manifestations for AC electric field-based Leidenfrost state suppression, since it suggests that the extent of suppression should decrease with frequency. This hypothesis is presently studied, and the influence of AC frequency on Leidenfrost state suppression is quantified. It is noted that Celestini and Kirstetter16 used AC voltages to suppress the Leidenfrost state. However, the frequency was only 0.5 Hz, which will not fundamentally affect the electrostatic suppression force, as explained ahead. It is also noted that the use of AC electric fields has some benefits over DC electric fields in terms of lower contact angle hysteresis and reduced ion absorption.21
The objective of this study is to understand the physics underlying reduced suppression of the Leidenfrost state under AC electric fields. First, high-speed imaging of liquid-vapor instabilities and heat transfer measurements are utilized to quantify AC frequency-dependent suppression. Second, an analytical model is developed to provide a physics-based understanding. The key result of this study is that the AC frequency can negate the influence of an applied electric field and completely eliminate suppression. This work also highlights the suitability of anodized aluminum as a dielectric for high temperature electrowetting applications (where polymer-based dielectrics fall short).
The experimental setup used in the present study is shown in Fig. 1. A 1.6 mm thick aluminum plate with a 25 μm thick layer of anodized aluminum was used as the substrate. The substrate was heated on a hot plate, and the surface temperature was measured with an infrared camera. AC and DC voltages were generated using a function generator and a high voltage amplifier (Piezo Systems). A 120 μm diameter wire biased the droplet and held it steady in the Leidenfrost state. Droplets were dispensed by a micropipette on the hot surface. Suppression of the Leidenfrost state was imaged by a high-speed camera (Photron Fastcam Mini) at speeds exceeding 10 000 frames per second; a macro lens (Tokina AT-X Pro 100 F2.8 D) was used.
Three fluids were used presently: isopropyl alcohol (IPA), deionized (DI) water, and methanol. It was observed that IPA and methanol droplets were stable during suppression of the Leidenfrost state. On the other hand, DI water droplets exhibited violent splashing, breakup, and satellite droplet emission during suppression. Similar behavior is reported in another similar study.16 Through experiments, it was observed that much more “stable” suppression of DI water droplets was possible by coating the surface with a thin (<100 nm), spin coated Teflon layer. All experiments were therefore conducted with a Teflon layer on the anodized aluminum dielectric.
The surface temperature for all experiments was 330 °C and is higher than the Leidenfrost temperature for all liquids. The volume of all droplets was fixed at 20 μl. Table I shows the measured Leidenfrost temperature for the three liquids and the threshold voltage to initiate Leidenfrost state suppression using a DC electric field. The Leidenfrost temperature depends on the fluid, surface texture/chemistry, and droplet volume. Presently, the Leidenfrost temperature was estimated by measuring the droplet lifetime at various temperatures; lifetime is minimum at the Leidenfrost temperature. The threshold voltage to suppress the Leidenfrost state was estimated from high magnification imaging of the vapor layer; instabilities at the liquid-vapor interface are seen at the threshold voltage as reported in previous studies.17–19 The threshold voltage varied from 65 to 75 V for the three liquids.
|.||Leidenfrost temperature (°C) .||Threshold DC voltage (on 330 °C surface) .|
|.||Leidenfrost temperature (°C) .||Threshold DC voltage (on 330 °C surface) .|
The influence of AC fields on Leidenfrost state suppression was studied by varying the AC frequency at a constant voltage. Figure 2 shows a set of visualizations for IPA droplets at AC voltages (rms) of 60, 80, and 100 V, with varying frequencies. At 80 V DC [Fig. 2(a)], instabilities and “liquid fingers” are clearly seen to protrude and bridge the vapor layer. The instabilities persist when the DC voltage is replaced by 80 V, 100 Hz AC voltage [Fig. 2(b)]. However at 80 V, 1000 Hz, AC voltage, the instabilities disappear [Fig. 2(c)], indicating that the Leidenfrost state is no longer suppressed. Exactly the same trend is observed at 100 V. Instabilities are seen at 100 V, 1 kHz AC [Fig. 2(d)] and 100 V, 10 kHz AC [Fig. 2(e)]. However, no instabilities are observed at 100 V, 100 kHz AC [Fig. 2(f)], indicating that the Leidenfrost state is not suppressed. The third row of Fig. 2 shows the influence of AC frequencies at voltages below the threshold voltage. Figure 2(g) shows the vapor layer in the absence of any applied voltage, and Fig. 2(h) shows the vapor layer under the influence of 60 V DC. Below the threshold voltage [Fig. 2(h)], the sinusoidal instabilities are not observed, although there are occasional disturbances at the liquid-vapor or liquid-air interfaces. However, the vapor layer thickness is less than the no voltage case [Fig. 2(g)]. Interestingly, at 60 V, 100 Hz AC [Fig. 2(i)], the vapor layer is thicker than the DC voltage [Fig. 2(h)], indicating that the electrostatic force on the droplet is reduced under AC conditions.
The above observations are evident in high-speed visualizations of Leidenfrost state suppression under DC and AC electric fields as seen in Fig. 3 (Multimedia view in the supplementary material). Very similar trends were obtained for water and methanol droplets. For every liquid, instabilities decreased at higher AC frequencies. At high enough frequencies, Leidenfrost state suppression ceased completely. The supplementary material includes images corresponding to similar experiments on water and methanol droplets.
In addition to visualizations, another analysis was conducted to quantify the influence of AC frequency on Leidenfrost state suppression. This analysis is based on measurements of the evaporation/boiling rate of droplets under suppression conditions. Greater suppression will enhance heat absorption by the droplet, leading to faster evaporation/boiling. The evaporation rate can be quantified by measuring the mass loss of the droplet versus time. Mass loss versus time was quantified using the image processing tool of MATLAB. Droplets were imaged from the point that they were pipetted till when they completely evaporated or detached from the surface onto the wire electrode (towards the end of the experiment). This detachment happens when the capillary attraction between the wire and the droplet overcomes its weight and electrostatic attraction force. Although the volume of the detached droplet is small compared to the initial volume, it was accounted for in the calculation of the evaporation rate. The supplementary material shows the droplet mass versus time curves for DI water droplets at 140 V DC and 140 V AC at 1 and 100 kHz.
Figure 4 shows the evaporation rates of 20 μl IPA droplets as a function of the AC frequency at four different voltages. It is noted that this is the average evaporation rate (based on mass loss versus time data of the evaporating droplet). The evaporation rate increased by 17%, 22%, 32%, and 51% at DC voltages of 70 (threshold voltage), 80, 100, and 140, respectively, as compared to the no voltage case. This is a direct consequence of increased wettability at higher electric fields, which enables faster heat pickup by the droplet. As the AC frequency is increased, the evaporation rate decreases, due to reduced suppression of the Leidenfrost state. At sufficiently high frequencies, the evaporation rate will approach the no electric field case, as observed for the 70, 80, and 100 V curves. The frequency required to completely eliminate Leidenfrost state suppression increases with voltage. Interestingly, the evaporation rate for the 140 V case did not show a marked decrease with increasing frequency. This is explained using the analytical model developed ahead, which shows that frequencies greater than 100 kHz will be needed to eliminate Leidenfrost state suppression at such voltages.
Similar results were also obtained for DI water and methanol droplets and are included in the supplementary material. A frequency dependent evaporation rate was observed in all experiments with the evaporating rate plateauing to no electric field limit at high frequencies. It is noted that Fig. 4 only reports the average evaporation rate over the lifetime of the droplet. In fact, the evaporation rate is higher initially (due to larger heat transfer area from a larger droplet) and decreases as the droplets get smaller.
The visualization and evaporation rate experiments indicate that frequency of the AC waveform can counter the applied voltage and can completely prevent suppression at high frequencies. Furthermore, the AC frequency required to negate the influence of the applied voltage increases with the voltage. The physics underlying these observations can be understood by analyzing past studies25–28 on electrowetting-based droplet actuation using AC voltages. These studies reveal that the electric field penetrates inside the droplet as the AC frequency increases, thereby reducing the field strength. Similarly, the absence of a concentrated electric field in the vapor layer at high frequencies reduces the electrostatic force, thereby reducing the extent of suppression. At sufficiently high frequencies, an electrically conducting droplet behaves as an electrically insulating droplet, due to penetration of the electric field inside the droplet.
An electromechanical model can help explain the observed experimental trends. From an electromechanical standpoint, every material can be modeled as a resistor and capacitor in parallel. The resistor captures the effects associated with electrical conductivity, while the capacitor captures the dielectric behavior of the material. Both these attributes are captured together in the complex permittivity ε*, defined as28
where k is the dielectric constant, σ is the electrical conductivity, and ω is the AC frequency. The first term represents the capacitance, while the second term represents the resistance. As the frequency is increased, the role of the electrical conductivity is reduced, and the material behaves as a pure capacitor.
As per the above framework, the current system involves three materials, each of which can be represented as a resistor in parallel with a capacitor. These are the liquid droplet, the vapor layer, and the dielectric layer. The supplementary material includes a detailed derivation of all components of this RC circuit. The frequency dependent effective capacitance Ceq of such a circuit is
where Rl, Rv, and Rd are the liquid, vapor, and dielectric layer resistances, respectively, and Cl, Cv, and Cd are the liquid, vapor, and dielectric layer capacitances, respectively. The liquid, vapor layer, and dielectric layer have their capacitance and resistance in parallel; the three materials are sequentially in series. The equivalent impedance is found by summing up the impedances of the liquid, vapor, and dielectric layer. The droplet impedance is estimated using the shape factor defined by Shapiro et al.29 The flat plate capacitor model is used for the vapor layer and the dielectric layer.
The effective capacitance is the key parameter as the change in the stored electrostatic energy provides the force for suppressing the Leidenfrost state. The electrostatic force on the droplet can be expressed as
The electrostatic force obtained from the above equation can be normalized with the force under DC voltage conditions. This normalized force is shown in Fig. 5 as a function of AC frequency for the three liquids considered in the study. IPA, DI water, and methanol have (dielectric constant30 and electrical conductivity) of (21 and 0.3 μS/cm), (55 and 1.8 μS/cm), and (27 and 0.7 μS/cm), respectively. For each liquid, the actuation force is maximum at low AC frequencies and is the same as that under a DC electric field. At such low frequencies, there is no electric field inside the liquid droplet (which is equipotential). Consequently, the entire voltage difference remains concentrated across the vapor layer and the dielectric layer. As the frequency increases beyond a threshold, the field starts penetrating inside the droplet. This reduces the effective electric field and consequently the electrostatic attraction force. At higher frequencies, the electrostatic force is completely eliminated, and the droplet behaves as a pure insulating material. The frequency at which the force starts decreasing from its maximum value increases with the electrical conductivity of the fluid. The frequency at which the force becomes zero also shows the same trend. This can be explained from Eq. (1), which shows that higher AC frequency is required to negate the influence of the applied voltage for fluids as the electrical conductivity increases. It is pointed out that this simplified scaling-analysis type of model does not directly validate the experimental observations reported in Fig. 4. However, it clearly suggests that that frequency-dependent reduction in electrostatic force is the reason for the reduced evaporation rates at higher frequencies.
An important finding in this work is the suitability of anodized aluminum as a dielectric for high temperature electrowetting applications. While there are multiple good polymeric dielectrics available21 for room temperature electrowetting applications, most of them are not well suited at high temperatures. Although the thickness (25 μm) of the dielectric (anodized aluminum) used presently was high, it exhibited pinhole-free, defect-free behavior at high temperatures. At 420 °C, the leakage current at 200 V was less than 1 μA in an electrowetting experiment with DI water. Repeating the experiment with a corrosive 1 M NaCl solution did not increase the leakage current. This dielectric did not exhibit a change in properties even after more than 10 h of high temperature experiments.
In conclusion, this study analyzes the physics associated with Leidenfrost state suppression using AC electric fields. It is clearly seen that the frequency of the AC waveform is an important consideration in addition to the applied voltage. An increase in frequency can counter the influence of the applied voltage, due to penetration of the electric field inside the liquid. At high frequencies, the influence of the applied voltage is completely negated. This study highlights the AC frequency as an important parameter in the electrostatic control of boiling heat transfer and cooling rate.
See supplementary material for images showing Leidenfrost state suppression of deionized water and methanol droplets, videos showing instabilities, and details of the analytical model to estimate the electrostatic force under an AC electric field.
The authors would like to acknowledge the National Science Foundation Grant No. CBET-1605789 for supporting this work.