Capillary enhanced phase change in a microfabricated self-oscillating fluidic heat engine (SOFHE)

This paper reports the design, fabrication, and characterization of a miniaturized version of a self-oscillating fluidic heat engine (SOFHE) for thermal energy harvesting. This new design includes capillary corners of a square cross-section, as well as an etched capillary path on the bottom wall that improves the performance in terms of stability and mechanical power owing to the enhanced phase change. The engine consists of a vapor bubble trapped in a microchannel by an oscillating liquid plug (acting as a piston) set in motion by periodic evaporation and condensation in the vapor bubble. The underlying physics of the oscillations is similar to those of a single-branch pulsating heat pipe. The channel is microfabricated by anodically bonding a grooved glass wafer (top and sidewalls) to a silicon wafer (bottom wall). To further increase the phase change, two more channels are fabricated with an etched capillary path on the bottom wall at two different widths of 25 and 50 µm and a depth of 100 µm. This is the first miniaturized SOFHE that generates a reliable amplitude in the millimeter range. By measuring the change in the volume of the vapor bubble and the frequency, we calculated the change in pressure using the momentum balance on the liquid plug, and then calculated the work, mechanical power, and power density. We observed that the addition of the etched capillary path at a width of 50 µm increased the amplitude (from 1.6 to 4 mm) leading to a fivefold increase in the generated power (from 8 to 40 µW). This study opens a new path towards designing different wicking structures to maximize the amplitude and power density of the SOFHE, making it a promising thermal energy harvester to power wireless sensors.

This paper reports the design, fabrication, and characterization of a miniaturized version of a self-oscillating fluidic heat engine (SOFHE) for thermal energy harvesting. This new design includes capillary corners of a square cross-section, as well as an etched capillary path on the bottom wall that improves the performance in terms of stability and mechanical power owing to the enhanced phase change. The engine consists of a vapor bubble trapped in a microchannel by an oscillating liquid plug (acting as a piston) set in motion by periodic evaporation and condensation in the vapor bubble. The underlying physics of the oscillations is similar to those of a single-branch pulsating heat pipe. The channel is microfabricated by anodically bonding a grooved glass wafer (top and sidewalls) to a silicon wafer (bottom wall). To further increase the phase change, two more channels are fabricated with an etched capillary path on the bottom wall at two different widths of 25 and 50 µm and a depth of 100 µm. This is the first miniaturized SOFHE that generates a reliable amplitude in the millimeter range. By measuring the change in the volume of the vapor bubble and the frequency, we calculated the change in pressure using the momentum balance on the liquid plug, and then calculated the work, mechanical power, and power density. We observed that the addition of the etched capillary path at a width of 50 µm increased the amplitude (from 1.6 to 4 mm) leading to a fivefold increase in the generated power (from 8 to 40 µW). This study opens a new path towards designing different wicking structures to maximize the amplitude and power density of the SOFHE, making it a promising thermal energy harvester to power wireless sensors.

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Keywords: micro heat engine, thermal harvesting, self-oscillation, phase change, capillary, single-branch pulsating heat pipe (Some figures may appear in colour only in the online journal) * Author to whom any correspondence should be addressed.
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Introduction
The move of our society towards an increasingly smart world has led to the emergence of the 'Internet of Things (IoT),' which consists of objects with embedded sensors that capture data and exchange it with other devices over the internet [1]. For example, smart cities take advantage of IoT for sustainable development practices, including transportation networks and waste management. To do so, a massive network of wireless sensors is implemented; thus, there is a need for durable and autonomous means to power them [2]. To address this increasing demand, energy harvesting, which generates electricity from ambient energy sources, has come into perspective. Thermal energy harvesters (TEH) are promising candidates for applications where waste heat is available. TEHs can convert thermal energy into electricity directly using thermoelectric generators (TEGs) or indirectly (thermal-tomechanical-to-electrical) using micro heat engines coupled with transducers. The performance of TEGs, which is based on the Seebeck effect [3], is limited by the figure-of-merit of the materials. The advantage of the latter is their flexibility in terms of design and room for optimization. The selfoscillating fluidic heat engine (SOFHE) is a novel micro heat engine first introduced and studied by the same research group [4][5][6][7][8][9][10][11]. The SOFHE was proposed to power wireless sensors when coupled with an electromechanical transducer [4] as a TEH. As shown in figure 1, the SOFHE harvests waste heat and converts it into mechanical energy, which, in turn, is converted into electrical energy by a transducer. It has a mechanical power density in the range of fractions of milliwatts cm −3 [5], which can be used for many wireless sensors with an average power requirement of microwatts. The SOFHE can provide the benefit of being maintenance-free, which is particularly valuable when accessibility is limited. As the SOFHE does not have moving parts that can wear out or consume materials like batteries, it is expected to continue functioning if the device is perfectly sealed to maintain hermiticity and retain the fluid inside. SOFHE's mechanical power could also be directly used for pumping when combined with appropriate valves [12], for cooling electronics, lab-on-chip, or other microfluidic applications.
The working principle of the SOFHE is similar to that of a single-branch pulsating heat pipe [13]. The SOFHE is a channel filled with working fluid, with one heated closed end (evaporator) and one cooled open end (condenser). When the closed end is heated, a vapor bubble forms and expands until it reaches an equilibrium point. Once the vapor is established, it will remain trapped by an oscillating liquid plug that acts as a piston (figure 2). The piston provides mechanical work through a unique oval-shaped phase change thermodynamic cycle [5]. There are other examples of micro heat engines, including micro gas turbines [14,15] and micro steam turbines [16][17][18], which demonstrate traditional Brayton and Rankine thermodynamic cycles, respectively. They offer high power (watt-scale), but have the complexity of high-speed rotating parts. The simple design of an SOFHE with no moving parts gives it an advantage over microturbines for applications with lower power requirements. Compared to other phase-change micro heat engines, including the so-called P3 engine (peak power at 0.8 µW) [19] and bi-stable membrane (mechanical power at 1.3 µW) [20,21], SOFHE offers a mechanical power that is 100X greater. It should be mentioned that unlike some other micro heat engines, the mechanical power density of the SOFHE has not yet been optimized, and there is room for further improvement. For example, in a mesoscale SOFHE, it was shown that both the mechanical power and power density increased as the length of the liquid plug decreased [5]. This is a promising outcome for the miniaturization of the SOFHE. Besides, it was observed that varying the phase change rate (evaporation-condensation) significantly boosts the power density [5].
The self-sustained oscillatory flow in the SOFHE is modeled as a damped spring-mass system, where the vapor bubble acts as the restoring force, the friction of the liquid plugs induces damping, and its mass provides inertia [22][23][24][25]. The force that sustains the oscillations in this system is the pressure generated by the change in the mass of the vapor due to cyclic evaporation and condensation. To perturb the equilibrium of this spring-mass system for oscillation start-up, the force generated by the phase change must be greater than the counteracting viscous force [8]. During start-up, the amplitude gradually increases until it saturates, owing to the nonlinearities that exist in the system. These nonlinearities might originate from different sources, such as phase change limitations or geometrical restrictions, which are discussed in detail by Tessier-Poirier et al [9]. It has been shown that the SOFHE power increases with the amplitude of the oscillation when the evaporation-condensation rate is enhanced (for a constant frequency) [5]. The common mechanism for the phase change (evaporation-condensation) in this thermally induced self-oscillatory flow is a thin film that is left behind the moving meniscus [26]. This makes the motion dependent on oscillation amplitude. To overcome this problem, liquid must be introduced into the evaporator to form a thin film that feeds the phase change and facilitates the startup. Adding wicking structures such as capillary grooves [27,28], corners [25,26], and wicking fibers [10,11] are promising solutions. In a mesoscale version of the SOFHE, which is a tube with a millimeter-scale inner diameter, the mechanical power of the SOFHE showed a significant increase (thirtyfold) by boosting the phase-change rate in the presence of a wicking fiber [5]. The wicking fiber forms capillary corners with the tube, pumps liquid from the liquid plug towards the evaporator, and intensifies the net evaporation rate. In the first microfabricated demonstration of SOFHE [7], which was fabricated by bonding two glass wafers that were wet-etched to form a microchannel, very small-amplitude vibrations (10 µm) were observed. To address the issue of a small amplitude in micro SOFHE and to establish a reliable start-up mechanism, we aim to increase the net evaporation rate. This was first performed by forming a square cross-section microchannel with sharp corners to imitate the role of the fiber observed in the mesoscale SOFHE. The initial results of this approach were presented at the PowerMEMS 2022 conference [6]. The current study extends this work by adding etched capillary paths to enhance and engineer wicking behavior. To evaluate the effect of the phase-change enhancement with these features, the amplitude and frequency were experimentally measured and compared for three different micro SOFHEs, including one with no etched capillary path and two with etched capillary path of 25 and 50 µm in width. To further understand the impact of phase-change enhancement in micro SOFHE, a discussion on the forces, thermodynamic work per cycle, power, and power density is also presented.

Device
The engine is a microfabricated square channel that benefits from its corners acting as a capillary path. The channel was formed by anodically bonded silicon (Si, thickness 500 µm) to a glass wafer (borofloate33, thickness 600 µm) to provide visual access inside the device and better thermal insulation. Before bonding, the channel was grooved on the glass wafer with a hydraulic diameter (D h ) of 375 µm using a dicing machine (Disco DAD-320). In some configurations, an additional capillary path was added by etching a trench in Si along the channel length. Figure 3 shows the cross section of the fabricated device, with a dashed trench representing the etched capillary path on the bottom wall. To create the trench, a twolevel masking process is followed, as shown in figure 4. The first level involves creating alignment marks on both Si (lithography and RIE) and glass wafers (lithography and hydrofluoric acid (HF) wet etching). Second-level masking involves creating a capillary path on a Si wafer by deep reactive ion etching (DRIE). The wafers were cleaned using solvent and Piranha. Before bonding, diluted HF was used to remove native oxide on the Si wafer. For the capillary trench, we considered two different widths (W) of 25 µm and 50 µm, with a depth (H) of 100 µm and a length of 20 mm. The total length of the device is L T = 8.5 cm, the thickness is H T = 1.1 mm, and the width is W T = 3 mm. The volume of micro SOFHE is therefore V SOFHE = L T * A = 0.26 cm 3 , where A = H T * W T . The heated end of the device was closed with glue, whereas the cooled end is open. Figure 5(a) shows a disassembled view of the experimental test rig designed to characterize the micro SOFHE. The main components are two aluminum blocks: one is heated by a cartridge heater, and the other is cooled by cold water from a thermostatic bath. The blocks were mounted on an insulating peek sheet with a slot to adjust the distance between   them. This distance, the so-called adiabatic zone, allows for a thermal gradient over the device, which was set to 2 mm. The device supports were designed to adjust the length of the device in contact with the hot and cold blocks. An Lshaped clamp was used to clamp the device support onto the blocks. A conductive thermal paste (TG-7) was used to reduce the contact thermal resistance between the device and device support. Thermocouples were integrated into the device supports to control the temperature of the hot (T H ) and cold (T C ) zones.

Test procedure
To start the test, the device was treated with oxygen plasma to clean and ensure hydrophilicity of the inner channel surfaces (at 100 W for 1 min). The device was filled with deionized water and mounted on blocks using a thermal paste. Figure 5(b) shows an image of the setup with the device mounted on the top. Regarding the working fluid, it can be changed based on the available thermal gradient. The lengths of the device in contact with the hot and cold blocks form the evaporator and condenser sections, respectively. Herein, the length is set at 3.5 and 4 cm for the evaporator and condenser, respectively. These specific lengths are chosen to simplify the handling and testing of the device. However, they will require optimization in future steps. The condenser temperature was set to 15 • C, and the heating process was initiated. A vapor bubble (occupying the cross section) forms in the evaporator and grows lengthwise until it reaches equilibrium. The equilibrium point was in the adiabatic zone. We then continued to increase the evaporator temperature until oscillations started at 120 • C. A high-speed camera mounted on a stereoscope recorded the position of the oscillating meniscus as a function of time in order to measure the amplitude and frequency of the oscillations. An image-processing MATLAB code was used to extract the positions from the recorded video. The uncertainty of the amplitude measurement is ±4%, which comes from the calibration to convert pixels into micrometers.
The device without an etched capillary path was characterized at four different evaporator temperatures (T H ). The tests were performed for two more devices with one capillary path etched on the bottom wall at widths of 25 and 50 µm.

Results
The new design of micro SOFHE takes advantage of the sharp capillary corners of a square cross section to pump liquid into the evaporator. Figure 6(a) (a frame from a recorded video during oscillations) shows the wicked liquid in the corners that ends at a triple point (interface of solid-liquid-vapor). It also shows a thin film behind the oscillating meniscus, which is distinguished by a moving shadow on the top wall. The recorded vidoe is accessible as supplementry materials. To better visualize the different parts, a 3D schematic of the oscillating meniscus is presented in figure 6(b). The line of triple points (formed by the thin film behind the meniscus) and the liquid wicked along the corner capillaries are the main contributors to the phase change because of their low thermal resistance [29]. Figure 7 shows the amplitude of the oscillations at startup temperature (120 • C). Positive and negative values indicate moving towards the condenser and evaporator, respectively. The measured peak-to-peak amplitude is 1 mm and the frequency of the oscillations is 36 Hz. The oscillations are sustained for hours with a constant amplitude, demonstrating highly reliable and repeatable behavior. This design also guarantees the start-up of oscillations without the need to insert an additional wicking structure, as is required for the mesoscale SOFHE [4,5,10,11]. Therefore, the start-up and sustainability of the micro SOFHE are achieved by increasing the rate of net evaporation-condensation through the corner capillary.
As discussed in our previous study [5] on characterizing mesoscale SOFHE, increasing the evaporator temperature (T H ) significantly increases the phase-change rate, which in turn increases the oscillation amplitude. Figure 8 shows the evolution of the meniscus position as a function of time as the evaporator temperature increased. The expected trend is observed in micro SOFHE, where the amplitude of the oscillations increases from 1 mm to 1.6 mm by increasing T H from 120 • C to 150 • C.
Observing the positive effect of the capillary pumping of the liquid through sharp corners drove the new design of the micro SOFHE, in which a capillary path is etched on the bottom wall. Thus, more liquid can be pumped towards the evaporator forming lines of triple point to intensify the net evaporation rate, leading to an increase in the amplitude. As shown in figure 9, the peak-to-peak amplitude increases from 1.6 mm to 2.6 mm by adding a capillary path with a width of 25 µm and even up to 4 mm for a trench width of 50 µm. The results showed better performance with an increase in the width of the capillary path. This can be explained by analyzing the capillary flow dynamics inside the capillary path. It can be considered a  closed channel (with the free surface acting as the fourth wall) if the aspect ratio (λ = H/W) of the channel is sufficiently large (λ > 1) [30], which is valid in our study (λ = 2 and 4). The length of liquid penetration along the capillary (L) is determined by the surface tension and friction forces, leading to Washburn's equation [31], where σ is the surface tension, θ is the contact angle, µ is the viscosity, r is the capillary radius, and t is the time. As the width of the capillary path increases, the length of the liquid penetration increases, providing a longer triple-point zone which is favourable for evaporation. Therefore, the net evaporation rate increases resulting in an increase in the oscillation amplitude.

Discussion
In this section, the micro SOFHE is characterized in terms of the mechanical power density to better understand the effect of this increase in amplitude on the SOFHE power. First, it is necessary to calculate the applied pressure on the liquid plug owing to the expansion, compression, and the phase change.
To do so, momentum balance is performed (equation (2)) on the control volume defined over the liquid plug, as shown in figure 10, where m l is the mass of the liquid plug (assumed to be constant), F m is the inertial force, A is the channel cross-sectional area, P ext is the external pressure (open end at atmospheric pressure), F P is the pressure force, F f is the friction force, and x is the acceleration of the oscillating meniscus. The friction force experienced by the liquid plug along the wall depends on the velocity profile, which is defined based on the kinematic Reynolds number (Re ω ≡ ωR 2 /υ). The velocity profile in a pulsatile flow can be considered a quasi-static Poiseuille profile for Re ω < 10 [32]. For the SOFHE filled with water with a hydraulic diameter of 375 µm and frequency of 36 Hz, Re ω = 8. Therefore, the friction force is well described by the Poiseuille flow [33]: where L l is the length of the liquid plug andẋ is the velocity of the oscillating meniscus. The forces applied to the liquid plug, including inertia, friction, and pressure, as a function of time are plotted in figure 11. Forces are intermediate variables used to calculate the work. Calculating the pressure and measuring the change in the volume of the vapor bubble enables us to plot the thermodynamic cycle (P-V) of the SOFHE, as shown in figure 12, at four different evaporator temperatures for the device with no etched capillary path. Integrating the area of the P-V cycles (equation (4)) yields the work performed in each cycle. As shown, increasing the oscillation amplitude created a larger P-V cycle that is capable of generating more work. A portion of this work is dissipated through the friction of the liquid plug. In the mesoscale version of the SOFHE, it was shown that at an optimum load, half of the cycle work is consumed to overcome friction [5]. This means that the net available work per  cycle that the SOFHE can provide to a transducer is half the cycle work (W net = W cycle /2), Knowing the available network per cycle and frequency of the SOFHE, the power (P = W net * f ) and power density (P d = P/V SOFHE ) can be calculated. Figure 13 shows the power as a function of the evaporator temperature at both the micro (solid line) and meso (dashed line) [5] scales. The power values are normalized by the maximum power at the highest temperature to better compare trends. The results show that the  increasing trend of power as a function of the evaporator temperature at the microscale is similar to that observed for the mesoscale SOFHE. This suggests that the miniaturization of the SOFHE does not affect the dependency of the power on the evaporator temperature. The power and power densities of the three devices are listed in table 1 along with the values for mesoscale SOFHE [5]. A comparison of the power reveals a five-fold increase (from 8 µW to 40 µW) by adding a capillary path with a width of 50 µm. The significant increase in power by intensifying the phase change through capillary pumping is a key outcome of this study, which opens a new path towards designing different wicking structures and optimizing them to maximize the amplitude of the oscillation, which enhances the power of the SOFHE, as well as the heat transfer of pulsating heat pipes.

Conclusion
In this study, the performance of a microfabricated SOFHE is enhanced by boosting the phase change through corner capillaries as well as etched capillary paths. The engine was microfabricated by anodic bonding of a Si wafer and grooved glass wafer to form a square cross-sectional microchannel with a hydraulic diameter of 375 µm. The sharp corners in the square channel act as capillary paths, pumping liquid from the liquid plug towards the evaporator. This intensifies the phasechange rate, which in turn increases the oscillation amplitude (a key parameter for increasing the SOFHE output power). This design yields a start-up and sustainability of oscillations with an amplitude in the range of millimeters and a frequency of 37 Hz. To further increase the phase change, capillary paths were etched on the bottom Si wall of the device using DRIE. This modification led to an increase in the amplitude, which in turn increased the mechanical power by five-fold. For future work, different wicking structures can be added to SOFHE to engineer the phase change. Thus, we can enhance the performance of the SOFHE to become a promising power supply for wireless sensors when coupled with an electromechanical transducer. This strategy also promises to enhance the performance of pulsating heat pipes, which are being increasingly considered for the thermal management of electronics.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).