The conditions of experiments carried out in parabolic flights and on Earth are listed in (SI1). Low gravity measurements were conducted in 3 days of parabolic flights in NASA Boeing 727. A flight provided two sets of consecutive parabolic arcs, each with 15-s freefall at acceleration ~ 10−2g E preceded and followed by periods of acceleration ~ 1.3g E for 50–60 s where g E is the normal gravity acceleration; the second set also included two parabolas simulating the gravity of the Moon (1.62 m/s2) and Mars (3.71 m/s2). Following guidelines,19 a flight setup was designed to withstand “crash g-forces” up to 9g E along horizontal axis, up to 2g E along positive vertical axis and up to 6g E along negative vertical axis (Supplementary information, SI1). The setup was equipped with two cuvettes shown in Fig. 1 for simultaneous testing of different liquids. Experiments were carried out on 3 M Novec HFE-7100 (3 M, St. Paul, MN) and distilled water from a local pharmacy with conductivity σ l ~ 2·10−4 S/m and dielectric constant ε 1 ~ 78 measured before experiments. Here we present data only for water. Due to the limited space of the paper, experiments on HFE-7100 for which a conventional boiling regime was observed will be reported elsewhere. For water at room temperature, L c equals 2.7 mm on Earth and 27 mm for freefall. A cuvette (Fig. 1) was loaded with 1 mL of water and then closed with a plastic lid. As a liquid in a cooling system utilized over a long period of time usually accumulates dissolved air, experiments were carried out with the cuvette lid that was not airtight to maintain atmospheric pressure inside the cuvette. A platinum temperature resistance sensor, serving as a heater, was embedded into a polydimethylsiloxane (PDMS) slab such that the heating surface was in contact with water (Fig. 1d). The ratios of the heating surface width and length (Fig. 1d) to the capillary length were respectively 0.74, 0.85 for experiments on Earth and 0.074, 0.085 in flight. The interior contact angles of water on the heater surface and PDMS measured at room temperature were respectively 74 ± 3° (hydrophilic) and 107 ± 2° (hydrophobic). The heater was connected in series with a resister R 0 and a direct current (DC) power source that provided voltage U DC to the heater (Fig. 1). The voltage drop across this resistor U R was measured to compute the voltage drop on the heater ΔU h = U DC −U R , the electrical current I h = U R /R 0 , the power I h ΔU h that varied from about 0.5 W to 5.5 W and the heater resistance R h = ΔU h /I h that was used for calculating its temperature T h from the linear calibration curve R h vs. T h . The values of heat flux q h = I h ΔU h /S h reported in Figs. 2–6 correspond to the total power provided to the heater. Expressions20 were used to estimate the heat loss from the heater through the power lead wires and directly into the PDMS slab. Calculations presented in SI1 indicate that the heat loss increased with raising the heater temperature from about 9% at T h ≈ 50 °C to 13% at T h ≈ 270 °C. Additional two parameters were measured on Earth due to flight limitations: (i) the temperature T s slightly below the water surface by probe 9 in Fig. 1a to estimate the bulk liquid temperature and (ii) the heater temperature T h when the heating power source was turned off by applying 3 V DC to the heater (Fig. 1c). For the latter, the generated power ~ 0.075 W might raise the heater temperature by ~ 2°C.

Fig. 1 Cell: a Front and side views: 1, cuvette with liquid; 2, cover; 3, camera, signal recorded by a laptop over the entire experiment; 4, connection to amplifier for generating high voltage pulses of alternating polarity; 5, grounded electrode; 6, temperature resistance sensor (heater); 7, PDMS slab; 8, energized electrode coated with Teflon at 2 mm from the heater, 9, temperature probe in ground experiments; 10, connection to heating circuit. Electrical circuits: b flight: 1, heating DC power source; c Earth: 1a, heating DC power source; 1b, 3 V DC power source; S, switch; (both b, c) 2, heater; 3, resistor; 4, connection to acquisition system; d photo of platinum sensor P0K1.232.4 W.B.010 in PDMS slab whose silver wires (diameter 0.25 mm, length 10.0 mm) were soldered to power lead copper wires (Gauge 36 copper wire, length ~4 mm); sensor sketch reproduced with permission from Innovative Sensor Technology, Las Vegas, NV Full size image

Fig. 2 Thermal regimes: a Flight, parabolas (number shown); 22.4 V DC & 4 kV/20 Hz pulses applied in freefall (top row) and switched off during acceleration (bottom row); b Earth, continuous heating, no HV pulses; T s and heating time shown; applied V DC: 10 (A); 20 (B); 30 (C) see heat flux for A, B, C in Fig. 4a. c Earth, heating cycles 20 V DC & 4 kV/20 Hz pulses 20 s on/60 s off, temperatures: 1, T s ; 2, T h Full size image

Fig. 3 Thermal regimes. a–d Bubble width w, height h, ratio h/w, volume V, and cap surface area S in heating period; curves terminate after departure of the first bubble: Flight 1, 20 V DC & 3 kV/20 Hz; 22.4 V DC & 4 kV/20 Hz; 22.4 V DC & 4 kV/10 Hz, pulses applied in freefall and switched off during acceleration; Earth 2–7, heating cycles 20 s on/60 s off (top row) and continuous heating (bottom row) with 4 kV/20 Hz pulses (empty symbols) and without HV pulses (filled symbols); applied V DC: 15 (2); 20 (3); 22.4 (4); 25 (5); 30 (6); 35 (7); inset 20 V DC. e, f Changes of the bubble volume ΔV due to water vapor condensation as heating was turned off and the air fraction in the bubble (1−ΔV/V) vs. the number N of heating cycles for regimes listed in (a–d). V, S, and ΔV were computed by integration of the shape profile along the bubble image (SI1). Results of statistical analysis of measurements are listed in SI1 Full size image

Fig. 4 Effects of increasing heating DC voltage: a Stabilized heat flux q h vs. heater temperature T h . Flight: 1, 20 V DC & 3 kV/20 Hz; 2, 22.4 V DC & 4 kV/20 Hz; 3, 22.4 V DC & 4 kV/10 Hz; Earth, heating cycles 20 s on/60 s off: 4, no HV pulses (points for 15, 20, 22.4, 25, 30, 35 V DC); 5, with 4 kV/20 Hz pulses (points for 20, 22.4 V DC); Earth, continuous heating: 6, no HV pulses (points for 5, 10, 15, 20, 22.4, 25, 27.5, 30, 35 V DC); 7, with 4 kV/20 Hz pulses (points for 5, 10, 15, 20, 22.4, 25, 30 V DC); 8–11, 20 V DC with 4 kV pulses at 1 (8); 10 (9); 50 (10); 100 (11) Hz. Points A, B, C mark regimes in Fig. 2b. Inset: Earth, continuous heating 20 V DC: T h vs. frequency of 4 kV pulses. b Earth, T s , continuous heating: without HV pulses for 15 (1), 20 (2), 22.4 (3), 25 (4), 30 (5), 35 (6) V DC and with 4 kV/20 Hz pulses for 20 (7), 22.4 (8) V DC. Inset: heating cycles 20 s on/60 s off without HV pulses for: 15 (9), 20 (10), 25 (11), 30 (12) V DC. c Earth, bubble height to width ratio h/w vs. T s for continuous heating: no HV pulses for 15 (1), 20 (2); 22.4 (3), 25 (4); 30 (5); 35 (6) V DC and with 4 kV/20 Hz pulses for 20 (7), 22.4 (8), 35 (9) V DC; heating cycles 20 s on/60 s off: no HV pulses for 15 (10), 20 (11), 22.4 (12), 25 (13), 30 (14), 35 (15) V DC and with 4 kV/20 Hz pulses for 15 (16), 20 (17), 22.4 (18), 25 (19), 30 (20), 35 (21) V DC. d Earth, relative changes of bubble volume ΔV/V as heating turned off vs. T s for heating cycles 20 s on/60 s off with 4 kV/20 Hz pulses (empty symbols) and without HV pulses (filled symbols): 15 (1), 20 (2), 22.4 (3), 25 (4), 30 (5), 35 (6) V DC. (e) The bubble volume V and cap surface area S normalized by the bubble height h vs. bubble height to width ratio 2 h/w for experiments on Earth, 1–21 as listed in (c), and in flight 22: 20 V DC & 3 kV/20 Hz; 22.4 V DC & 4 kV/20 Hz; 22.4 V DC & 4 kV/10 Hz. The dashed line represents the spherical cap. (f) Earth, times of bubble departure vs. liquid temperature T s for 1, heating cycles 20 s on/60 s off and 2, continuous heating. Points for 15 V DC (only for regime 2 as a bubble remained on the heater after 40 min of cycles), 20, 22.4, 25, 30, 35 V DC (data with and without 4 kV/20 Hz pulses within error bars) arranged from left to right. Inset: T s vs. heat flux. Results of statistical analysis of measurements are listed in SI1. Error bars in (a) and (f) represent standard deviations Full size image

Fig. 5 Flow patterns in the cuvette vertical plane: a Flight, left: freefall, 22.4 V DC with 4 kV/20 Hz pulses; right: acceleration, no heating and pulses. b, c Earth, continuous heating: b 22.4 DC, c 30 V DC; with 4 kV/20 Hz pulses (left), without pulses (right). d, e Earth, heating cycles 20 V DC 20 s on/60 s off: d with 4 kV/20 Hz pulses; e without HV pulses; heating ON (left), OFF (right). Symbols indicate trajectories of 10 individual microbubbles for a and individual 75–90 µm blue polyethylene microspheres (1.00 g/cm3, Cospheric, Santa Barbara, CA) on Earth: b 12 particles for left and 11 for right; c 12 for left and right; d 10 for left and right; e 8 for left and 5 for right Full size image

Fig. 6 a Schematic of single-bubble boiling: 1, layer of thickness δ 1 and length l 1 at the bubble footprint where cold liquid flowing into the bubble with velocity v 1 vaporizes; 2, vapor streaming toward the bubble cap with velocity v v ; 3, non-condensable air constituents accumulating away from the bubble cap; T e and T c , evaporation and condensation temperatures; h and D, bubble height and base diameter. b Earth, the Nusselt number Nu for heat transfer between bubble cap and surrounding liquid vs. T s for continuous heating and heating cycles, 1–21 as listed in Fig. 4c Full size image

Since electric fields are widely used to enhance boiling heat transfer,18,21,22,23,24 the cuvette was equipped with electrodes to investigate the field effects on single-bubble boiling. Conventional electric techniques are limited to low conducting liquids because of using bare electrodes inserted into the liquid. To avoid this limitation, a train of successive rectangular high-voltage (HV) pulses of alternating polarity, U p = 3–4 kV at frequency 1/t p up to 100 Hz, was applied to water via the insulated energized electrode inserted into the water and the grounded electrode placed under the cuvette (Fig. 1a). The power supplied by HV pulses was less than 0.2 W (SI1). As the electric stress exerted on a liquid is proportional to the square of the field strength, the application of these pulses kept the electric stress at a constant level. The motion of charge carriers in a liquid subjected to an electric field depends on the ratio25 between the charge relaxation time t rel = ε 0 ε 1 /σ 1 and the period of HV pulses t p , where ε 0 is the vacuum permittivity. As t rel ~ 5μs≪t p in our experiments, ions in water followed the field, thereby reducing the accumulation of charge due to voltage reversals. The proposed design offers the ability of applying an electric force to liquids with much higher electrical conductivity as the chance of short circuit, sparking, and electro-corrosion are drastically reduced.

All flight heating tests were performed in the presence of HV pulses (SI1). Heating DC voltage 20 V or 22.4 V and HV pulses were simultaneously turned on when the aircraft began to freefall. Once the aircraft began to accelerate, they were turned off to avoid the contribution of buoyancy and electric field driven convection. They were also turned off as the aircraft maneuvered for about 10 min to begin flying the second set of parabolas.

A large bubble rapidly formed on the heater during the first freefall. Its footprint was gradually increasing in size, until anchoring on the heater edges after a couple of minutes. It was staying on the heater over the first set of parabolas and detached during the acceleration period of one of parabolas during the second set (Fig. 2a, SI2, video1). Specifically, a bubble formed in the first freefall was remaining on the heater for total of 20 parabolas (32 min) in the first flight, 27 (41 min) in the second flight and 19 parabolas (36 min) in the third flight. As the firstly formed bubble detached, another one formed and stayed on the heater until the end of the flight. During a freefall, a bubble staying on the heater emitted sporadically tiny bubbles that were carried away with the flow. As the aircraft was accelerating, these tiny bubbles rose to the water surface and popped up due to buoyancy. The heater temperature and heat flux during a freefall period stabilized within 2 s after applying DC voltage. Variations of heat flux values from parabola to parabola measured at the same heating regime were lying within 2–4% (SI1).

Experiments on Earth were carried out under conditions of continuous heating and heating cycles with DC voltage 20 s on/60 s off (SI1). Variations of heat flux values measured at the same heating regime were lying within 1–6% (SI1). A consistent performance of single-bubble boiling was observed for both heating modes. To avoid rapid deterioration of the PDMS slab around the heater, most experiments were conducted for heater temperatures below 270 °C. Photos in Fig. 2b illustrate bubbles formed under continuous heating. Tiny bubbles appeared on the heater at 10 V DC for which T h was below 100 °C (Fig. 2b, regime A) were mainly due to the release of air dissolved in water as its solubility decreased with temperature. A single bubble formed on the heater when T h was above 100 °C. Side and top images in Fig. 2b B show the evolution of the first bubble appeared at 20 V DC. The first bubble formed at 30 V DC is shown on images in Fig. 2b regime C from 20 to 140 s. As can be seen in Fig. 2b regimes B & C, the bubble foot gradually expanded until reaching the heater edge. While the heater temperature T h and heat flux q h stabilized within several seconds after applying DC voltage, the bulk temperature of water for both heating modes gradually rose due to the low rate of heat transfer out of the cuvette. This feature was used to investigate the effect of water temperature on single-bubble boiling. The timescale of changes in water temperature T s for continuous heating was about 5 min for voltage greater than 10 V DC (SI1). The amplitude of water temperature variation in a heating cycle was in the range 2–6 °C, gradually increasing with applied DC voltage. The timescale of changes in water temperature from cycle to cycle were much smaller than that for continuous heating since the electric power averaged over a cycle was four times smaller. Plots and photos in Fig. 2c illustrate variations of T h , T s and the bubble size in a typical heating cycle. When the heater temperature dropped down once the heating was off, the bubble shrank due to condensation of water vapor (Fig. 2a in flight and Fig. 2c on Earth). While the heater temperature and heat flux did not change in the process of boiling, the height h, volume V, and cap surface area S of the pinned bubble were gradually increasing due to the rising water temperature (Fig. 3a–d). Fig. 3e, f illustrates a change in the bubble volume ΔV caused by vapor condensation after the heating was turned off and the air volume fraction in the bubble (calculated as 1−ΔV/V) with the number N of heating cycles.

Points A, B, C in Fig. 4a mark regimes shown in Fig. 2b. The maximum efficiency of HV pulses was achieved at 20 Hz (Fig. 4a inset) at which the heat flux increased by about 10% at the same heater temperature. In flight and in both heating modes on Earth, the heat flux q h of a pinned bubble was found to rise linearly to 1.2 MW/m2 with increasing heater temperature T h to about 280 °C as (Fig. 4a, SI1)

$${{q}}_{\mathrm{h}}\left( {{\mathrm{kW/m}}^2} \right) = \left( {4.63 \pm 0.15} \right)\left( {{T}_{\mathrm{h}} - 19.28^\circ {\mathrm{C}}} \right)$$ (1)

with the coefficient of determination r2 = 0.970. Deviations between values given by this equation and measurements are normally distributed random quantities at the 95% confidence level (SI1). The remarkable independence of q h and T h from a gradually rising water temperature (Fig. 4(b) was caused by self-adjustment of the bubble size. As Fig. 4(c, d) show, data points in Fig. 3 on the bubble height to width ratio h/w and the fraction of water vapor in the bubble ΔV/V being plotted against T s fell within a relatively narrow band for all heating regimes up to T s ~ 80°C. While the bubble size increased with T s , the fraction of water vapor in the bubble tended to decrease. Fig. 4(e) illustrates the dependence of the bubble volume and cap surface area normalized by bubble height to width ratio 2 h/w ratio; the bubble base diameter was about 2 mm in flight and on Earth. Data points for flight experiments fell close to the curve for a spherical cap and data for all experiments on Earth grouped together below this curve. A bubble residing on the heater eventually divided into two parts by forming a large bubble that departed from the heater and a small bubble pinned to the heater. The remaining bubble grew to about the same size and then divided by forming another departing bubble. This process repeated itself several dozens of times, each time faster and faster, and finally produced a vapor plume whose size was increasing with water temperature (Fig. 2(b) C, images at 360 s and 420 s, SI3, video2). The lifetime of the first bubble formed on the heater after applying DC voltage was much longer for heating cycles than for continuous heating due to a slowly rising water temperature (Fig. 4(f). For both heating modes, the departure of this bubble occurred in the range of liquid bulk temperatures T s ~ 50−80°C and showed the same dependence on the heat flux (Fig. 4f inset, SI1):

$${{T}}_{\mathrm{s}}\left( {\,^\circ {\mathrm{C}}} \right) = \left( {27.2 \pm 0.93} \right){{q}}_{\mathrm{h}}\left( {{\mathrm{MW/m}}^2} \right) + 44.96 \pm 1.13^\circ {\mathrm{C}}$$ (2)

with the coefficient of determination r2 = 0.966. Deviations between values given by this equation and measurements are normally distributed random quantities at the 95% confidence level (SI1).

Flow velocities around a pinned bubble shown in Fig. 5 were computed by tracking individual tiny bubbles formed in flight (seen in Fig. 2a) and beads seeded in the water in Earth experiments. Two toroidal eddies circulating around the bubble in the opposite directions were formed in flight (Fig. 5a). They pushed the hot water away from the bubble interface into the bulk and the cooler water from the bulk toward the bubble base with velocity ~ 1–3 mm/s. Similar eddies and a narrow vertical plume, rising from the bubble top with the velocity nearly twice greater than in the vortex flows, appeared under heating on Earth (Fig. 5b–e). However, the plume contribution to the heat flux was remarkably insignificant (Fig. 4(a). The vortex flows intensity slightly increased with increasing the applied DC voltage and decreased as the heating was turned off. Application of HV pulses made the vortex flows more stable. In flight and on Earth, the top of a pinned bubble was observed to oscillate (SI3, video2) at frequencies v b ~ 2−4Hz with amplitude A b that increased with water temperature from 10–30 µm at T s ~ 25 °C to 100 µm at T s ~ 80°C and was not affected by HV pulses. Velocities of bubble oscillations ~v b A b = (20−120)μm/s were much smaller than vortex flow velocities (Fig. 5).