Heat-driven micro jet pumping apparatus

Abstract

A pumping apparatus may have a self-oscillating fluidic heat engine having a tube with a closed end, the tube configured to enclose a liquid plug trapping a vapor bubble in the closed end, the tube configured to be exposed to a thermal gradient for the liquid pump to effect pumping oscillations; and a pumping device having a nozzle at a fluid connection with an open end of the tube, a suction chamber fluidly connected to the tube via the nozzle, the suction chamber having a pumping inlet, and a diffuser portion fluidly connected to the suction chamber and having an outlet; wherein the pumping oscillations of the self-oscillating fluidic heat engine induce a pressure variation in the suction chamber, and a pressure head in the diffuser portion.

Description

HEAT-DRIVEN MICRO JET PUMPING APPARATUSCROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims the benefit of United States Patent Application No. 63 / 703,619, filed on October 4, 2025, the entire contents of which are incorporated herein by reference.TECHNICAL FIELD

[0002] The present disclosure relates to a device for harvesting thermal energy dissipated by certain devices, for example, a hot surface of an integrated circuit chip or any other electronic component, equipment, etc. The present disclosure also relates to the conversion of this thermal energy into motive force in passive devices, such as passive cooling devices.BACKGROUND

[0003] Some devices have been provided to harvest thermal energy released by a hot source and to convert it into electricity. As an example, US 2016 / 0241168 A1 describes an engine for thermal energy harvesting to generate electricity. It is composed of a self-oscillating fluidic heat engine (SOFHE) coupled with a piezoelectric transducer. The SOFHE can be described as having a vapor bubble trapped by an oscillating liquid plug acting as a piston that forms inside a capillary channel. This system needs a certain thermal gradient to start oscillations. It can be driven by waste heat.

[0004] Moving towards high power microelectronics for artificial intelligence (Al) and high computing, the traditional thermal management with air may not be sufficient and / or may be an energy expenditure. Liquid cooling becomes a promising approach to address this issue, but necessitates using an electrically-powered pump to circulate the liquid. In particular, due to the small size of electronic chips, compact and efficient micro pumps may be needed. A number of micro pumps are micro version of traditional pumps that consist of a chamber with varying volume connected to mechanical valves. Using valves may cause complications (delicatecomponents to fabricate and install) and reliability concerns (leakages with use). Besides, actuators outputting relatively large forces may be required to activate the micro valves. Therefore, valveless approaches for micro pumping expect to address these challenges. For valveless micro pumps, most of the approaches take the advantage of the fluid properties and electric-fluid interactions, including electroosmosis, electro-magnetic, and electro-static. This makes these approaches fluid dependent with a relatively small pumping capacity. In addition, to run majority of micro pumps, an external electrical power supply is required. For electronics cooling, it is not efficient to use electrical power for cooling while waste heat is available. Solutions are sought for these drawbacks.SUMMARY

[0005] In one aspect, there is provided a pumping apparatus comprising: a selfoscillating fluidic heat engine having a tube with a closed end, the tube configured to enclose a liquid plug trapping a vapor bubble in the closed end, the tube configured to be exposed to a thermal gradient for the liquid pump to effect pumping oscillations; and a pumping device having a nozzle at a fluid connection with an open end of the tube, a suction chamber fluidly connected to the tube via the nozzle, the suction chamber having a pumping inlet, and a diffuser portion fluidly connected to the suction chamber and having an outlet; wherein the pumping oscillations of the self-oscillating fluidic heat engine induce a pressure variation in the suction chamber, and a pressure head in the diffuser portion.

[0006] Further in accordance with the first aspect, for instance, the pumping device is a monolithic component.

[0007] Still further in accordance with the first aspect, for instance, the pumping device has a 3D printed body.

[0008] Still further in accordance with the first aspect, for instance, the nozzle has a conical geometry.

[0009] Still further in accordance with the first aspect, for instance, the pumping inlet is in plane to which an axis of the nozzle is normal.

[0010] Still further in accordance with the first aspect, for instance, the tube has a generally square cross-section.

[0011] Still further in accordance with the first aspect, for instance, a wicking structure is formed in a bottom surface of the tube.

[0012] Still further in accordance with the first aspect, for instance, the wicking structure is a capillary path.

[0013] In accordance with a second aspect, there is provided a system or a system with an integrate cooling system comprising: at least one of the pumping apparatus as described above; a fluid circulation circuit in fluid communication with the inlet and the outlet of the pumping apparatus; a heating load in heat exchange with the fluid in the fluid circulation circuit, for the fluid to absorb heat from the heating load; and a cooling load in heat exchange with the fluid in the circulation circuit for the absorbing heat from the fluid; wherein the pumping apparatus is exposed to a thermal gradient to induce fluid flow in the fluid circulation circuit.

[0014] Further in accordance with the second aspect, for instance, a plurality of the pumping apparatus are in series relative to the fluid circulation circuit.

[0015] Still further in accordance with the second aspect, for instance, a plurality of the pumping apparatus is in parallel relative to the fluid circulation circuit.

[0016] Still further in accordance with the second aspect, for instance, the thermal gradient includes heat from the heating load provided to the pumping apparatus.

[0017] Still further in accordance with the second aspect, for instance, the cooling system is entirely passive.

[0018] Still further in accordance with the second aspect, for instance, the cooling system is valveless.

[0019] Still further in accordance with the second aspect, for instance, the heating load is an integrated chip.

[0020] Still further in accordance with the second aspect, for instance, the heating load is an electronic device or system.DESCRIPTION OF THE DRAWINGS

[0021] Reference is now made to the accompanying figures in which:

[0022] Fig. 1 is a block diagram of a cooling system harvesting heat to operate, the cooling system including a heat-driven micro jet pumping apparatus in accordance with the present disclosure;

[0023] Fig. 2 is a cross-section view, not to scale, of the heat-driven micro jet pumping apparatus of Fig. 1 ;

[0024] Fig. 3 is an image of the heat-driven micro jet pumping apparatus of Fig. 1 ;

[0025] Fig. 4 is a graph showing characterizing curves for the heat-driven micro jet pumping apparatus of Fig. 1 ;

[0026] Figs. 5A and 5B are block diagrams illustrating an arrangement of multiple ones of the heat-driven micro jet pumping apparatus, in parallel and in series to increase flow and / or pressure of the fluid;

[0027] Fig. 6 is a schematic diagram showing a method for fabricating a tube of a self-oscillating fluidic heat engine of the heat-driven micro jet pumping apparatus of Fig. 1 ; and

[0028] Fig. 7 is a schematic perspective view showing a meniscus between vapour bubble and liquid plug in one possible configuration of the tube of the self-oscillating fluidic heat engine of the heat-driven micro jet pumping apparatus of Fig. 1..DETAILED DESCRIPTION

[0029] Referring to the drawings and more particularly to Fig. 1 , there is illustrated a cooling system harvesting heat to operate. The cooling system includes a heat- driven micro jet pumping apparatus 10 in accordance with the present disclosure. Inaddition to the pumping apparatus 10, the cooling system may further include a fluid circulation circuit 12 in fluid communication with an inlet and the outlet of the pumping apparatus 10. For example, the circuit 12 is a circuit of tubing, pipes, or the like, in which a fluid flows. The fluid may be at least partially in a liquid state. For instance, the fluid is water, glycol or any other coolant. The cooling system may be in heat exchange with a heating load 14. More particularly, the heating load 14 is in heat exchange with the fluid in the fluid circulation circuit 12, for the fluid to absorb heat from the heating load. The heat exchange may be conductive and / or convective. In a variant, the cooling system is operated to cool the heating load 14. The heating load 14 may or may not be part of the cooling system. For example, it may be possible to install other components of the cooling system onto an existing heating load 14. The cooling system may further include a cooling load 16. The cooling load 16 may be in heat exchange with the fluid in the circulation circuit 12 for the absorbing heat from the fluid. The heat exchange may be conductive and / or convective. The cooling load may take various forms, such as a radiator, fins, etc.

[0030] As explained below, the pumping apparatus 10 is exposed to a thermal gradient to induce fluid flow in the fluid circulation circuit 12, such that the fluid may sequentially absorb heat from the heating load 14, and then release heat at the cooling load 16, cycling back to the pumping apparatus 10. As a result, the cooling system may cool the heating load 14. The cooling system 10 may be said to be entirely passive (i.e., self-powered, autonomous, without an electrically powered pump), as it may operate solely using heat present at the heating load, and thus may be fully operational on waste heat, without any other energy input. However, it is contemplated to have some other energy input in the cooling system, for example as part of the cooling load 16 (e.g., a heat sink fan to assist in releasing heat). In a variant, it may thus be the pumping that is entirely passive, notably as the heating load may be reclaimed heat (e.g. electrical resistance) and / or heat harvested from a device that requires cooling.

[0031] Referring to Figs. 2 and 3, the heat-driven micro jet pumping apparatus 10 is shown in greater detail. For simplicity, the heat-driven micro jet pumping apparatus 10 may be referred to as a pumping apparatus 10 herein. The pumping apparatus 10 may include a self-oscillating fluidic heat engine 20, and a pumping device 30 connected to the self-oscillating fluidic heat engine 20. A cooperation between theself-oscillating fluidic heat engine 20 and the pumping device 30 may generate a pumping action to generate fluid flow, for example in the cooling system, or in other uses. Stated differently, the pumping apparatus 10 is not limited to usage in the cooling system.

[0032] The self-oscillating fluidic heat engine 20 may have a tube 21. The tube 21 may have a closed end 21A that defines an end of an evaporator segment of the tube 21 , and an open end 21 B that is part of a cooling (condensing) segment of the tube 21. The tube 21 is configured to enclose a liquid plug trapping a vapor bubble in the closed end 21A. The tube 21 is configured to be exposed to a thermal gradient, for example by way of a heating block 22A and a cooling block 22B for the liquid pump to effect pumping oscillations in Fig. 3. In Fig. 2, the thermal gradient is shown as waves of waste heat for the heating, and ambient for the cooling, indicating that the cooling may be achieved by the ambient conditions in a variant. The heating block 22A may use ambient heat (e.g., such as from the heating load 14 in Fig. 1) to generate the heat required for the pumping. The heat from the heating block 22A may be harvested in any appropriate way, including by conductive contact, by convection and / or by a coolant. The cooling block 22B may be cooled in any appropriate way, including exposure to ambient, convection, etc, heat exchange with the fluid circulation circuit 12.

[0033] The pumping device 30 has a hollow body defining an internal fluid passage. The hollow body may include a nozzle 31 at a fluid connection with the open end 21 B of the tube 21. A suction chamber 32 may be fluidly connected to the tube 21 via the nozzle 31. In a variant, it may be said that the pumping inlet 32A is in plane to which an axis of the nozzle 21 is normal (the axis being horizontal (from left to right) on the sheet of Fig 2) - the plane is thus generally perpendicular to the plane of the sheet of Fig. 2 and is aligned with the vertical (top to bottom). The suction chamber may have a pumping inlet 32A that may be in fluid communication with the fluid circulation circuit 12, in one contemplated use. The pumping device 30 may further have a diffuser portion 33. The diffuser portion 33 may be fluidly connected to the suction chamber 32. The diffuser portion 33 may for example have a throat portion 33A, and a flaring portion 33B extending downstream from the throat portion 33A. The diffuser portion 33 may include or define an outlet 33C. The outlet 33Cmay be in fluid communication with the fluid circulation circuit 12, in one contemplated use.

[0034] Therefore, the heat driven oscillations of the vapor bubble-liquid plug of the self-oscillating fluidic heat engine 20 induce a pressure variation in the suction chamber 32, and a pressure head in the diffuser portion 33, generating a pumping action on the fluid in the fluid circulation circuit 12. While the self-oscillating fluidic heat engine 20, the pumping action may result in a relatively continuous flow of fluid in the fluid circulation circuit 12.

[0035] Thus, the present disclosure may be said to be related to a heat driven micro-jet pump for microfluidic applications. It is composed of the self-oscillating fluidic heat engine (SOFHE) 20 coupled with a pumping device 30. The SOFHE 20 thus operates on the principle that a vapor bubble trapped by an oscillating liquid plug acts as a piston that is formed inside a capillary channel, i.e., that of the tube 21. The SOFHE 20 needs a certain thermal gradient to start oscillations. It can be driven by waste heat.

[0036] The pumping device 30 is composed of the nozzle 31 , the suction chamber 32, and the diffuser portion 33, that may include the throat portion 33A. The nozzle 31 accelerates the motive flow provided by the engine 20 (through the oscillations), which creates a lower pressure in the suction chamber 32, pulling liquid from the inlet 32A (where the liquid has to be pumped). The motive flow is mixed with the flow in the throat / diffuser for momentum transfer. The velocity of the flow is then converted to pressure head in the diffuser portion 33. Therefore, in one use, waste heat is converted to pumping work to displace the liquid from an inlet reservoir to an outlet point. In a variant, this heat driven pumping apparatus 10 shows a pumping capacity of tens of milliliters per minute and a pumping head of tens of mm H2O. The pumping apparatus 10 presents a promising solution for microfluidic applications, particularly for actively cooling microprocessors, where waste heat is available.

[0037] As shown in Figs. 2 and 3, the driver of the pumping device 30 is the SOFHE 20, whose tube 20 may have a relatively small diameter, such as an inner diameter of 2 mm that is filled with a working fluid. The tube 21 must be partially heated to form the bubble and to create a thermal gradient across the tube 21 to reachoscillations, achieved for example by the heating block 22A and a cooling block 22B. The engine 20 may achieve a maximum pressure change of ±15 kPa during the compression-expansion cycle. To harness this pressure for pumping, the open end 21 B of the tube 21 is connected to a pumping device 30. The flow from the SOFHE 20 is accelerated in the nozzle 31 , which creates a lower pressure (Venturi effect) in the suction chamber 32, pulling liquid from the inlet 32A. The velocity of the flow is then converted to pressure head in the diffuser portion 33. By doing so, the waste heat provided to the SOFHE 20 is converted to fluid pumping. In a variant, the pumping device 30 is 3D printed, and / or a monolithic block.

[0038] The pumping performance may be characterized by measuring the flow rate (using a measuring cylinder and a stopwatch) at different pressure heads. In experiments, the measurements were carried out at different operating temperatures of the SOFHE 20. Referring to Fig. 4, the characteristic curves for the pumping apparatus 10 may exhibit an almost linear trend at various operating temperatures. At zero head, the maximum flow rate increased from 21 to 46 ml / min when rising operating temperature from 110 to 140 °C while the maximum measured head (zero flow rate) increased from 23 to 100 mm H2O. The pumping apparatus 10 can be further optimized as a function of the design parameters, including diameter and length of nozzle, throat, diffuser, and the ratio of the nozzle-diffuser diameter. This heat-driven pumping apparatus 10 presents a promising solution for microfluidic applications, particularly for actively cooling microprocessors, or other applications where waste heat is available. Considering the 200 W generated heat flux per microprocessor, available temperature difference of 20°C to cool a chip, using water with a specific heat capacity of 4.18 KJ / Kg. °C, a pump with a pumping capacity of 142 ml / min is required to remove the target heat flux.

[0039] As the temperature of the microprocessor cannot exceed 80°C, the system must use a working fluid with lower boiling temperature than maximum chip temperature such as dielectric fluid Novec 7000 with a boiling point of 34°C. To remove the target heat flux of 200 W using Novec 7000 with an available temperature difference of 20°C, a pumping capacity of 329 ml / min is required (specific heat capacity 1.3 KJ / Kg. °C and density 1.4 g / cm3). Therefore, accommodating 6-7 of the pumping apparatus 10 can remove the target heat flux.

[0040] In operation of the SOFHE 20, a hot source is in contact with a portion of tube 21 , referred to as the “hot portion”. A cold source is in contact with another portion of tube 21 called the “cold portion”. The hot and cold portions neighbor each other, that is, they are sufficiently close to allow the operation described hereafter. Hot portion is located on the side of the closed end 21 A of tube 21 and cold portion is located between hot portion and open end 21 B, in the vicinity of the hot portion. The temperature of hot source is higher than the boiling point temperature of the liquid in the SOFHE 20, and the temperature of cold source is lower than the boiling point temperature of the liquid in the SOFHE 20. Thus, after placing tube 21 in contact with the hot and cold sources, the temperature of fluid is higher than its boiling point at the level of hot portion and lower than its boiling point at the level of cold portion (i.e., condensing segment). A bubble of fluid in the vapor state then forms in tube 21 at the level of hot portion (i.e., evaporation segment). The bubble positions on the closed end side 21A where it occupies, in directions transverse to the tube 21 , the entire space available in the tube 21 .

[0041] Due to the fact that, in hot portion, the temperature of fluid is higher than its boiling point, fluid in the liquid state evaporates. The evaporation of part of fluid in the liquid state causes an increase in the volume of bubble, which induces fluid flow in the nozzle 31. The volume increase of bubble has carried on and the volume of bubble has reached a maximum value. Bubble then extends all the way into cold portion of the tube 21. The vapor of bubble then starts condensing, which causes a decrease in the volume of bubble, whereby oscillation occurs. The evaporation may be caused by heat reclaimed from a device, or may be induced by a thin film heater (e.g., in lab on chip), etc.

[0042] The SOFHE 20 generates pressure through compression-expansion of a vapor bubble that is trapped by an oscillating liquid plug in a capillary tube 21. This pressure provides motive flow to the nozzle 31 of the pumping device 30 where the flow is accelerated. This creates a lower pressure in the suction chamber 32 that pulls the liquid from the inlet 32A. The flow finally passes through a diffuser portion 33 where the velocity is converted to pressure head. This heat driven pumping device 30 is capable of generating maximum pressure head (zero flow rate) of 10s mm H2O and maximum flow rate (zero head) of 10s ml / min. Stated differently, the SOFHE 20 relies on a vapor bubble trapped in a microchannel (i.e., tube 21) by anoscillating liquid plug (acting as a piston) set in motion by periodic evaporation and condensation of the fluid. The underlying physics of the oscillations is similar to those of a single-branch pulsating heat pipe.

[0043] Figs. 5A and 5B are block diagrams illustrating an arrangement of multiple ones of the heat-driven micro jet pumping apparatus 10. In Fig. 5A, the pumping apparatuses 10 are arranged in parallel relative to the fluid circulation circuit 12. In Fig. 5B, the pumping apparatuses 10 are arranged in series relative to the fluid circulation circuit 12. The arrangements of Figs. 5A and 5B ,ay increase flow and / or pressure of the fluid in comparison to a single one of the pumping apparatuses 10.

[0044] The pumping apparatus 10 may be used to innovate in cooling electronics for its simplicity of design: the pumping apparatus 10 operates with no moving part and is simple to design. The pumping apparatus 10 may use a passive approach using waste heat: the driver of the pumping apparatus 10 is the heat engine 20 that needs heat to run. This gives the pumping apparatus 10 an advantage over the conventional micro pumps where waste heat is available like microelectronic components. The pumping apparatus 10 may have relatively high pumping capacity: the pumping apparatus 10 has a pumping capacity that is two orders of magnitude higher than the existing micro pumps in the literature. The pumping apparatus 10 may thus be used to cool electronic components where high heat flux removal is required.

[0045] The pumping apparatus 10 may be used in numerous applications, for example, in cooling applications for microelectronics: microelectronics generate significant amounts of heat during operation, which leads to performance degradation and the lifespan reduction. The pumping apparatus 10 can manage this heat by circulating cooling fluids, which absorb and carry away the heat from the electronic components. The pumping apparatus 10 is compact and can be miniaturized to fit within the confined spaces of microelectronic devices. This enables efficient cooling without adding significant bulk or weight to the overall system, making the pumping apparatus 10 well suited for portable electronic devices and applications where space is limited. The pumping apparatus 10 offers working with waste heat that is an advantageous over existing micro pumps working withelectricity. Comparing to the existing heat-driven micro-pumps, the pumping apparatus 10 offers a higher flow rate.

[0046] In accordance with another use, the pumping apparatus 10 may be used in micropumping for chemical and / or biological applications: Miniaturization of fluidic components allow for so called Laboratory on Chip. Such miniature devices enable very controlled reactions using minute amounts of chemicals or primary organic samples (blood, bacteria, viruses). This makes the devices more efficient and more sensitive. At the core of lab-on-chip, fluidic circulation is required. Creating a small flow using rotary pump is harder to implement at this scale, while creating oscillating flows is easier using piezo, electrostatic or pneumatic actuators. The conversion of such oscillating flow into constant flow can be done using the pumping apparatus 10 of the present application.

[0047] The SOFHE 20 relies on a vapor bubble trapped by an oscillating liquid plug acting like a piston in a tube that may be of mm-scale diameter. Pressure build-up in the vapor bubble can provide net mechanical work that can then be converted into work by coupling the SOFHE 20 to the pumping device 30 in the pumping apparatus 10. In a variant, the pumping apparatus 10 may have its mechanical power density enhanced using different approaches, such as increasing the heat source temperature, adding wicking structures inside the tube, and / or decreasing the liquid length.

[0048] In a variant, the addition of working features may have a critical impact on the average rate of phase change, which may consequently increase the mechanical power density. Decreasing the length of the liquid plug may also improve the mechanical power density by decreasing the friction loss and volume as well as increasing the frequency. Thus, in a variant, the phase change may be manipulated using a wicking fiber inserted in the tube 21 . Adding a wicking fiber may lead to oscillations with a different phase change profile. To maximize work done by phase change on the liquid plug, the phase change force may need to be optimally in phase with velocity. To enhance the phase change, a wicking fiber may be inserted inside the tube 21 , extending from the condenser segment into the evaporator segment of the tube 21. In an embodiment, the fiber forms corners with the inner wall of the glass tube and is in contact with the liquid plug so it can pumpliquid towards the evaporator segment. This increases the thin film length for evaporation and also makes the length of the film independent of the oscillation amplitude. Other wicking structures may include a capillary path, a path of micropillars, etc.

[0049] The tube 21 may be fabricated in any appropriate way and may have any appropriate shape, including cylindrical (i.e., round cross-section). In a variant, the tube 21 is microfabricated by anodically or direct bonding a grooved glass or silicon wafer (top and sidewalls) to a silicon wafer (bottom wall). To further increase the phase change, two more channels may be fabricated with an etched capillary path on the bottom wall at two different widths of 25 and 50 pm and a depth of 100 pm, such that the resulting tube 21 of the SOFHE 20 may generate a reliable amplitude in the millimeter range.

[0050] In a variant, the engine 20 has a generally square cross-section that benefits from its corners acting as a capillary path. The tube 21 with square cross-section may be fabricated in any appropriate manner, such as by anodically bonding silicon (thickness 500 pm) to a glass wafer (borofloate33, thickness 600 pm) to provide visual access inside the tube 21 and suitable thermal insulation. Before bonding, a channel may be grooved on a glass wafer using a dicing machine with a hydraulic diameter (Dh) of 375 pm. In some configurations, an additional capillary path may be added by etching a trench in Si along the channel length. Referring to Fig. 6, an exemplary and schematic method for fabricating the tube 21 is shown, with silicon and glass being used as examples, though other materials could be used. In the variant of Fig. 6, to create a trench, a two-level masking process is followed. A 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 may then be cleaned (e.g., using solvent and Piranha). Before bonding, diluted HF may be used to remove native oxide on the Si wafer. For the capillary trench, exemplary widths were used, such as (l / l / ) of 25 pm and 50 pm, with a depth (H) of 100 pm and a length of 20 mm. In an example, the total length of the tube 21 is LT=8.5 cm, the thickness is / - / r=1 .1 mm, and the width is l / l / ?-=3 mm. The volume of such a configuration of the SOFHE 20 is therefore VSOFHE = LT*A =0.26 cm3, where A= HT* WT. The heated end 21A of the SOFHE 20 was closed with glue, whereasthe cooled end 21 B was open. Such a configuration of SOFHE 20 takes advantage of the sharp capillary corners of a square cross section to pump liquid into the evaporator segment. With such a configuration, there may result 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 schematically shown in Fig. 7 relative to the meniscus. The line of triple points (formed by the thin film behind the meniscus) and the liquid wicked along the corner capillaries may be the main contributors to the phase change because of their low thermal resistance. Observing the positive effect of the capillary pumping of the liquid through sharp corners may therefore favor such a configuration for the SOFHE 20 of the pumping apparatus 10, in which a capillary path is etched on the bottom wall. Thus, more liquid can be pumped towards the evaporator segment to intensify the net evaporation rate, leading to an increase in the amplitude.

[0051] 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 (A=H / W) of the channel is sufficiently large A >1), as is the case for the SOFHE 20 (A=2 and 4). The volumetric flow in the capillary path is a function of the length of liquid penetration along the capillary and the cross- sectional area. The length of liquid penetration along the capillary ( / _) is determined by the surface tension and friction forces, leading to Washburn’s equation.zii

[0052] '

[0053] where a is the surface tension, 6 is the contact angle, is the viscosity, r is the capillary radius, and t is the time. As the width of the capillary path increased, the length of the liquid penetration increased, and the cross-sectional area led to an increase in the capillary-pumped volumetric flow. A higher amount of pumped liquid intensifies the net evaporation rate, resulting in an increase in the oscillation amplitude.

[0054] Thus, though optional, the performance of a microfabricated self-oscillating fluidic heat engine (SOFHE) 20 in the pumping apparatus may be enhanced byboosting the phase change through corner capillaries as well as etched capillary paths. The sharp corners in the square channel act as capillary paths, pumping liquid from the liquid plug towards the evaporator segment. This intensifies the phase-change rate, which in turn increases the oscillation amplitude (a key parameter for increasing the SOFHE output power). To further increase the phase change, capillary paths may be provided on the bottom wall of the engine 20.

[0055] The pumping device 30 may be described as being a valveless mechanism, and an ejector or Tesla valve, can be employed. The design shown herein for the pumping device 30 may be 3D printed as a possibility among others, and may have a circular cross-section, among other possible shapes (the nozzle 31 being for example conical or frusto conical as an example). The ejector thus includes the nozzle 31 that accelerates the flow, creating a jet directed towards the diffuser portion 33. In the diffuser portion 33, the inertia of the flow is maintained, and the diverging section of the diffuser 33 converts the velocity of the flow into pressure.

[0056] A valveless mechanism may introduce the challenge of backflow throughout the entire cycle. Therefore, in the design process, it is crucial to consider the lowest resistance in forward flow while ensuring the highest resistance in backward flow to minimize the impact of backflow. Parameters such as the length and diameter of the nozzle 31 and diffuser portion 33 as well as the length of the diverging part of the diffuser, need to be optimized to achieve optimal performance.

[0057] By implementing a valveless mechanism, such as described herein in an embodiment of the pumping device 30, in conjunction with the SOFHE 20, the mechanical power output can be effectively utilized for microfluidic pumping applications. This approach offers the advantage of maintaining the generated pressure without the need for check valves, thereby enhancing the overall mechanical efficiency of the pumping apparatus 10. This being said, check valves may be used.

[0058] The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without departing from the scope of the invention disclosed. Still other modifications which fall within the scope of the present invention will be apparent to those skilled in theart, in light of a review of this disclosure, and such modifications are intended to fall within the appended claims.

Claims

CLAIMS1 . A pumping apparatus comprising: a self-oscillating fluidic heat engine having a tube with a closed end, the tube configured to enclose a liquid plug trapping a vapor bubble in the closed end, the tube configured to be exposed to a thermal gradient for the liquid pump to effect pumping oscillations; and a pumping device having a nozzle at a fluid connection with an open end of the tube, a suction chamber fluidly connected to the tube via the nozzle, the suction chamber having a pumping inlet, and a diffuser portion fluidly connected to the suction chamber and having an outlet; wherein the pumping oscillations of the self-oscillating fluidic heat engine induce a pressure variation in the suction chamber, and a pressure head in the diffuser portion.

2. The pumping apparatus according to claim 1 , wherein the pumping device is a monolithic component.

3. The pumping apparatus according to claim 2, wherein the pumping device has a 3D printed body.

4. The pumping apparatus according to any one of claims 1 to 3, wherein the nozzle has a conical geometry.

5. The pumping apparatus according to any one of claims 1 to 4, wherein the pumping inlet is in plane to which an axis of the nozzle is normal.

6. The pumping apparatus according to any one of claims 1 to 5, wherein the tube has a generally square cross-section.

7. The pumping apparatus according to any one of claims 1 to 6, wherein a wicking structure is formed in a bottom surface of the tube.

8. The pumping apparatus according to claim 7, wherein the wicking structure is a capillary path.

9. A cooling system comprising:at least one of the pumping apparatus according to any one of claims 1 to 8; a fluid circulation circuit in fluid communication with the inlet and the outlet of the pumping apparatus; a heating load in heat exchange with the fluid in the fluid circulation circuit, for the fluid to absorb heat from the heating load; and a cooling load in heat exchange with the fluid in the circulation circuit for the absorbing heat from the fluid; wherein the pumping apparatus is exposed to a thermal gradient to induce fluid flow in the fluid circulation circuit.

10. The cooling system according to claim 9, including a plurality of the pumping apparatus in series relative to the fluid circulation circuit.

11. The cooling system according to claim 9, including a plurality of the pumping apparatus in parallel relative to the fluid circulation circuit.

12. The cooling system according to any one of claims 9 to 11 , wherein the thermal gradient includes heat from the heating load provided to the pumping apparatus.

13. The cooling system according to any one of claims 9 to 12, wherein the cooling system is entirely passive.

14. The cooling system according to any one of claims 9 to 13, wherein the cooling system is valveless.

15. The cooling system according to any one of claims 9 to 14, wherein the heating load is an integrated chip.

16. The cooling system according to any one of claims 9 to 14, wherein the heating load is an electronic device or system.

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