Accelerometer for gravity reduction applications

Abstract

A corner flow accelerometer device for reduced gravity applications includes a capillary, where the capillary is partially filled with capillary fluid, and where the capillary includes at least one corner configured to enhance capillary flow. A corner flow accelerometer device for reduced gravity applications includes a hollow square prism including capillary tubes, where the square prism is partially filled with a capillary fluid including silicone oil, and where the square prism is anchored to a weight within a gyroscope body. The gravity monitoring method comprises the following steps: providing the corner flow accelerometer device; measuring the fluid height or meniscus curvature caused by capillary flow; calculating a dimensionless Bond number based on the measured fluid height or meniscus curvature, wherein the dimensionless Bond number includes a ratio between a force of gravity and a surface force; and calculating a force of gravity based on the Bond number.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Application No. 63 / 336,564, filed on April 29, 2022, the entire contents of which are incorporated herein by reference. Background Art

[0003] The quantitative measurement of gravitational acceleration (g) has long been a matter of scientific interest in the broad fields of physical sciences involving metrology (the scientific study of measurement), geophysics (the branch of earth science that deals with physical processes and phenomena occurring especially on and near the Earth), and geodesy (the science of measuring the size, shape, rotation, and orientation of the Earth in space). In metrology, for example, since the value of g affects the measurement of force or any physical quantity involving standard forces (such as amperes, pressure, etc.), its accuracy affects the accuracy of standard units in many areas of metrology (including mechanics, electricity, thermometry, fluid dynamics). Geophysics and geodesy, on the other hand, are primarily interested in variations in gravity, which vary with location and with time at a given location due to the Earth's rotation, the deviation of its surface from an equipotential spheroid, and density variations occurring within the Earth.

[0004] The plethora of gravity measuring devices (commonly referred to as gravimeters) that have been developed over the past few centuries to support the growing field of geodesy and metrology are primarily based on how gravity interacts with mass. These include gravimeters that function in an absolute mode, such as using a falling body or using a pendulum to determine g by measuring time (or period) and length, or gravimeters that function in a relative mode, such as devices using a mass-spring system, whereby the force on the test mass changes as the gravitational field changes, and these small changes in gravity are detected by noting small changes in the corresponding weight or by mass displacement. (See Marson, I. and J.E.Faller, g-the acceleration of gravity: its measurement and its importance 1986 J.Phys.E:Sci.Instrum.19 22)

[0005] Many versions of gravimeters have been developed to measure the strength of the gravitational field: such as tilted zero-length spring designs using metal and quartz springs, virtual spring feedback designs that use magnetic levitation instead of spring elements, and gradiometers that measure the gradient or spatial rate of change of components of the gravitational field. (See Chapin, D., Gravity Instruments: Past, Present, Future, The Leading Edge, January, 1998)

[0006] Because gravity measurement devices (such as absolute and relative gravimeters) rely on the extensive properties of matter (i.e., mass), they have significant limitations and disadvantages. Gravimeters are relatively large and cumbersome, not easily transported, require a controlled temperature environment and expensive, complex designs, and have inherent nonlinearities and tradeoffs that make highly accurate, precise, and repeatable g measurements under field conditions technically challenging and difficult to achieve. (See Krasnow, US Pat. No. 2,303,845, 1942; Carter, WE et al, New Gravity Meter Improves Measurements, Eos, Vol. 75, No. 8, February 22, 1994)

[0007] Therefore, there is a need to develop new types of gravity measurement devices that can overcome many of the shortcomings of conventional gravimeters that rely primarily on the extensive properties of matter, and instead rely on the intensive properties of matter, which depend only on the type of matter in the sample and not on the amount of matter. These new types of gravity measurement instruments offer new capabilities and applications that extend far beyond those physical science fields that utilize conventional gravity measurement systems and span a wide range of industrial sectors, basic and applied research, and even health dosimetry needs. For example, this is a valuable condition for both microgravity acceleration environment research (as indicated by the presence of active rack isolation systems on the ISS) and private industry manufacturing of materials (such as optical fibers) where the reduction of material defects can bring profits back to Earth. (See Volfson, L.; Starodubov, D. Fiber Optic Manufacturing in Space. US20170233282A1, August 17, 2017) (See Dubbs, C. Realizing Tomorrow the Path to Private Spaceflight; Outwardodyssey; University of Nebraska Press: Lincoln, 2011) In addition, recent findings from studies of astronauts exposed to microgravity for extended periods of time in space indicate that there is a dose-response relationship for exposure to extreme gravity environments, which can benefit from new gravity dosimetry techniques. (See Trudel, G., et al, Characterizing the effect of exposure to microgravity on anemia: more space is worse, Am J Hematol. 2020; 95: 267-273)

[0008] Since current technology lacks the design requirements required for these applications, there is a need in the art for improved systems, devices and methods that can exploit the intensive properties of matter, such as surface tension and other intensive properties of matter, which provide a basis for new gravity measurement techniques and applications (such as angular flow accelerometers for measurements of reduced gravity). (See Liu, YM et al, The Possibility of Changing the Wettability of Material Surface by Adjusting Gravity, AAAS Research Volume 2020, Article ID 2640834; Love, SG, Particle Aggregation in Microgravity: Informal Experiments on the International Space Station, Meteroritics & Planetary Science 49 Nr 5, 732-739 (2014)) Summary of the invention

[0009] Some embodiments of the invention disclosed herein are set forth below, and any combination of these embodiments (or portions thereof) may be made to define other embodiments.

[0010] Accordingly, the present invention is directed to improved gravity measurement methods, devices and systems that substantially obviate one or more limitations and disadvantages of the related prior art.

[0011] According to one or more embodiments of the present invention, there is provided a closed bounded volume forming an internal cavity of finite size, the internal cavity having at least one solid surface and containing at least one fluid or fluid suspension containing particles, at least one element of which has an intrinsic material property that is responsive to gravity.

[0012] In one aspect, an accelerometer device for reduced gravity applications comprises: a sealed capillary having a first end and a second end and a length between the first end and the second end, the capillary forming an interior cavity including at least one interior surface; wherein the capillary is partially filled with a capillary fluid; and wherein the capillary includes at least one corner running along at least a portion of the length at an edge of the at least one interior surface, the at least one corner being configured to enhance capillary flow.

[0013] In one embodiment, the at least one corner is located at an intersection between two or more interior surfaces.

[0014] In one embodiment, the capillary tube is anchored to a weight within the gyroscope body.

[0015] In one embodiment, the capillary is transparent or translucent.

[0016] In one embodiment, the interior surface comprises an indication surface.

[0017] In one embodiment, further comprising at least one wedge or fin secured to the interior surface.

[0018] In one embodiment, the at least one corner is in the range of 1 to 1000 corners.

[0019] In one embodiment, the capillary comprises an n-gonal prism, a square prism, a rectangular prism, a triangular prism, a pentagonal prism, a hexagonal prism, an octagonal prism, a trapezoidal prism or a polygonal prism.

[0020] In one embodiment, the cross-section of the lumen of the capillary comprises a square, a rectangle, a parallelogram, a rhombus, a trapezoid, a trapezoid, a rhombus, a triangle, a curved triangle, a teardrop, a crescent, a pentagon, or a polygon.

[0021] In one embodiment, the capillary fluid includes a polar liquid including water or ethanol, or a non-polar liquid including silicone oil.

[0022] In one embodiment, the capillary fluid has a volume of 1 pL to 1000 mL.

[0023] In one embodiment, the capillary comprises at least one of: a ceramic with high intrinsic wetting properties, a glass ceramic with tunable wetting properties, a borosilicate glass, titanium dioxide, silicon dioxide, a polymer with high intrinsic wetting properties, a polymer with tunable wetting properties, acrylics, epoxies, polyethylene, polystyrene, polyvinyl chloride, polytetrafluoroethylene, polydimethylsiloxane, polyester, and polyurethane.

[0024] In one embodiment, the capillary has a length in the range of 1 μm to 50 m, a width in the range of 1 nm to 1 m, a height in the range of 1 nm to 1 m, and an internal volume in the range of 1 μL to 10L.

[0025] On the other hand, an accelerometer system for reducing gravity applications comprises: the above-mentioned accelerometer device; at least one sensor proximate to the accelerometer device, the at least one sensor being configured to measure fluid height or meniscus curvature caused by capillary flow in the accelerometer device; and a computing system communicatively connected to the at least one sensor, the computing system comprising a processor and a non-transitory computer-readable medium storing instructions, the instructions, when executed by the processor, performing steps including the following: calculating a dimensionless Bond number based on the measured fluid height or meniscus curvature, wherein the dimensionless Bond number comprises a ratio between the force of gravity and the surface force; and calculating the force of gravity based on the Bond number.

[0026] In one embodiment, the at least one sensor comprises an electrical sensor or an optical sensor.

[0027] In one embodiment, the system is configured to measure gravitational acceleration forces in the range of 0 g to 5 g, where g is equal to 9.8 m / sec. 2 .

[0028] On the other hand, a method for monitoring gravity acceleration includes: providing the above-mentioned accelerometer device; measuring the fluid height or the curvature of the curved liquid surface caused by capillary flow; calculating a dimensionless Bond number based on the measured fluid height or the curvature of the curved liquid surface, wherein the dimensionless Bond number includes the ratio between the force of gravity and the surface force; and calculating the force of gravity based on the Bond number.

[0029] In one embodiment, the fluid height or meniscus curvature is measured via at least one sensor proximate to the corner flow accelerometer device.

[0030] In one embodiment, the at least one sensor comprises an electrical sensor or an optical sensor.

[0031] In one embodiment, the Bond number is given by Definition, where ρ is the density, g is the acceleration due to gravity, H is the characteristic meniscus height, and σ is the surface tension. For values ​​of B0 < 1, the surface forces dominate over the forces of gravity, while for values ​​of B0 > 1, the forces of gravity dominate over the surface forces. For values ​​of B0 ~ 1, the forces of surface forces and gravity are approximately equal.

[0032] In another aspect, a corner flow accelerometer device for gravity reduction applications includes a hollow square or rectangular prism including a capillary, wherein the prism is partially filled with a capillary fluid including silicone oil, and wherein the prism is anchored to a weight within a gyroscope body.

[0033] In another aspect, an accelerometer device for reduced gravity applications comprises: a closed bounded volume forming an interior cavity having at least one solid surface; at least one fluid within the cavity; wherein the fluid comprises particles in suspension; and wherein at least one of the fluid and the particles in suspension has an intrinsic material property that is responsive to gravity.

[0034] In one embodiment, the intrinsic material property responsive to gravity is surface energy in nature.

[0035] In one embodiment, the intrinsic material property responsive to gravity is electrostatic in nature.

[0036] In one embodiment, the solid, fluid and / or suspended material forming the gravity measurement system is dielectric in nature and the fluid contains particles in a size range where surface-dominated electrostatic forces are greater than mass-proportional inertial forces, which favors particle aggregation in proportion to the reduced gravity environment.

[0037] In one embodiment, the suspension comprises dielectric particles comprising semiconductor quantum dot material of nanoscale dimensions, whereby aggregation of the particles in a reduced gravity environment promotes quenching of quantum dot photoluminescence. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The foregoing objects and features and other objects and features will become apparent with reference to the following description and accompanying drawings, which are included to provide an understanding of the present invention and constitute a part of the specification, in which like reference numerals represent like elements, and in which:

[0039] Figure 1A An exemplary capillary-based angular flow accelerometer device for reduced gravity applications is shown in accordance with some embodiments.

[0040] Figure 1B An exemplary cross section of a device according to some embodiments is shown. (See Weislogel MM. Compound capillary rise. Journal of Fluid Mechanics. 2012 Oct; 709: 622-47)

[0041] Figure 2 is a graph showing a general capillary characteristic geometric response (H) dependent on gravity according to some embodiments.

[0042] Figure 3 is a graph of experimental results showing that corners provide a distinct response relative to classical capillary action according to some embodiments.

[0043] Figure 4is a graph of experimental results showing the geometry dependence of corner driving force, according to some embodiments.

[0044] Figure 5 An exemplary computing environment is depicted in which aspects of the invention may be practiced according to some embodiments. DETAILED DESCRIPTION

[0045] It should be understood that the drawings and description of the present invention have been simplified to illustrate elements relevant to a clearer understanding of the present invention, while many other elements found in the systems and methods for angular flow accelerometers for reduced gravity applications have been excluded for clarity. It will be appreciated by those of ordinary skill in the art that other elements and / or steps are desired and / or required in implementing the present invention. However, since these elements and steps are well known in the art, and since they are not convenient for a better understanding of the present invention, discussion of such elements and steps is not provided herein. The disclosure herein relates to all such variations and modifications of such elements and methods known to those skilled in the art.

[0046] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention belongs. Although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present invention, exemplary methods and materials are described.

[0047] As used herein, the following terms each have the meaning associated with them in this section.

[0048] The articles "a" and "an" are used herein to refer to one or to more than one (ie, to at least one) of the grammatical object of the article. By way of example, "an element" means one element or more than one element.

[0049] As used herein, "about" when referring to a measurable value such as an amount, a temporal duration, etc., is meant to encompass variations of ±20%, ±10%, ±5%, ±1%, and ±0.1% relative to the specified value, as such variations are appropriate.

[0050] Scope: Throughout this disclosure, various aspects of the present invention can be presented in a range format. It should be understood that the description of the range format is only for convenience and brevity, and should not be interpreted as an inflexible limitation on the scope of the present invention. Where appropriate, the description of the range should be considered to have specifically disclosed all possible sub-ranges and each numerical value within the range. For example, the description of a range such as from 1 to 6 should be considered to have specifically disclosed sub-ranges (such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6, etc.), and each number within the range (e.g., 1, 2, 2.7, 3, 4, 5, 5.3 and 6). This applies regardless of the width of the range.

[0051] The nomenclature used herein is defined in Table 1 below:

[0052] Table 1:

[0053]

[0054]

[0055]

[0056] In one embodiment, the capillary flow accelerometers discussed herein ideally meet the need for a low-cost support device that is visually easy to interpret, similar to how a leveler fulfills its purpose on Earth.

[0057] γ S =γ SL +γ L cosθ (1)

[0058] In 1805, Thomas Young introduced Equation 1, which describes the surface tension between solid and vapor, solid and liquid, and liquid and vapor as γ, respectively. S , γ SL and γ L The contact angle (θ) is given by the balance of forces given by the three phases meeting at one point in the case described. Although elegant, Equation 1 has sparked debate and has led to a re-examination of this balance of forces from the perspective of energy minimization and the thermodynamic view of surface tension as surface energy.

[0059] The debate has not yet subsided, because recent scientific advances in nanoscale research have even carefully examined the correctness of Young's formula. (See Hawa, T., et al., Internal Pressure and Surface Tension of Bare and Hydrogen Coated Silicon Nanoparticles. The Journal of chemical physics 2004, 121 (18)) (See Wang, EN, et al., Uni-Directional Liquid Spreading on Asymmetric Nanostructured Surfaces. Nature materials 2010, 9 (5), 413-417) (See Demirel, MC, et al., An Engineered Anisotropic Nanofilm with Unidirectional Wetting Properties. Nature materials 2010, 9 (12), 1023-1028) (See Liu, Y., et al., Contact Line Pinning and the Relationship between Nanobubbles and Substrates. J. Chem. Phys. 2014, 140 (5), 054705)

[0060] Specifically, with respect to the question of the relationship between gravity and Young's contact angle, it has been found through microgravity experiments that gravity actually contributes significantly to the contact angle of drops as small as 5 μL in both drop towers and parabolic arc flights. (See Ababneh, A., et al., Effect of Gravity on the Macroscopic Advancing Contact Angle of Sessile Drops. The Canadian Journal of Chemical Engineering 2006, 84(1), 39-43) (See Diana, A., et al., Sessile Drop Wettability in Normal and ReducedGravity. Microgravity Sci.Technol.2012,24(3),195-202)(See Zhu,Z.-Q.,et al.,Influence of Bond Number on Behaviors of Liquid Drops Deposited onto SolidSubstrates.Microgravity Sci.Technol.2012,24(3),181-188)(See Calvimontes,A.The Measurement of the Surface Energy of Solids by Sessile DropAccelerometry.Microgravity Sci.Technol.2018,30(3),277-293)

[0061] By analyzing the small slope solution, it has been shown that even for a sessile drop as small as 1 μL, when When the contact angle is 1 / 20 mm / s, gravity cannot be ignored. (See Calvimontes) (See Allen, JS An Analytical Solution for Determination of Small Contact Angles from Sessile Drops of Arbitrary Size. Journal of Colloid and Interface Science 2003, 261 (2), 481-489) Therefore, the contact angle does depend on gravity, but from the perspective of human vision, this effect is not significant for direct indication using this relationship. When the dialogue extends from the contact point to the contact line, it is also difficult to use reliably for both physical and practical reasons. Physically, since little is known about the stress singularity at the moving contact line, this will lead to design metrics relying more on empirical data. (See Kistler, SFHydrodynamics of wetting. InWettability (ed. JCBerg), Surfactant Science Series 1993, vol. 49, 311-429) (See Dussan, EB On the Spreading of Liquids on Solid Surfaces: Static and DynamicContact Lines. Annual review of fluid mechanics 1979,11(1),371-400)(See Hu,XY,et al.,Moving Contact Line with Balanced Stress Singularities.arXiv:0806.3847[physics]2008)

[0062] In fact, in order to apply the knowledge of the moving contact line, a smooth, flat and chemically homogeneous surface condition must be maintained throughout the life of the accelerometer, which places an undue burden on both manufacturers and users. (See Sheng, Y.-J., et al., Effects of Geometrical Characteristics of Surface Roughness on Droplet Wetting. J. Chem. Phys. 2007, 127 (23), 234704) To overcome these obstacles, this paper discloses a material system that completely wets the interior of the indicating surface (the condition of θ = 0 in Formula 1), thereby allowing the neglect of stress singularities and contact line pinning related calculations, in fact making the indicating surface less susceptible to corrosion during its life, and allowing the use of inexpensive chemically heterogeneous materials.

[0063] It is helpful to identify potential sources of force that can balance gravity to provide an equilibrium state that can be interpreted as an indication. Some of these sources of force that can be used to balance gravity include, but are not limited to: van der Waals interactions, which include short-range electromagnetic forces between molecules and / or atoms and have only neutral charges; overlap of double electrical layers, which include electrical interactions generated by overlap of double electrical layers around particles in solution; atomic spatial interactions of absorbed polymers, which include short-range interactions generated by overlap of absorbed polymer layers on particles; ridge forces, which include bridges formed between particles of polymer binders and / or surfactants; hydration forces, which include overlap of hydrogen-bonded water molecules on hydrophilic surfaces on particles; depletion, which includes negative absorption of solutes and polymers by having less affinity for the surface than the solvent. (See Hosokawa M, Naito M, Nogi K, Yokoyama T. Nanoparticle Technology Handbook [Internet]. Saint Louis, NETHERLANDS, THE: Elsevier; 2012)

[0064] The basic categories and some examples of possible mechanisms for indication are presented in Table 2 below. These categories have their own potential for indication, but most likely the most ideal solution includes a combination of these categories. For example, although the rest of this disclosure will focus only on internal surfaces as a solution, improved indication can be achieved by including quantum dots floating in the liquid filling the corners. In this scenario, quantum dots will provide visual feedback for indication, and introduce additional surface forces and masses that can be used for the system to be used and additional phenomena (such as electrostatic condensation, etc.) that can be used for measurement purposes. Although the categories of Table 2 can be mixed and matched explicitly when searching for solutions, it should also be noted that some categories have inherently adopted multiple mechanisms and may not be straightforward to implement. For example, gravity perception in biology can use mechanical membrane strain as a stimulus for membrane ion transport (providing indications to cells). It can be immediately observed that in both examples of quantum dots added to corner flow and / or biological cell membrane utilization, there are challenges of complexity. The increase in complexity accordingly makes it more difficult to design a composite mechanism in theory. When faced with such difficulties, the solution may usually rely more on empirical methods, which is not conducive to adaptive design because empirical methods also have their scalability limitations.

[0065]

[0066] The ideal system is sensitive, adaptive, works in real time, robust, has a long life, is inexpensive, requires no maintenance, and is simple. Mechanical gravity monitoring systems include ceramics, quartz, springs, and MEMS. Electromagnetic gravity monitoring systems include superconducting materials, suspension, magnetic fluids, cold atom interferometers, piezoresistance, and superconducting materials. Thermal / static / dynamic gravity monitoring systems include temperature-controlled surface tension, phase separation, and sedimentation. Internal surface gravity monitoring systems include wetting and capillary applications. External surface gravity monitoring systems include particles. Quantum gravity monitoring systems include atom interferometry and phonons in zero-temperature superfluids. Optical gravity monitoring systems include pressure-sensitive materials and reflective grazing angle deposited films. Biological gravity monitoring systems include gravity sensing in flagella and plants, membrane ion channels, and cytoskeletal and exoskeletal adaptations.

[0067] The internal surface gravity monitoring system meets the requirements of being sensitive, adaptive, working in real time, robust, having a long life, cheap, maintenance-free and simple.

[0068] As a starting point, a mechanical spring accelerometer with a reference mass connected via a spring is probably the most intuitive example. It is simple in theory and is a proven concept, embodied in the example of the Italian Spring Accelerometer (ISA). This mechanical spring accelerometer can achieve up to 3×10 -8 (m / s 2))'s high accuracy is demonstrated by its ability to characterize the interior of exoplanets via gravity anomalies. (See F., et al., ISA, a High Sensitivity Accelerometer in the Interplanetary Space. Space Sci Rev 2020, 216(8), 145)

[0069] Although previous work is diverse, historically, numerical methods have been emphasized for capillary flows relative to the less numerically oriented methods proposed by Weislogel. (See Weislogel, MM; Ross, HD Surface Settling in Partially Filled Containers upon Step Reduction in Gravity, 1990) PS Ayyaswamy et al. established the foundation for capillary flow in corners under negligible gravity by studying laminar flow in grooves and solving for the friction factor coefficient. (See Ayyaswamy, PS, et al., Capillary Flow in Triangular Grooves. Journal of Applied Mechanics 1974, 41 (2), 332-336) Building on the work of Ayyaswamy, Dong et al. explored the capillary rise at corners as a function of liquid viscosity, surface tension, contact angle, overall tube size, and roundness of the corner. (See Dong, M., et al., The Imbibition and Flow of a Wetting Liquid along the Corners of a Square Capillary Tube. Journal of Colloid and Interface Science 1995, 172(2), 278-288) Non-circular porous flow research has also made contributions, especially the non-dimensional flow resistance quantification by Ransohoff and Radke through the application of Galerkin finite element numerical techniques, which obtained values ​​similar to the friction factor in application. (See Ransohoff, TC, et al., Laminar Flow of a Wetting Liquid along the Corners of a Predominantly Gas-Occupied Noncircular Pore. Journal of Colloid and Interface Science 1988, 121(2), 392-401) The application of flow resistance values ​​in the opposite case of bubble rise in a corner column filled with liquid, as studied by Bico and Querré, demonstrated the influence of this early research.(See Bico, J. et al., Rise of Liquids and Bubbles in Angular Capillary Tubes. Journal of Colloid and Interface Science 2002, 247 (1), 162-166) Another non-circular hole study was conducted by AR Kovscek et al., which also utilized flow resistance values, where gravity was included in the derivation as a simple pressure gradient applied term. (See Kovscek, AR, et al., Gas Bubble Snap-off under Pressure-Driven Flow in Constricted Noncircular Capillaries. Colloids and Surfaces A: Physicochemical and Engineering Aspects 1996, 117 (1), 55-76).

[0070] Finally, Weislogel's paper work in 1996 laid the foundation for the corner ascent in the absence of gravity used in the present disclosure. (See Weislogel, MM Capillary Flow in an Interior Corner, NASA Technical Memorandum 107364, 1996) Additional subsequent contributions to the model came from Weislogel and Litcher in 1998 and then from Ramté and Weislogel in 2009. (See Weislogel, MM; Lichter, S. Capillary Flow in an Interior Corner. Journal of Fluid Mechanics 1998, 373, 349-378) (See Ramé, E.; Weislogel, MM Gravity Effects on Capillary Flows in Sharp Corners. Physics of Fluids 2009, 21(4), 042106) Closed-form dimensionless expression solutions were produced for the position and velocity of the tip of the liquid column. These solutions, especially those for constant volume, can be used directly to indicate negligible gravity.

[0071] Referring now in detail to the drawings, in which like reference numerals represent like parts or elements throughout the several views, in various embodiments, systems and methods of angular flow accelerometers for gravity reduction applications are presented herein.

[0072] According to one or more embodiments of the present invention, there is provided a closed bounded volume forming an internal cavity having a finite size, the internal cavity having at least one solid surface, and the cavity containing at least one fluid or fluid suspension comprising particles, at least one material element of the particles having an intrinsic material property responsive to gravity.

[0073] Figure 1A-1B An exemplary capillary-based angular flow accelerometer device 100 for gravity reduction applications is shown in accordance with some embodiments. An exemplary design of the angular flow accelerometer includes a capillary 101 (e.g., number of corners N=4 or similar) partially filled with a liquid 102 (e.g., silicone oil or the like) (e.g., acrylic or the like), but any suitable shape, volume, and / or number N of corners 104 may be utilized. In some embodiments, the capillary 101 is anchored to an optional weight 107, which is within an optional gyroscope body 106, which is shown and is configured to align the capillary 101 with a nearby center of gravity. The capillary 101 within the gyroscope body 106 can be configured similar to a floating compass, where the capillary 101 is positioned inside the gyroscope body 106. The gyroscope body 106 can be of any suitable type, including a classic gyroscope body with 3 circular frames and 3 sets of hinges, such as Figure 1A The compass-shaped gyroscope shown and / or a sphere filled with liquid. In some embodiments, the friction in the hinge of the gyroscope needs to be proportionally weak compared to the weight of the liquid and the force of gravity that is desired to be detected. As used herein, "corner" and "edge" are used interchangeably to describe embodiments of a corner flow accelerometer device, where an edge can be used to describe the shape of the device and a corner can be used to describe the inner portion of the edge of a shape (where increased capillary action occurs).

[0074] In some embodiments, a corner flow accelerometer device 100 for gravity reduction applications includes a sealed capillary 101 having a first end and a second end and a length therebetween, the capillary 101 forming an internal cavity including at least one internal surface 105, wherein the capillary 101 is partially filled with a capillary fluid 102, and wherein the capillary 101 includes at least one corner 104 that runs along at least a portion of its length at an edge of at least one internal surface 105, the corner 104 being configured to enhance capillary flow 103.

[0075] In some embodiments, at least one corner 104 is located at an intersection between two or more interior surfaces 105. In some embodiments, capillary 101 is anchored to a weight inside the gyroscope body. In some embodiments, capillary 101 is transparent or translucent. In some embodiments, interior surface 105 includes an indicator surface. In some embodiments, device 100 further includes at least one wedge or fin secured to interior surface 105. In some embodiments, at least one corner 104 is in the range of 1 to 1000 corners.

[0076] In some embodiments, the capillary 101 includes an n-gonal prism, a square prism, a rectangular prism, a triangular prism, a pentagonal prism, a hexagonal prism, an octagonal prism, a trapezoidal prism or a polygonal prism, any closed bounded volume or any other suitable shape or combination thereof. In some embodiments, the capillary 101 includes a cylindrical body or a sphere having a triangular wall. In some embodiments, the capillary 101 includes a sphere having a ribbed wall or a wedge-shaped wall. In some embodiments, the capillary 101 includes rounded corners and / or sharp corners. (See Tang Y, Yue B, Yan Y. Improved method for implementing contact angle condition in simulation of liquid sloshing under microgravity. International Journal for Numerical Methods in Fluids. 2019; 89 (4-5): 123-42) In some embodiments, the capillary 101 includes a wedge-shaped surface. In some embodiments, the cross-section of the lumen of the capillary 101 includes a square, a rectangle, a parallelogram, a rhombus, a trapezoid, an irregular trapezoid, a rhombus, a triangle, a curved triangle, a teardrop, a crescent, a pentagon, a polygon, or any other suitable shape or combination thereof. Further exemplary cross-sections are shown in FIG. Figure 1B, and examples are described in detail in Weislogel et al. (see Weislogel MM. Compound capillary rise. Journal of Fluid Mechanics. 2012 Oct; 709: 622-47). In some embodiments, the capillary 101 comprises a ceramic with high intrinsic wetting properties, a glass ceramic with adjustable wetting properties (contact angle <90 degrees) (e.g., borosilicate glass, titanium dioxide, silicon dioxide, etc.), a polymer with high intrinsic wetting properties or a polymer with adjustable wetting properties (contact angle <90 degrees) (e.g., acrylic resin, epoxy resin, polyethylene, polystyrene, polyvinyl chloride, polytetrafluoroethylene, polydimethylsiloxane, polyester and polyurethane), etc. In some embodiments, the length of the capillary is in the range of 1 μm to 50 m, the width is in the range of 1 nm to 1 m, the height is in the range of 1 nm to 1 m, and the internal volume is in the range of 1 μL to 10 L.

[0077] In some embodiments, the capillary 101 comprises a spherical enclosed volume having wedge-shaped walls and / or walls divided into flat surfaces with corners between the flat surfaces. This is a 3D shape that can indicate gravity without the need for a gyroscope body. Similar to how a liquid climbs along a corner with reduced gravitational acceleration, Figure 2As shown, the same principle applies to a sphere, where the bubble will move further and further away from the wall as the gravitational acceleration decreases. (See Tang Y, Yue B, Yan Y. Improved method for implementing contact angle condition in simulation of liquid sloshing under microgravity. International Journal for Numerical Methods in Fluids. 2019; 89(4-5): 123-42.) (See Veldman AEP, Gerrits J, Luppes R, Helder JA, Vreeburg JPB. The numerical simulation of liquid sloshing on board spacecraft. J Comput Phys. 2007; 224(1): 82-99.) Note that in the case of a contact angle of 0 (θ = 0, completely wetted surface), the droplet will spread infinitely along rounded or pointed internal corners. (See Chen Y, Weislogel MM, Nardin CL. Capillary-driven flows along rounded interior corners. Journal of Fluid Mechanics. 2006 Nov; 566: 235-71.) In a closed volume, a floating surface that does not form an angle with the wall can be used as a space with a minimum distance between the floating surface and the container wall that the liquid climbs. (See Weislogel MM, Jenson R, Chen Y, Collicott SH, Klatte J, Dreyer M. The capillary flow experiments aboard the International Space Station: Status. Acta Astronautica. 2009 Sep; 65 (5-6): 861-9.]) Examples of floating surfaces that help indicate microgravity can be found in Weislogel et al. In some embodiments, a floating wall and / or a floating shape such as a sphere or polygon is included.Examples include tapered rectangular containers (see Weislogel MM, Jenson R, Chen Y, Collicott SH, Klatte J, Dreyer M. The capillary flow experiments aboard the International SpaceStation: Status. Acta Astronautica. 2009 Sep; 65 (5-6): 861-9.), regular n-gons, rectangles, combined rounded rectangles, selective but equilateral wetted portions, combinations of sharp corners and rounded corners, concave portions, blade structures, and / or irregular polygons. (See Weislogel MM. Compound capillary rise. Journal of Fluid Mechanics. 2012 Oct; 709: 622-47.).

[0078] In some embodiments, the capillary fluid 102 includes a polar liquid (e.g., water, ethanol) or a non-polar liquid (e.g., silicone oil). In some embodiments, the capillary fluid has a volume of 1 μL to 10 L. In some embodiments, the capillary fluid has a volume of 1 pL to 10 ML. In some embodiments, the capillary 101 and the capillary fluid 102 include any suitable combination of solids and liquids that produce a wetted surface.

[0079] In some embodiments, a angular flow accelerometer system for gravity reduction applications includes a angular flow accelerometer device 100 as described above; at least one sensor proximate to the angular flow accelerometer device 100, configured to measure fluid height or meniscus curvature due to capillary flow in the angular flow accelerometer device 100; and a computing system communicatively connected to the at least one sensor, comprising a processor and a non-transitory computer-readable medium storing instructions, which instructions, when executed by the processor, perform the following steps: calculating a dimensionless Bond number based on the measured fluid height or meniscus curvature, wherein the dimensionless Bond number includes a ratio between the force of gravity and the surface force; and calculating gravity based on the Bond number. In some embodiments, at least one sensor includes an electrical sensor or an optical sensor. In some embodiments, the system is configured to measure 0g to 5g (g=9.8m / sec 2 ) range.

[0080] In some embodiments, a gravity acceleration monitoring method includes: providing a corner flow accelerometer device 100 as described above; measuring a fluid height or a meniscus curvature due to capillary flow; calculating a dimensionless Bond number based on the measured fluid height or meniscus curvature, wherein the dimensionless Bond number includes a ratio between a force of gravity and a surface force; and calculating the force of gravity based on the Bond number. In some embodiments, the fluid height or the meniscus curvature is measured via at least one sensor proximate to the corner flow accelerometer device 100. In some embodiments, the at least one sensor includes an electrical sensor or an optical sensor.

[0081] In some embodiments, the Bond number is given by , where ρ is the density, g is the acceleration due to gravity, H is the characteristic meniscus height, and σ is the surface tension. In some embodiments, the Bond number based on the surface curvature is given by , where f is the surface curvature function, ρ is the density, g is the acceleration due to gravity, H is the characteristic meniscus height, and σ is the surface tension. In some embodiments, the Bond number based on curvature and column length is given by Definition, where f is the surface curvature function, It is the tip position ρ is the density, g is the acceleration due to gravity, H is the characteristic meniscus height, and σ is the surface tension.

[0082] In some embodiments, the Bond number of the system can be adjusted to adjust it to the appropriate acceleration range. o >1) will configure the system to indicate high gravity, characterized by a flat liquid surface (e.g., a liquid surface with low curvature) and minimal climb onto corners, and a small Bond number (B o <1) will cause the liquid to climb corners (e.g., liquid surfaces with low curvature). Variables such as surface tension and characteristic length can be selected so that the working gravity acceleration force B o 1, there is a chance that the ratio will become greater or less than 1 during gravity force fluctuations. In some embodiments, to achieve a desired Bond number, the gravity environment (g) and size (H) can be selected, and a material library can be searched to select a preferred liquid surface tension, and then a solid material that can be perfectly wetted by the liquid can be selected.

[0083] The corner 104 allows for significant capillary flow 103 at the solid surface and has a dimensionless closed-form solution for the case of perfect wetting (θ=0), which is applied to create a graph of the adaptive design. The governing equation below (Equation 2) captures the height, time, and friction components. (See Weislogel, MM Capillary Flow in an Interior Corner, 1996)

[0084]

[0085] The dimensionless Bond number is the ratio between the acting gravity force and the surface force, which can be directly incorporated into Equation 2 above:

[0086]

[0087] In some embodiments, for the case of α=30°, D=22.6 mm, and μ=2 cS designs, moving from g to μg changes the acceleration sense when reaching its new equilibrium position in 0.25 s. The liquid length can be easily predicted by the following formula:

[0088]

[0089] The meniscus curvature is the driving force for the rise in liquid height (h'), which can be adjusted by geometrically varying the number of sides (N) of the tube (see Weislogel 1998):

[0090]

[0091] To easily understand how the capillary flow accelerometer 100 will work, water can be deposited into a square or rectangular container with a hydrophilic surface. o>>1), most of the meniscus will be flat, but the edges can be observed to see that the curvature of the meniscus increases to accommodate the contact angle condition. When these edges meet at corner 104, as the curvature increases further, the effect of surface tension is seen to increase, which causes the liquid tip 103 to be higher than the flat meniscus and the liquid along the edge. This can be interpreted as a pressure gradient forced by the contact angle of the meniscus curvature balanced by hydrostatic pressure. If the tabletop exercise then enters a reduced gravity environment, the balance provided by the hydrostatic pressure will decrease and allow the liquid to climb further up corner 104. Concus and Finn mathematically solved these large capillary flows at internal corners. (See Concus, P.; Finn, R. On the behavior of a capillary surface in awedge. Proc Natl Acad Sci US A 1969, 63 (2), 292-299) For a surface to exist as a boundary with a contact angle, the conditions in formula 6 must be met, otherwise the surface becomes unbounded or does not exist at all. (See Concus, P.; Finn, R. On Capillary Free Surfaces in a Gravitational Field. Acta Mathematica 1974, 132 (none), 207-223)

[0092] θ<π / 2-α (6)

[0093] Where θ is the contact angle and α is the corner half angle. This will be called the Concus-Finn condition, which places the first requirement on the corner geometry. The goal of this disclosure is to provide the reader with general conditions and dimensionless parameters to create a roadmap for the design of a capillary flow accelerometer that meets their needs, such as to provide an indication of a specific range of gravitational acceleration. As shown below, an indicator made for use on the surface of the Earth will incorporate a geometry with a small α to provide sufficient capillary force. If the same material system is used in the Earth's orbit, α can be chosen to be higher because less capillary force is needed to balance with the hydrostatic pressure. (See Dong)

[0094] To provide the reader with general design requirements, the dimensionless governing formulas developed by Weislogel in his initial doctoral dissertation and subsequent follow-up with Lichter are used. (See Weislogel 1998) (See Weislogel 1996) Weislogel's work then expanded from sharp corner geometries to rounded corner geometries and how they relate to capillary flows in microgravity conditions. (See Ramé) (See Weislogel, MM Capillary Flow in Interior Corners: The Infinite Column. Physics of Fluids 2001, 13 (11), 3101-3107) (See Chen, Y., et al., Capillary-Driven Flows along Rounded Interior Corners. Journal of Fluid Mechanics 2006, 566, 235-271). In addition, geometries such as polygons and composite flows are proposed in cases where the system would be impaired by multiple wedges. (See Weislogel, M. Capillary Flow in Containers of Polygonal Section: Theory and Experiment. Theory and Experiment 2001, 26) (See Weislogel, MM Compound Capillary Rise. Journal of Fluid Mechanics 2012, 709, 622-647). For such complex geometries, numerical data on friction factors are usually required. In order to reduce the dependence on such data, a nondimensionalization scheme was included in Weislogel's work. (See Weislogel, MM; Chen, Y.; Bolleddula, D. A Better Nondimensionalization Scheme for Slender Laminar Flows: The Laplacian Operator Scaling Method. Physics of Fluids 2008, 20 (9), 093602) Most importantly, Weislogel's derivation was checked against experiments conducted in a microgravity environment, as this would be the environment in which a capillary flow accelerometer could be designed.(See Concus, P.; Finn, R.; Weislogel, M. Measurement of Critical Contact Angle in a Microgravity Space Experiment. Experiments in Fluids 2000, 28(3), 197-205) A pressure gradient is established along the corner in the wetting liquid due to the increased interfacial curvature. (See Weislogel 1996).

[0095] Internal corner flows derive their basis from related studies of capillary flows over wedges, edges, grooves, and holes in microgravity. (See Kovscek, AR; Radke, CJ Gas Bubble Snap-off under Pressure-Driven Flow in Constricted Noncircular Capillaries. Colloids and Surfaces A: Physicochemical and Engineering Aspects 1996, 117(1), 55-76) (See Concus, P. & Finn, R. 1990 Capillary surfaces in microgravity. In Low-Gravity Fluid Dynamics and Transport Phenomena.(ed.JNKoster&R.L.Sani)(See Progress in Astronauticsand Aeronautics,Vol.130,pp.183-204.AIAA)(See Mason,G.&Morrow,N.1991Capillarybehavior of a perfectly wetting liquid in irregular triangulartubes.J.Colloid Interface Sci.141,262-274) (see Langbein, D.1990The shape andstability of liquid menisci at solid edges.J.Fluid Mech.213,251-265)(See Wong,H.,Morris,S.&Radke,CJ1992Three-dimensional menisciin polygonalcapillaries.J.Colloid Interface Sci.148,317-336)

[0096] Early work established methods to solve the capillary problem, but it was only applicable to small containers with slow flow because of the assumptions of parallel flow and negligible inertia and stream curvature. (See Ransohoff 1988) (See Ransohoff, TC, Gauglitz, PA & Radke, CJ 1987 Snap-off of gas bubbles insmoothly constricted noncircular capillaries. AIChE J. 33, 753-765) After introducing the dimensionless Bond (B) which is the ratio of gravity to surface tension and the ratio of surface tension to inertia, respectively. o ) and Suratmen (Su) numbers directly challenge these early assumptions:

[0097]

[0098] where μ is the dynamic viscosity, ρ is the density, σ is the surface tension, H is the characteristic interface size, and g is the acceleration due to gravity. Su can be considered the Reynolds number of the capillary, where σ / μ is the capillary velocity. (See Ramé) In order to maintain significant capillary forces in the system, its characteristic interface size should scale with the capillary length, Pressure scaling is accomplished using the ratio of surface tension to characteristic interface dimensions and the xy plane curvature function (f). (See Weislogel 1996) When applied to microgravity, Su is scaled by 10 relative to surface gravity. 3 (See Dong, M. & Chatzis, I. 1995 The imbibition and flow of a wetting liquid along the corners of a square capillary tube. J. Colloid Interface Sci. 172, 278-288) Substituting this result into the viscous time scaling (t viscous ~ρH / μ), which is expected to increase by 10 relative to its surface gravity counterpart 6 (See Weislogel 1996) (See Weislogel 1998) basically show that corner flow will produce obvious characteristic length and timely response.

[0099]

[0100]

[0101] Table 3 presents a nondimensional approach for solving the corner flow problem while relating the general characteristic interface dimensions from Equations 7 and 8 to the height of the meniscus relative to the x-axis. As described herein in the nondimensional approach, prime numbers are used to represent dimensional terms. The velocity term is incorporated into the geometry (with α) through a balance of pressure and viscous forces. (See Weislogel 1996) To determine the position of the meniscus along the yz plane and time, passive covering film and no-slip conditions are assumed. The dimensionless parameters of Table 3 are then passed through the Navier-Stokes and continuity formulations. In addition, to supplement the analysis, the velocity, pressure, and meniscus position along the yz plane are consumed asymptotically based on the slenderness ratio. The resulting interface curvature, described by the magnitude of f, plays the role of the capillary driving force as shown in Equation 9 and depends on α and θ coupled into δ, where δ≡π / 2-α-θ. (See Weislogel 1996)

[0102] To perform the above steps, the conditions of symmetry around y = 0 and constant curvature (R' = fh', where R' is the dimensionless radius of curvature) are used. Most importantly, both the slender column and the slight curvature conditions are used during the design and must be maintained. 2 f<<1 ensures a slight curvature on the x-axis, and the slender column is defined as ∈ 2 <<1. (See Weislogel 1996) This approach is supplemented by the fact that the slender column condition has also been used for film profile flows in the case of ascending film flows and for moving film accelerations, etc., which are also solved with the Navier-Stokes scheme at low to moderate Reynold numbers. (See Kheshgi, HS Profile Equations for Film Flows at Moderate Reynolds Numbers. AIChE Journal 1989, 35(10), 1719-1727)

[0103]

[0104] where the sign of f indicates the direction of the driving force and hence the direction of the flow about the z axis, which occurs through a cross-sectional area governed by the cross-sectional area function which is derived geometrically and is given below. (See Weislogel 1996)

[0105]

[0106] Note that this function has The working range of the surface curvature function is characterized as a driving force by its influence on the pressure gradient of the corner flow. Weislogel combined Figure 4 The key design diagram for determining the corner angle is shown. (See Weislogel 1996) Note that under the condition of θ = 0 as considered herein, the curvature parameter becomes δ≡π / 2-α and obeys the Concus-Finn condition in the range 0<δ<π / 2.

[0107] The resulting governing equations 11 and 12 show that the velocity of the liquid depends on the slope of the meniscus. (See Weislogel 1996) Consistent with the above solution and supported by experiments for square capillaries, it should be noted that the velocity of the liquid also varies with the square root of the tube size. (See Dong 1995) More generally, the structures of Equations 11 and 12 also apply to unstable-nonlinear heat fluxes by conduction. (See Mayer, FJ; McGrath, JF; Steele, JWA Class of Similarity Solutions for the Nonlinear Thermal Conduction Problem. J. Phys. A: Math. Gen. 1983, 16 (14), 3393-3400)

[0108]

[0109] Conveniently, the meniscus height h(t,z) becomes the focus of the control equation and is also one of the key metrics to aid in the indication. i ) also plays a role as it is the focus of the numerical method to solve this problem. To incorporate the solution obtained by Ransohoff-Radke for the dimensionless flow resistance (β) and Ayyaswamy numerical solution for the dimensionless friction factor (K), equations 13 and 14 can be used respectively:

[0110]

[0111] In the case of rectangular, triangular and trapezoidal cross-section laminar flows, there are also mathematical estimates of the strip friction factor by scaling the 2D Laplacian operator with errors between 3% and 7%. (See Weislogel 2008) For tan 2 (α)<<1, {(π / 2-α) 2 <<1&δ 2 <<1}, hydraulic diameter equivalent, θ=α=π / 4 and {θ=π / 3 & α=π / 6}, there are complementary asymptotic solutions for the strip friction factor. (See Weislogel 1996) Both numerical data and analytical methods have their conditions, so for the original geometric design, they can only be used as starting estimates to be refined by testing such a design.

[0112] When the bubbles are axisymmetric, their shape is independent of θ. The transition of bubble symmetry is located at Ca~0.1. (See Kolb, WB; Cerro, RL The Motion of Long Bubbles in Tubes of Square Cross Section*. Physics of Fluids A: Fluid Dynamics 1993, 5(7), 1549-1557) Oh is the time scaling ratio for the surface tension force to recover to viscosity. When high frequency disturbances are of concern, Oh can be a useful design metric because Oh 2 <<1 The system will be underdamped and Oh 2 >>1 The system is damped by viscous forces: (see Weislogel 1996)

[0113]

[0114] Dimensionless Boussinesq viscosity (Bo η ) represents the surface viscous dissipation. At small angles, viscous forces become dominant. (See Ransohoff)

[0115]

[0116] Design parameters include surface tension, viscosity, liquid density, number of wedges, container radius and height. Flow resistance is a function of surface viscosity, corner angle, contact angle and corner roundness. Surface viscosity can increase flow resistance by up to 4 times. Reducing the surface flow area increases flow resistance, for example, a higher degree of corner roundness will result in increased flow resistance. (See Ransohoff) Smaller systems are less sensitive to inertial disturbances. In some embodiments, additional internal curved walls are used to make it round while ensuring the slender column condition.

[0117] A large reservoir will produce a set of solutions that tend to be similar to the solutions of the classical experiment for immersing the end of a capillary in a liquid pool. In these experiments, the infinite volume assumption can be applied, and the results show that its size changes. On the other hand, the geometry is also introduced from infinite volume to finite volume, and any reservoir designed will therefore be used as a competitive capillary. A method to solve the reservoir problem can be completed as a whole with the formula presented in this article, but it can also be divided into two problems. Since the reservoir does not have to be used as an indicator, it is not limited to perfectly wetting the gas / liquid / solid system, nor is it limited to applying the slender column requirement, providing additional design freedom. Although under zero gravity, the two capillary forces can be directly related to produce the corner liquid length, under gravity, the hydraulic pressure gradient introduced by gravity must be considered, and therefore the connected reservoir position is considered. In the simplest case, the large reservoir is located at the bottom (closer to the center of gravity relative to the indicating surface), with a large single sphere hydrophobic surface, and the resulting liquid column length should match the above-mentioned classical results. This is consistent with previously listed studies on friction factors, suggesting that the geometry and liquid:vapor ratio of the accelerometer containers discussed herein can be tailored for visual interpretation without substantially sacrificing functionality, as long as the available surface area for liquid climb is kept constant.

[0118] The key convenience is the simplicity of such an indicator both in use and potential manufacture. The device can be equipped with an electrical sensor or an optical sensor. The phenomenon of surface tension balancing the pressure of liquids and gases can be miniaturized and is expected to work better at a smaller scale.

[0119] The surface settling time is proportional to the response time. In some embodiments, the maximum response time from g to μg is about 4 seconds.

[0120] Dimensionless:

[0121] dimension:

[0122] In some embodiments, the oil comprises PDMS-EO diblock copolymer surfactant-poly(dimethylsiloxane-b-ethylene oxide) (bcp) 0.0 Conc. bcp mmol / L in water having a 50 / 50 or 40 / 60 mass ratio with ethylene.

[0123]

[0124] Individual gas phase bubbles may be broken by inertial interference, which should be managed. This starts with ensuring that the surface is wetted to prevent bubbles from adhering through the contact line and utilizing the defoaming properties of silicon. (See Aziz, T., et al. Modified Silicone Oil Types, Mechanical Properties and Applications. Polym. Bull. 2019, 76 (4), 2129-2145) Geometrically, the design needs to avoid contraction of the liquid path because breakage of the gas thread (elongated bubbles) may occur. (See Kovscek) However, if the device is large enough, it is possible that two or more bubbles in the local equilibrium position are at a certain distance from each other. Although this is not a problem for the indicating surface under negligible gravity, once gravity is introduced, a single bubble should be restored. From a design perspective, corner flow geometries such as smooth square capillaries inherently assist faster bubble transport by ensuring a thicker liquid film between the gas and the solid surface. (See Bico, J.; Quéré, D. Rise of Liquids and Bubbles in Angular Capillary Tubes. Journal of Colloid and Interface Science 2002, 247(1), 162-166) (See Bico, J.; Tordeux, C.; Quéré, D. Rough Wetting. EPL 2001, 55(2), 214) In the case of sealed square capillaries filled with silicone oil, the experimental results show consistency with the geometry-adjusted Poiseuille law:

[0125] V b =(4.8*10 -5 D 2 ρg)η (22)

[0126] Among them, V b , ρ, g, η are the bubble velocity, liquid density, gravitational acceleration, and liquid viscosity, respectively. The velocity of the bubble can be zero when the liquid / gas interface does not have enough energy to deform from its ideal spherical shape to continue moving forward. To intuitively understand when a bubble is trapped, refer to the classic cylindrical capillary example solved by Bretherton. (See Bretherton, Francis Patton. The motion of long bubbles in tubes. Journal of Fluid Mechanics 1961, 10 (2) 166-188)

[0127] r<0.918κ-1 (twenty three)

[0128] Where, the capillary length κ is equal to When the conditions are met, the bubble is stuck, but from a design point of view, a more flexible general description of the bubble would be useful. The dimensionless parameters related by Kolb and Cerro describe the contribution of gravity, viscous forces, and capillary forces (Formulas 22-24) to the evolution of a long asymmetric bubble film in a downward flow in a square capillary tube. (See Kolb, WB; Cerro, RL The Motion of Long Bubbles in Tubes of Square Cross Section. Physics of Fluids A: Fluid Dynamics 1993, 5 (7), 1549-1557)

[0129]

[0130] where the pressure gradient in the z direction is given by the bubble radius R s Or the asymptotic bubble radius R s∞ The dimensionless local flow coefficient (ψ) describes the local flow distribution. Kolb shows the solution of the local flow distribution. (See Kolb, WB; Cerro, RL Film Flow in the Space between a Circular Bubble and a Square Tube. Journal of Colloid and Interface Science 1993, 159 (2), 302-311) Most importantly, Equation 24 provides a balance between the capillary pressure, momentum and gravity from the bubble at the angle of the square capillary, while utilizing scalable dimensionless terms. (See Kolb 1993) A similar balance is seen in the above formula, but from the perspective of the liquid, the two angles are ultimately consistent in some respects. For example, by setting the internal bubble reference pressure to zero, the pressure can be related to the curvature of the curved liquid surface that drives the corner flow, so that an understanding of the corner flow can be obtained from Equation 24.

[0131] In another embodiment, an accelerometer device for gravity reduction applications includes: a closed bounded volume forming an interior cavity having at least one solid surface; at least one fluid within the cavity; wherein the fluid includes particles in suspension; and wherein at least one of the fluid and the particles in suspension has an intrinsic material property that is responsive to gravity.

[0132] In one embodiment, the intrinsic material property responsive to gravity is surface energy in nature. In one embodiment, the intrinsic material property responsive to gravity is electrostatic in nature. In one embodiment, the solid, fluid and / or suspended material forming the gravity measurement system is dielectric in nature, and the fluid contains particles in a range of magnitudes where the surface-dominated electrostatic forces are greater than the mass-proportional inertial forces, which facilitates particle aggregation proportional to the reduced gravity environment. In one embodiment, the suspension contains dielectric particles, the dielectric particles contain semiconductor quantum dot materials of nanoscale size, whereby particle aggregation in a reduced gravity environment promotes quenching of quantum dot photoluminescence.

[0133] In summary, the reduced gravity corner flow indication is essentially distinct, fast and passive. The overall design has the potential to be scaled down and integrated into digital systems in the future. Future indicating surfaces could include wedges and fins, as foundational work already exists for such geometries. Most importantly, a 360° indicating surface design that does not require a gyroscopic body would be an ideal next step.

[0134] Experimental Example

[0135] The present invention is now described with reference to the following examples. These examples are provided for illustrative purposes only, and the present invention should in no way be construed as being limited to these embodiments, but rather should be construed to encompass any and all variations that become evident as a result of the teaching provided herein.

[0136] Without further description, it is believed that one of ordinary skill in the art can use the foregoing description and the following illustrative examples to make and use the present invention and practice the claimed methods. Therefore, the following working examples specifically point out exemplary embodiments of the present invention and should not be construed as limiting the remainder of the present disclosure in any way.

[0137] A device similar to that shown in Figure 1 was prototyped. The motion of positioning the accelerometer to obtain a reading of gravity was accomplished by a double-walled transparent gyroscope body. A transparent lubricant was placed between the walls to facilitate movement. Once positioned, the silicone oil was ready to begin reaching its new equilibrium position to indicate. In this prototype design, the wall depth was 6.1 mm, and the column travel length was 16 mm, and the chamber was filled with silicone oil of viscosity 5 cS. Now, if the accelerometer were to enter a free fall (as in a drop tower experiment), an unsteady state indication would be reached in about 2 seconds. This is consistent with both the theory and the drop tower experiment presented in this article. The error between theory and experiment was always less than 10%. The 2 second mark is for the liquid column to first reach its equilibrium height in an unsteady state, after which there may be oscillatory behavior that is viscous damping before reaching a stable state at the 16 mm mark.

[0138] Figure 2is a graph showing the general capillary characteristic geometric response (H) in dependence on gravity according to some embodiments. Note the high slope magnitude under reduced gravity, which is an ideal mechanism for reduced gravity applications.

[0139] Figure 3 is a graph showing that corners provide a significant response relative to classical capillary action according to some embodiments.

[0140] The initial geometric flexibility in the variation of the number of sides N was explored. The resulting cross-sectional shape of the tube is symmetrical on both axes and polygonal due to the requirements of the current theoretical model. Due to these constraints, the number of sides in the current model controls the corner angles. As the number of corners increases, the tube cross section becomes round, causing it to become a classical capillary ( Figure 3 ). During the design phase, the dimensioned characteristic height under constant height conditions can be calculated using Formula 25:

[0141]

[0142] The chamber shape dictates the average meniscus curvature It is the driving force of the system acting in pressure balance. The 2-axis symmetry condition is derived from the use of the mean curvature formula 26, where Ω is the cross-sectional area, an increase of which will reduce the curvature and therefore the driving force:

[0143]

[0144] When N reaches infinity, Equations 25-26 describe the capillary. In this case, the average meniscus curvature can be simplified and described by Equation 27:

[0145]

[0146] Figure 3 The length of the liquid column over time is compared to the case of an infinite reservoir, which shows the indicated benefit of using a corner rather than a circular tube. Also shown is an example of hypothetical liquid behavior in a wedge, which is not fully integrated into theoretical models at present, but some basic work has been done to demonstrate the possible benefits of utilizing them. To illustrate the benefits, the infinite reservoir case was chosen to examine the well-known capillary rise in a circular tube, which has historically been performed by immersing a long capillary column in a large pool.

[0147] While comparisons are made with classical capillary devices to show how the corners are inherently beneficial, the time response of the liquid at constant volume is of greater interest. The modeling of the liquid settling into its new equilibrium position upon a step change in acceleration is described in both dimensionless and dimensional form in Equations 28-29 (the latter of which has been constructed through empirical correlations):

[0148]

[0149] The above formula is strictly applicable to a cylindrical container with no corners and perfect wetting (θ = 0), but it does provide insight into the response time for designs with corners. Figure 3 It is seen that the corner design is enlarged relative to the barrel design without changing the nature of the response, so understanding is gained.

[0150] Figure 2 The characteristic response is shown as a function of the square root of surface tension divided by density and gravity. The basis of the characteristic response is a Dow Corning l =913kg / m 3 and γ = 0.0197 N / m provided by polydimethylsiloxane (PDMS, silicone oil). In addition to the specific materials used, Figure 2 The point is to show that once gravity is reduced, the corner flow accelerometer will be inherently sensitive to gravity. This is an example of a highly scaled characteristic with capillary length. In order to obtain a more specific understanding of the liquid length response (dimensioned along the z-axis) rather than the general characteristic (dimensionless along the x-axis), the Weislogel and Litcher similarity solution can be referenced. The similarity solution is derived from the governing equation 11, and with the imposition of a constant volume condition and a step change to negligible gravity at t=0, the result is shown in equation 30 below.

[0151] To gain an intuitive understanding of how Equation 30 applies, reference is made to the drop tower experiment performed by Wieslogel and Litcher.

[0152]

[0153] The results of Wieslogel and Litcher show the displacement of the meniscus between an initially flat and a steady state, and the damping effect of the viscosity increase, where low viscosity shows oscillatory behavior before reaching a steady state, and high viscosity is overdamped and requires additional time to converge to a steady state value.

[0154] Upon a step change in gravity, the surface will settle to its new equilibrium position, but if gravity is negligible, the solution for the semi-infinite column will not converge. For a finite column with negligible gravity, the fluid will climb to the top of the chamber and then distribute itself in the corners perpendicular to the z-axis. Specifically, the liquid isolates the gas from the walls. Therefore, for negligible gravity, it is worth exploring the problem from the perspective of the bubble as well.

[0155] Individual gas phase bubbles may be disrupted by inertial disturbances and this should be managed. This starts with ensuring wetted surfaces to prevent bubbles from adhering through contact lines and taking advantage of the silicone defoaming properties.

[94] Geometrically, the design needs to avoid constrictions in the liquid path, since gas thread breakage (elongated bubbles) may occur.

[84] If the device is large enough, a situation may arise where two or more bubbles are at some distance from each other in a local equilibrium position. While this is not a problem for the indicating surface under negligible gravity, a single bubble should be restored once gravity is introduced. From a design perspective, corner flow geometries such as smooth square capillaries inherently assist faster bubble transport by ensuring a thicker liquid film between the gas and the solid surface. [83，95] In the case of a sealed square capillary filled with silicone oil, the experimental results show consistency with the geometry-adjusted Poiseuille's law described in Equation 22.

[0156] The design control parameters from the above model have been identified as the surface tension, density, viscosity, reduced surface viscosity of the liquid, and the dimensions of the chamber (such as corner angles, side lengths and height, etc.). Due to the use of perfect wetting conditions, the contact angle has not been included in the list. This condition allows the calculation of the moving contact line to be skipped, and the contact line interacts with the heterogeneous surface of the wall. In principle, a uniform surface can be applied, as well as applying the contact angle as an additional control parameter, but such a requirement will burden the manufacturer, and then the burden will be passed on to the user via the price tag of the increased price. In addition, the maintenance of the uniform surface will add an additional maintenance burden and reduce the life of the accelerometer. The moving contact line will also expose the surface to trapped bubbles. On the other hand, in the case of complete wetting, there are both more available theories and more empirical experiments that can be relied on. In order to meet both the complete wetting conditions and low cost, it was decided to use an acrylic chamber with silicone oil.

[0157] When silicone oil is used, its surface tension can be manipulated with additives such as surfactants. Surface tension enhances the equilibrium curvature of the meniscus as shown in Equation 26 for the average meniscus curvature. This parameter also feeds directly into the Bond number, which is also present in the governing Equation 26. Increasing the surface tension increases the height of the equilibrium position of the liquid and vice versa. Ultimately, surface tension opposes gravity. Another aspect of the interaction is density, which works with gravity because of its effect on mass. Both are used to establish a pressure gradient that ultimately dictates the equilibrium conditions. Due to complete wetting, the surface tension of the solid is not included.

[0158] Viscosity plays a key role in the damping of the liquid position response, where increasing viscosity increases the degree of damping. Although the surface viscosity (also known as the Boussinesq surface) is reduced, the dimensionless approach to this problem requires shear viscosity.

[0159] The corner angle (controlled here by the number of sides N) is the key metric. Figure 4 It is shown how the corner angle directly affects both the curvature and the cross-sectional flow area function. The curvature controls the strength of the response and the cross-sectional area controls the speed of the response, as higher cross-sectional areas allow for larger flow rates along the channel. This is key not only to the system, but also to the indication capability of the accelerometer, as indication is done by looking at the liquid column length. In this body of work, the possible corner angle increments are locked by N-sided polygons with 2-axis symmetry conditions, but future improvements to the liquid curvature model will allow for greater flexibility. This is not a distant dream, as the basis for wedges, rounded corners and fins, as well as other irregular shapes, already exist.

[0160] The length of the channel will dictate the indicated distance. Keeping everything else constant, increased length will allow for improved indication of reduced gravity. Together with the wall depth (length of the wall measured from corner to corner), the two parameters dictate the size of the accelerometer. An increase in the size of the accelerometer will result in more inertial control, while a decrease in size will cause surface forces to become more dominant.

[0161] Figure 4 is a graph showing the geometric dependence of the corner driving force according to some embodiments. Curvature (f) and cross-sectional flow function (F A ) Both for corner geometries varying from top to bottom with α = 72°, 60°, 45°, 30°, 15° and 10°. The dashed lines show the limits of both functions due to the conditions used. (See Weislogel 1996)

[0162] Computing Environment

[0163] In some aspects of the invention, software that executes the instructions provided herein may be stored on a non-transitory computer-readable medium, wherein when the software is executed on a processor, some or all of the steps of the invention are performed.

[0164] Aspects of the present invention relate to algorithms executed in computer software. Although some embodiments may be described as being written in a specific programming language, or executed on a specific operating system or computing platform, it should be understood that the system and method of the present invention are not limited to any specific computing language, platform, or combination thereof. The software executing the algorithm described herein may be written, compiled, or explained in any programming language known in the art (including but not limited to C, C++, C#, Objective-C, Java, JavaScript, MATLAB, Python, PHP, Perl, Ruby, or Visual Basic). It should also be understood that elements of the present invention may be executed on any acceptable computing platform (including but not limited to servers, cloud instances, workstations, thin clients, mobile devices, embedded microcontrollers, televisions, or any other suitable computing devices known in the art).

[0165] Portions of the present invention are described as software running on a computing device. Although the software described herein may be disclosed as operating on one particular computing device (e.g., a dedicated server or workstation), it should be understood that in the art, software is portable in nature, and for purposes of the present invention, most software running on a dedicated server may also run on any of a wide range of devices including desktop or mobile devices, laptops, tablet computers, smart phones, watches, wearable electronic devices or other wireless digital / cellular phones, televisions, cloud instances, embedded microcontrollers, thin client devices, or any other suitable computing device known in the art.

[0166] Similarly, portions of the present invention are described as communicating over various wireless or wired computer networks. For purposes of the present invention, the terms "network," "networked," and "networking" are understood to encompass wired Ethernet, fiber optic connections, wireless connections including any of the various 802.11 standards, cellular WAN infrastructure (such as 3G, 4G / LTE, or 5G networks), (Bluetooth), Low Energy (BLE) or A communication link, or any other method by which one electronic device can communicate with another electronic device. In some embodiments, elements of the networking portion of the present invention may be implemented via a virtual private network (VPN).

[0167] Figure 5 The following discussion is intended to provide a brief general description of a suitable computing environment in which the present invention may be implemented. Although the present invention is described above in the general context of program modules executed in conjunction with an application program running on an operating system on a computer, those skilled in the art will recognize that the present invention may also be implemented in combination with other program modules.

[0168] Typically, program modules include routines, programs, components, data structures, and other types of structures that perform specific tasks or implement specific abstract data types. In addition, it will be appreciated by those skilled in the art that the present invention can be practiced with other computer system configurations, including handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers, etc. The present invention can also be practiced in a distributed computing environment, where tasks are performed by remote processing devices linked through a communication network. In a distributed computing environment, program modules can be located in local and remote memory storage devices.

[0169] Figure 5 An illustrative computer architecture for computer 500 is depicted for practicing various embodiments of the present invention. Figure 5 The computer architecture shown illustrates a conventional personal computer, including a central processing unit 550 ("CPU"), a system memory 505 (including random access memory 510 ("RAM") and read-only memory ("ROM") 515), and a system bus 535 that couples the system memory 505 to the CPU 550. A basic input / output system, containing the basic routines that help transfer information between elements within the computer, such as during startup, is stored in the ROM 515. The computer 500 also includes a storage device 520 for storing an operating system 525, applications / programs 530, and data.

[0170] The storage device 520 is connected to the CPU 550 through a storage controller (not shown) connected to the bus 535. The storage device 520 and its associated computer-readable media provide non-volatile storage for the computer 500. Although the description of computer-readable media contained herein refers to a storage device (such as a hard disk or CD-ROM drive), it should be understood by those skilled in the art that computer-readable media can be any available media that can be accessed by the computer 500.

[0171] By way of example and not limitation, computer readable media may include computer storage media. Computer storage media include volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storing information such as computer readable instructions, data structures, program modules or other data. Computer storage media include, but are not limited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid-state memory technology, CD-ROM, DVD or other optical storage, cassettes, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer.

[0172] According to various embodiments of the present invention, the computer 500 may operate in a networked environment using logical connections to remote computers through a network 540, such as a TCP / IP network (such as the Internet or an intranet). The computer 500 may be connected to the network 540 through a network interface unit 545 connected to the bus 535. It should be understood that the network interface unit 545 may also be used to connect to other types of networks and remote computer systems.

[0173] The computer 500 may also include an input / output controller 555 for receiving and processing input from a plurality of input / output devices 560, including a keyboard, mouse, touch screen, camera, microphone, controller, joystick, or other types of input devices. Similarly, the input / output controller 555 may provide output to a display screen, printer, speaker, or other types of output devices. The computer 500 may be connected to the input / output device 560 via a wired connection (including, but not limited to, optical fiber, Ethernet, or copper wire) or wirelessly (including, but not limited to, Bluetooth, near field communication (NFC), infrared, or other suitable wired or wireless connections).

[0174] As briefly mentioned above, a plurality of program modules and data files may be stored in the storage device 520 and RAM 510 of the computer 500, including an operating system 525 suitable for controlling the operation of the networked computer. The storage device 520 and RAM 510 may also store one or more applications / programs 530. In particular, the storage device 520 and RAM 510 may store applications / programs 530 for providing various functions to the user. For example, the applications / programs 530 may include many types of programs, such as word processing applications, spreadsheet applications, desktop publishing applications, database applications, game applications, Internet browsing applications, email applications, messaging applications, and the like. According to an embodiment of the present invention, the applications / programs 530 include multi-function software applications for providing word processing functions, slide presentation functions, spreadsheet functions, database functions, and the like.

[0175] In some embodiments, the computer 500 may include various sensors 565 for monitoring the environment around the computer 500 and the environment inside the computer 500. These sensors 565 may include a global positioning system (GPS) sensor, a light sensor, a gyroscope, a magnetometer, a thermometer, a proximity sensor, an accelerometer, a microphone, a biometric sensor, a barometer, a humidity sensor, a radiation sensor, or any other suitable sensor.

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[0244] The disclosure of each patent, patent application and publication cited herein is incorporated herein by reference in its entirety. Although the present invention has been disclosed with reference to specific embodiments, it is apparent that other embodiments and variations of the present invention may be conceived by those skilled in the art without departing from the true spirit and scope of the present invention.

Claims

1. An accelerometer device for use in reduced gravity applications, comprising: a sealed capillary having a first end and a second end and a length between the first end and the second end, the capillary forming an interior cavity including at least one interior surface; wherein the capillary tube is partially filled with a capillary fluid; and Wherein the capillary comprises at least one corner extending along at least a portion of the length at an edge of the at least one interior surface, the at least one corner being configured to enhance capillary flow.

2. The device according to claim 1, wherein: The at least one corner is at an intersection between two or more interior surfaces.

3. The device according to claim 1, wherein: The capillary tube is anchored to a weight within the gyroscope body.

4. The device according to claim 1, wherein: The capillary is transparent or translucent.

5. The device according to claim 1, wherein: The interior surface includes an indicator surface.

6. The device of claim 1 further comprising at least one wedge or fin secured to the interior surface.

7. The device according to claim 1, wherein: The at least one corner is in the range of 1 to 1000 corners.

8. The device according to claim 1, wherein: The capillary comprises an n-gonal prism, a square prism, a rectangular prism, a triangular prism, a pentagonal prism, a hexagonal prism, an octagonal prism, a trapezoidal prism or a polygonal prism.

9. The device according to claim 1, wherein: The cross-section of the lumen of the capillary tube includes a square, a rectangle, a parallelogram, a rhombus, a trapezoid, an irregular trapezoid, a rhombus, a triangle, a curved triangle, a teardrop, a crescent, a pentagon, or a polygon.

10. The device according to claim 1, wherein: The capillary fluid includes a polar liquid including water or ethanol, or a non-polar liquid including silicone oil.

11. The device according to claim 1, wherein: The capillary fluid has a volume of 1 pL to 1000 mL.

12. The device according to claim 1, wherein: The capillary comprises at least one of: a ceramic with high intrinsic wetting properties, a glass ceramic with tunable wetting properties, a borosilicate glass, titanium dioxide, silicon dioxide, a polymer with high intrinsic wetting properties, a polymer with tunable wetting properties, an acrylic resin, an epoxy resin, polyethylene, polystyrene, polyvinyl chloride, polytetrafluoroethylene, polydimethylsiloxane, polyester and polyurethane.

13. The device according to claim 1, wherein: The capillary has a length ranging from 1 μm to 50 m, a width ranging from 1 nm to 1 m, a height ranging from 1 nm to 1 m, and an internal volume ranging from 1 μL to 10 L.

14. An accelerometer system for use in reduced gravity applications, comprising: The accelerometer device of claim 1; at least one sensor proximate to the accelerometer device, the at least one sensor configured to measure fluid height or meniscus curvature due to capillary flow in the accelerometer device; as well as A computing system communicatively connected to the at least one sensor, the computing system comprising a processor and a non-transitory computer-readable medium storing instructions that, when executed by the processor, perform steps comprising: Calculating a dimensionless Bond number based on the measured fluid height or meniscus curvature, wherein the dimensionless Bond number includes a ratio between a force due to gravity and a surface force; as well as The force of gravity is calculated based on the Bond number.

15. The system of claim 14, wherein: The at least one sensor comprises an electrical sensor or an optical sensor.

16. The system of claim 14, wherein: The system is configured to measure gravitational acceleration forces in the range of 0 g to 5 g, where g is equal to 9.8 m / sec 2 .

17. A method for monitoring gravity acceleration, comprising: Providing the accelerometer device of claim 1; Measuring fluid height or meniscus curvature due to capillary flow; Calculating a dimensionless Bond number based on the measured fluid height or meniscus curvature, wherein the dimensionless Bond number includes a ratio between a force due to gravity and a surface force; as well as The force of gravity is calculated based on the Bond number.

18. The method according to claim 17, wherein: The fluid height or meniscus curvature is measured via at least one sensor proximate to the corner flow accelerometer device.

19. The method according to claim 18, wherein: The at least one sensor comprises an electrical sensor or an optical sensor.

20. The method according to claim 17, wherein: The Bond number is given by Defined as, where ρ is the density, g is the acceleration due to gravity, H is the characteristic meniscus height, and σ is the surface tension.

21. An accelerometer apparatus for use in reduced gravity applications, comprising: A closed bounded volume forming an interior cavity having at least one solid surface; at least one fluid within the chamber; wherein the fluid comprises particles in suspension; and Wherein at least one of the fluid and the particles in suspension has an intrinsic material property that is responsive to gravity.

22. The device according to claim 21, wherein The intrinsic material property that responds to gravity is essentially surface energy.

23. The device according to claim 21, wherein The intrinsic material properties that respond to gravity are electrostatic in nature.

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