Millimeter-scale liquid metal droplet thermal switch

Recent advances in electronic devices have resulted in increased power density (power-to-volume ratio) and specific power (power-to-weight ratio) of both stationary and mobile systems.¹ The trend of replacing traditionally mechanical systems with smaller electrical systems has created a demand for lighter and more compact electronic devices.^1,2 Yet, the ability to control the flow of heat from hot spots is a key constraint for the design and operation of electrical systems, particularly at the millimeter scale.² For power electronics, heat generation can be temporally and spatially irregular, leading to temperature spikes and gradients that can negatively affect system performance and reliability. While passive systems that use thermal buffers based on phase change materials can partially mitigate these issues,³ technologies that enable active thermal switching would enable additional freedom in the design and operation of electro-thermal systems.^4–6 A thermal switch can be defined using electronic analogs,^7,8 as a thermal circuit element which controls the effective thermal conductivity between hot and cold reservoirs, and is hence capable of turning heat transfer “ON” or “OFF”. A thermal switch can realize active thermal management of high power electronics for temperature equalization, a key design challenge for power sharing among parallel-connected devices. Thermal switches can also enable the temperature reduction of temperature sensitive devices located in close proximity to heat sources.⁹ Furthermore, a versatile and robust thermal switch would enable additional thermal circuit elements such as thermal diodes and thermal rectifiers.⁵ A key measure of the thermal switch performance is the switching ratio, defined as the ratio of effective thermal resistance of the ON to the OFF state. In previous work,¹⁰ a hydrogen gas gap-based thermal switch operating at low temperature (<170 K) achieved a thermal resistance ratio of >700. More recently, mercury and carbon nanotube (CNT) based thermal switches have been reported with thermal resistance ratios of 224 and 27.8, respectively, at room temperature.¹¹ 

This paper describes a novel millimeter-scale thermal switch based on Galinstan liquid metal. Galinstan, due to its low melting temperature (−19 °C), relatively high thermal conductivity, and low toxicity, is a promising microchannel coolant.¹² In contrast to previous research focusing on actuating the thermal reservoirs,¹³ the present approach actuates the liquid metal droplet to connect or disconnect the reservoirs. The low friction coefficient allows the droplet to be easily actuated,^14,15 and we demonstrate hydraulic pressure, electrostatic fields, or gravitational potential as potential actuation mechanisms. Detailed modeling and experimental measurements show the thermal switching ratios of >15 for “wet” liquid-filled channels and >70 for “dry” vapor-filled channels.

Figure 1 shows the liquid metal thermal switch concept. When the metal droplet bridges the two thermal conductors [Fig. 1(a)], the switch is in the ON state, resulting in heat flow from the heat source (red block) to the heat sink (blue block). When the metal droplet moves away from the bridge location [Fig. 1(b)], heat transfer is reduced due to the filling of the bridge by a liquid or vapor fluid (k_electrolyte = 0.03–0.6 W/mK), resulting in the OFF state. The Galinstan liquid metal and liquid/vapor electrolyte were chosen due to the large difference between their thermal conductivities.¹⁶ A scaling analysis of the thermal resistances reveals R_ON ∼ d/(k_Galinstan·A) and R_OFF ∼ d/(k_electrolyte·A), resulting in a theoretical switching ratio of R_OFF/R_ON ≈ 27 for liquid and ≈550 for vapor. Figure 1(c) shows the device designed to measure this switching ratio. The device incorporates a silicone (poly dimethyl siloxane) insulator material (k_silicone ≈ 0.15 W/mK) and two Aluminum Nitride (Shapal Hi-M) solid block conductors (k_shapal = 92 W/mK). The conductor material (Shapal) was chosen mainly due to electrochemical compatibility between the electrolyte, liquid metal, and conductor block material (see supplementary material, Sec. I). Because the thermal conductivity of Shapal is much larger than that of the silicone insulator, heat flow can be modeled as one-dimensional [Fig. 1(d)] with input heat flow rate, Q_IN, and output heat flow rate, Q_OUT. The heat flows through the hot side block conductor, through the channel gap occupied with the metal droplet or the electrolyte, through the cold side block conductor, and finally out to the heat sink. The 1D model is particularly helpful for analyzing the interfacial thermal resistance (R_INT) and effects of natural convection on the thermal resistance of the metal droplet (R_DROPLET) and the electrolyte (R_ELECTROLYTE), in order to determine the total ON state (R_ON = 2R_INT + R_DROPLET) and OFF state thermal resistances (R_OFF = 2R_INT + R_ELECTROLYTE) and switching ratio.

Fabrication of the thermal switch device [Fig. 1(c)] began with a 10:1 mixture of Sylgard 184 silicone elastomer base and Sylgard 184 silicone elastomer curing agent that was poured into molds for the conductors and the channel. After 6 h of curing at 100 °C in air, the cured silicone pieces were bonded together with a silicone gel. After a period of 24 h for gel solidification, the electrolyte and Galinstan were injected into the channel sequentially. To create dry channels, the electrolyte was extracted after injection, leaving vapor residue in the channel. The NaOH solution was selected in order to reduce the Galinstan oxide layer and thus reduce the droplet friction due to its high surface energy and large contact angle (see supplementary material, Sec. II for additional fabrication details).^16,17

To evaluate the thermal performance of the thermal switch, three thermistors (LSMC700A010KD002, Selco Products) with an accuracy of ±0.1 °C were inserted into 600 ± 100 μm diameter micro-machined holes on each block conductor together with a thermal compound (silver paste, Arctic Silver 5) reducing contact resistances. These thermistors were connected in series to a current sourcemeter and a DAQ acquiring voltage signals across each thermistor, which were converted to resistances and temperatures according to the Steinhart-Hart equation.¹⁸ The heated block was attached by a thermally conductive tape and rubber bands to a copper reservoir electrically heated via two embedded cartridge heaters. The cooled block was attached similar to a liquid cooled aluminum reservoir using a 1:1 mixture of Ethylene Glycol and DI water as the cooling fluid. The entire thermal switch device was thermally insulated by a thick layer (≈5 cm) of fiberglass material (k_fiberglass = 0.04 W/mK). Around 3 h after the power supply and the chiller were turned on, the system reached dynamic equilibrium and the thermistor voltage signals were recorded and converted to temperatures automatically using LabVIEW.

Figure 2 shows the measured temperatures from one device using the temperature distribution assumed from the 1D model. The device in Fig. 2 had a 1.96 mm thick channel, filled with 1 M/L NaOH solution. The temperature data points for each block in the ON/OFF states were Pearson correlated with coefficients of −1.000, −0.919, −0.994, and −0.995, respectively, verifying the 1D assumption. In the ON state, the average heat flow rate [Q = (Q_IN + Q_OUT)/2] is ≈1.83 ± 0.04 W, with a temperature difference (ΔT = T₁ − T₂) across the channel as identified by the dashed lines corresponding to 6.01 ± 0.12 °C. In the OFF state, the average heat flow rate Q is ≈1.45 ± 0.04 W, with a larger temperature difference ΔT of 42.09 ± 0.11 °C. Figure 2(b) shows the data presented in Fig. 2(a) with a higher resolution for the temperature profile across the droplet or electrolyte solution in the channel, according to the thermal resistance model (inset). The slopes of the ON and OFF state temperature profiles indicate different effective thermal resistances. The experiment was repeatable for relatively long timescales (∼1 week) for different heat flow rates and different temperature differences (see supplementary material, Sec. III for a detailed summary of all measured temperatures and heat transfer rates). To investigate the effects of channel geometries and fluid medium inside the channel on the performance of thermal switches, six experiments were conducted on devices having 0.90 mm, 1.96 mm, and 2.80 mm thick channels filled with either an aqueous solution of NaOH (wet) or NaOH vapor (dry). A summary of the experimental results is shown in Table I.

Table I shows high contrast between the effective thermal resistances of the ON/OFF states for both wet and dry channels having different channel geometries. Figure 3 shows the heat flow rate through the switch as a function of the temperature difference across the switch (Fig. 1, ΔT = T₁ − T₂) for different channel geometries in both ON (blue lines) and OFF (red lines) states. The inverse slope of each line fit to the data is defined as the effective thermal resistance (R = ΔT/Q). For wet channels [Fig. 3(a)], the thermal resistance increased with the increasing channel thickness in both ON and OFF states. For dry channels [Fig. 3(b)], the same trend appeared in the ON state; however, the thickest dry channel in the OFF state [Fig. 3(b), line C] had the lowest effective thermal resistance. Natural convection resulting from buoyancy effects inside the channel may account for the channel-size dependence of the OFF-state thermal resistance. Indeed, the Rayleigh number, an indicator of buoyancy-driven fluid motion in the channel, is 4217 for Wet Channel A with ΔT = 50 °C and 54 952 for Wet Channel C with ΔT = 50 °C. The supplementary material provides additional analyses of heat transfer in the channel, including interfacial thermal resistance between the droplet and the channel wall, and natural convection in the channel. Analysis of the interfacial thermal resistance at the liquid metal/Shapal interface revealed an estimated equivalent NaOH layer thickness of ≈11 μm.

In order to quantify the thermal switch performance and to gain an understanding of the underlying physics governing thermal switch design and optimization, we analyzed the switching ratio

where R_OFF and R_ON are the thermal switch effective thermal resistances and ΔT and Q are the temperature difference and the heat flow rate. Figure 4 shows the measured switching ratios as a function of channel thickness for all channels tested. Error bars were calculated using the propagation of error technique based on measurement errors and slope deviations from Figs. 2 and 3 (see supplementary material, Sec. V). Thermal switches with dry channels had much higher switching ratios than those with wet channels due to the lower thermal conductivity of NaOH vapor (0.03 W/mK) when compared to 1 M/L NaOH aqueous solution (0.6 W/mK). For both dry and wet channels, the switching ratio decreased with the increasing channel thickness, owing to the contributions of interfacial thermal resistance and natural convection inside the channels. For wet channels, the maximum measured switching ratio was 15.6 ± 1.4 at a corresponding heat flux of ≈9 ± 0.1 W/cm² in the ON state when the heat source was ≈50 ± 0.1 °C. For dry channels, the maximum measured switching ratio was 71.3 ± 7.6 at a corresponding heat flux of 10 ± 0.1 W/cm² in the ON state when the heat source was 55 ± 0.1 °C. The results demonstrate the capability of liquid metal droplet thermal switches to actively manipulate heat transfer with relatively high heat flow rates at low temperatures (<100 °C).

Liquid metal droplet actuation is an important aspect of integrating our thermal switch with millimeter scale electronics. In the present study, actuation of the 8 mm long Galinstan slug in a 5 mm wide and 2 mm thick closed silicone channel filled with 1 M/L NaOH aqueous solution was attained with 1 V/cm electric fields supplied with tungsten electrodes inserted at the axial channel ends. Using electrostatic actuation, switching speeds of ∼5 s were achieved, with negligible generation of bubbles at the tungsten electrodes. To avoid bubble formation at higher electric fields, hydraulic actuation of the droplet slug was also implemented (see supplementary material, Sec. VI). Furthermore, dry channel thermal switches were actuatable with gravity simply by tilting the channel at a small angle (≈5°). The relative ease and versatility of actuation stem from the presence of the thin (≈10 μm) lubricating wetting layer of NaOH solution between the metal slug and the channel wall, which acts to minimize friction. Although demonstrated here with electrical, hydraulic, and gravitational actuation forces, future work should further investigate the underlying physics governing liquid metal slug motion in an attempt to identify the limiting actuation frequencies and required power. The timescale to move the droplet is comparable to the other thermal time constants in the system. For the three channels tested, the thermal time constants of the liquid metal droplet, liquid-filled channel, and vapor-filled channel were 0.13–0.88 s, 4.5–15.6 s, and 6.0–14.0 ms, respectively. The supplementary material contains additional analyses of the system time constants.

Compared with previous thermal switch devices,^10,11 our work differs by utilizing the contact material (liquid metal droplet) as the actuation object to bridge or break the heat flow path between hot and cold reservoirs flexibly. While the measured switching ratios are large, there is still room for improvement via the tailoring of the interfacial thermal resistances in the ON state and suppressing natural convection in the OFF state. To further increase the performance, careful selection of working materials such as higher conductivity liquid metals and concurrent lower thermal conductivity lubricating fluids must be undertaken with a key focus on compatibility due to robustness considerations for thermal switches in real life application. Our devices survived ≈100 h in steady experimental testing conditions. Long term device failure occurred due to evaporation of the NaOH electrolyte. In the future, packaging of the thermal switch should be explored to prevent evaporation or leakage. Furthermore, we suspect that the chemical stability of the liquid metal droplet in the channel may also affect long term operation.

In summary, this work demonstrates a novel millimeter scale thermal switch based on the motion of a liquid metal droplet in a fluid filled channel. Thermal resistances and switching ratios for various fabricated thermal switch devices having both wet and dry solutions and differing thicknesses were measured and analyzed. Experimental results show that switching ratios as high as 15.6 for wet channels and 71.3 for dry channels are possible, promising for applications in thermal management systems. As an important component in thermal circuit system design, the thermal switch developed here may unlock new approaches for thermal management and circuit topologies. When integrated with power electronics, a cooling system, and perhaps a thermal buffer element such as a phase change material, the thermal switch could allow active management of heat flows and isothermalization of electronics, leading to improvements in performance or system reliability. The thermal switch also has the potential for use in, and enhancement of, energy storage and energy conversion systems, such as thermal batteries or solar thermal systems.¹⁹ This work provides a framework for the development of millimeter-scale thermal switches capable of spatial and temporal thermal dissipation control.

See supplementary material for thermal characterization, modeling, and analysis of the device experiments as well as detailed heat transfer calculations.

This work was supported by the National Science Foundation Engineering Research Center for Power Optimization of Electro Thermal Systems (POETS) with cooperative Agreement No. EEC-1449548. N.M. gratefully acknowledges funding support from the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology.