Accelerometer for Microgravity Applications

Abstract

The corner flow accelerometer device for microgravity includes a capillary tube, the capillary tube is partially filled with a capillary fluid, and the capillary tube includes at least one corner configured to enhance the capillary flow. The corner flow accelerometer device for microgravity includes a hollow regular quadrangular prism including the capillary tube, the regular quadrangular prism is partially filled with a capillary fluid including silicone oil, and the regular quadrangular prism is fixed to a weight in the gyroscope body. The gravity monitoring method includes providing the above-described corner flow accelerometer device, measuring the height of the fluid or the meniscus curvature by the capillary flow, calculating a dimensionless Bond number based on the measured height of the fluid or the meniscus curvature, the dimensionless Bond number includes the ratio of gravity to surface force, and calculating gravity based on the Bond number.

Description

Technical Field

[0001] This application claims priority to U.S. Provisional Application No. 63 / 336,564, filed Apr. 29, 2022, which is incorporated herein by reference in its entirety.

Background Art

[0002] The quantitative measurement of the acceleration due to gravity (g) has long been of scientific interest in a wide range of physical sciences, such as metrology (the scientific study of measurement), geophysics (a branch of the earth sciences dealing particularly with physical processes and phenomena occurring within the earth and its vicinity), and geodesy (the science of measuring the size, shape, rotation, and orientation of the earth in space). For example, in metrology, the value of g affects the measurement of force or physical quantities including standard forces such as the ampere and pressure, and thus its accuracy affects the accuracy of standard units in many metrological fields including mechanics, electronics, thermodynamics, and fluid dynamics. On the other hand, geophysics and geodesy mainly focus on the variations in gravity that change depending on location and at a given time, due to the rotation of the earth, the deviation of the earth's surface from an equipotential spheroid, and density fluctuations occurring within the earth.

[0003] To support the growing field of geodesy, generally known as gravimetry, numerous gravity measuring devices have been developed over the past few centuries, mainly based on how gravity interacts with mass. These gravimeters include gravimeters that function in an absolute mode, such as those that use falling objects or pendulums to measure time (or period) and length to determine g, and gravimeters that function in a relative mode, such as devices that use a mass-spring system, where the force applied to a test mass changes in response to fluctuations in the gravitational field, and attention is paid to the corresponding small fluctuations in weight, or these small changes in gravity are detected by the displacement of the mass (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).

[0004] To measure the strength of the gravitational field, many versions of gravimeters have been developed, such as the zero-length spring design using metal or quartz springs, the virtual spring feedback design replacing the magnetic levitation spring element, and the gradiometer for measuring the gradient or spatial rate of change of the components of the gravitational field (see Chapin, D., Gravity Instruments: Past, Present, Future, The Leading Edge, January, 1998).

[0005] Gravitational measurement devices, such as absolute and relative gravimeters, have significant limitations and drawbacks because they depend on the extensive property of matter, i.e., mass. Gravimeters are relatively bulky, not easily portable, require a controlled temperature environment, and have an expensive and complex design with an essential non-linearity and trade-off that make it technically difficult and challenging to achieve high-precision, accurate, and reproducible measurements of g under field conditions (see Krasnow, US 2, 303, 845, 1942; Carter, W.E. et al, New Gravity Meter Improves Measurements, Eos, Vol.75, No.8, February 22, 1994).

[0006] Therefore, it is necessary to develop a new type of gravity measurement device that can overcome many of the drawbacks of conventional gravimeters that mainly depend on the extensive properties of substances. Instead, it is necessary to develop a gravity measurement device that depends on the intensive properties of substances and only depends on the type of substance in the sample, rather than the amount of substance. Such a new type of gravity measuring instrument goes far beyond the field of physical science that uses conventional gravity measurement systems and provides new functions and applications across a wide range of industrial fields, basic research, applied research, and even the needs of health dose measurement. For example, for civilian manufacturers who can benefit on the ground by reducing defects in materials such as optical fibers and by studying the microgravity acceleration environment, as seen in the presence of the active black isolation system installed on the ISS (see Volfson, L.; Starodubov, D. Fiber Optic Manufacturing in Space. US20170233282A1, August 17, 2017), (see Dubbs, C. Realizing Tomorrow the Path to Private Spaceflight; Outward odyssey; University of Nebraska Press: Lincoln, 2011). Also, recent findings from studies conducted on astronauts exposed to microgravity for long periods in space indicate that there is a dose-response relationship for exposure to extreme gravity environments that can benefit from new gravity dose measurement 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).

[0007] In the current technology, due to the lack of design requirements necessary for such applications, in this technical field, there is a need for improved systems, devices, and methods that can utilize intensive properties such as surface tension among the intensive properties of substances. Such properties form the basis of new gravity measurement technologies and applications such as corner flow accelerometers for measuring the decrease in gravity (see Liu, Y-M et al, The Possibility of Changing the Wettability of Material Surface by Adjusting Gravity, AAAS Research Volume 2020, Article ID 2640834; Love, S.G., Particle Aggregation in Microgravity: Informal Experiments on the International Space Station, Meteroritics & Planetary Science 49 Nr 5, 732-739(2014)).

SUMMARY OF THE INVENTION

[0008] Some embodiments of the invention disclosed herein are shown below, and other embodiments can be defined by any combination of these embodiments (or a part thereof).

[0009] Accordingly, the present invention is directed to improved gravity measurement methods, devices, and systems that substantially avoid one or more limitations and drawbacks of the related prior art.

[0010] According to one or more embodiments of the present invention, there is provided a container with a sealed boundary that forms a finite-sized lumen containing at least one fluid or suspension fluid containing particles having at least one element with at least one solid surface and having inherent material properties that respond to gravity.

[0011] In one aspect, a sealed capillary tube having a first end, a second end, and a long portion therebetween, the capillary tube forming a lumen including at least one inner surface, the capillary tube being partially filled with a capillary fluid, the capillary tube including at least one corner running along at least a portion of the long portion at an end of at least one inner surface configured to facilitate capillary flow.

[0012] In one embodiment, at least one corner is at an intersection between two or more inner surfaces.

[0013] In one embodiment, the capillary tube is fixed to a weight within a gyroscope body.

[0014] In one embodiment, the capillary tube is transparent or translucent.

[0015] In one embodiment, the inner surface includes an indicating surface.

[0016] In one embodiment, the device further comprises at least one wedge or fin attached to the inner surface.

[0017] In one embodiment, at least one corner is in the range of 1 to 1000 corners.

[0018] In one embodiment, the capillary tube includes an n-sided prism, a square prism, a prism, a triangular prism, a pentagonal prism, a hexagonal prism, an octagonal prism, a trapezoidal prism, or a polygonal prism.

[0019] In one embodiment, the cross-section of the lumen of the capillary tube includes a square, a rectangle, a parallelogram, a diamond, a trapezoid, a rhombus, a triangle, a curved triangle, a teardrop, a crescent, a pentagon, or a polygon.

[0020] In one embodiment, the capillary fluid includes a polar liquid containing water or ethanol, or a non-polar liquid containing silicone oil.

[0021] In one embodiment, the capillary fluid has a volume ranging from 1 pL to 1000 mL.

[0022] In one embodiment, the capillary tube includes at least one of ceramic having high inherent wetting properties, glass ceramic having adjustable wetting properties, borosilicate glass, titanium dioxide, silica, polymer having high inherent wetting properties, polymer having adjustable wetting properties, acrylic, epoxy, polyethylene, polystyrene, polyvinyl chloride, polytetrafluoroethylene, polydimethylsiloxane, polyester, and polyurethane.

[0023] In one embodiment, the capillary tube 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 10 L.

[0024] In another aspect, a corner flow accelerometer system for microgravity applications includes the corner flow accelerometer device described above, at least one sensor proximate to the corner flow accelerometer device configured to measure the height of the fluid or the meniscus curvature due to capillary flow within the corner flow accelerometer device, and a computing system communicatively connected to the at least one sensor, the computing system including a processor and a non-transitory computer-readable medium storing instructions that, when executed by the processor, perform steps of calculating a dimensionless Bond number based on the measured height of the fluid or the meniscus curvature, the dimensionless Bond number including a ratio between gravity and surface force, and calculating gravity based on the Bond number.

[0025] In one embodiment, the at least one sensor includes an electrical sensor or an optical sensor.

[0026] In one embodiment, the system is configured to measure the acceleration due to gravity in the range of 0 g to 5 g (g = 9.8 m / sec 2 ²).

[0027] In another aspect, a method for monitoring the acceleration due to gravity includes providing a corner flow accelerometer device as described above, measuring the height of a fluid or the meniscus curvature due to capillary flow, calculating a dimensionless Bond number based on the measured height of the fluid or the meniscus curvature, where the dimensionless Bond number includes the ratio between gravity and surface force, and calculating gravity based on the Bond number.

[0028] In one embodiment, the height of the fluid or the meniscus curvature is measured via at least one sensor proximate to the corner flow accelerometer.

[0029] In one embodiment, the at least one sensor includes an electrical sensor or an optical sensor.

[0030] In one embodiment, the Bond number is

Equation

[0031] In another aspect, a corner flow accelerometer device for microgravity includes a hollow regular prism or prism including a capillary tube, the prism being partially filled with a capillary fluid including silicone oil, and the prism being fixed to a pendulum within a gyroscope body.

[0032] In another aspect, an accelerometer device for microgravity includes a container with a sealed boundary forming a lumen having at least one solid surface, and at least one fluid within the lumen, the fluid including suspended particles, and at least one of the fluid and the suspended particles having a characteristic material property that responds to gravity.

[0033] In one embodiment, the characteristic material property that responds to gravity is surface energy.

[0034] In one embodiment, the characteristic material property that responds to gravity is electrostatic properties.

[0035] In one embodiment, the solid, fluid, and / or suspended material forming the gravity measurement system is a dielectric, and the fluid includes particles of a size in a range that is advantageous for particle aggregation in proportion to the reduction of the gravity environment, where the surface-dominant electrostatic force is greater than the mass-proportional inertial force.

[0036] In one embodiment, the suspended particles include dielectric particles including nanoscale semiconductor quantum dot material, whereby aggregation of the particles in an environment with reduced gravity promotes quenching of the photoluminescence of the quantum dots.

Brief Description of the Drawings

[0037] The foregoing objects and features, as well as other objects and features, will become apparent by reference to the following description and the accompanying drawings. These drawings are described to provide an understanding of the present invention and form a part of this specification, and in these drawings, like numerals represent like elements, and in the following drawings, like numerals represent like elements.

Fig. 1A

Fig. 1B

Fig. 2

Fig. 3

Fig. 4

Fig. 5

[0038] It should be understood that the figures and descriptions of the present invention are simplified to explain related elements for a clearer understanding of the present invention, while excluding many other elements found in the system and method of the corner flow accelerometer for microgravity for the purpose of clarity. Those skilled in the art will be able to recognize that other elements and / or steps are desirable and / or necessary in practicing the present invention. However, such elements and steps are well known in the art and do not contribute to a better understanding of the present invention, so discussions regarding such elements and steps are not provided herein. The disclosure herein is directed to all such variations and modifications to such elements and steps known to those skilled in the art.

[0039] Unless otherwise defined, all technical and scientific terms used in this specification shall have the same meaning as commonly understood by one of ordinary skill in the art to which this 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.

[0040] As used herein, each of the following terms has the meaning associated therewith in this section.

[0041] The articles "a" and "an" are used herein to refer to one or more (i.e., at least one) of the grammatical objects of the article. By way of example, "an element" means one element or more than one element.

[0042] As used herein, "about" when referring to a measurable value such as an amount, a duration, etc. means including variations of ±20%, ±10%, ±5%, ±1%, ±0.1% from a particular value, and such variations are appropriate.

[0043] With respect to ranges, throughout this disclosure, various aspects of the invention can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as a rigid limitation on the scope of the invention. Where appropriate, a description of a range should be considered to specifically disclose not only the individual numerical values within that range but also all possible sub-ranges. For example, a description of a range such as from 1 to 6 should be considered to specifically disclose 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., as well as the individual numerical values within that range, such as 1, 2, 2.7, 3, 4, 5, 5.3, 6. This applies regardless of the breadth of the range.

[0044] The nomenclature used in this specification is defined in Table 1 below.

Table 1

[0045] In one embodiment, the capillary flow accelerometer discussed herein is ideal for meeting the need for a low-cost assistive device that can be easily interpreted visually. It is similar to a spirit level in fulfilling that purpose on the ground.

Number

[0046] In 1805, Thomas Young published Equation (1), which describes the contact angle (θ) resulting from the balance of forces given by three phases meeting at a point where the surface tensions of solid-vapor, solid-liquid, and liquid-vapor are represented by γ s , γ SL , and, γ L respectively. Although elegant, Equation (1) has sparked debate, and this balance of forces has been reexamined from the perspective of energy minimization and from a thermodynamic perspective that treats surface tension as surface energy.

[0047] Due to scientific progress in recent nanoscale research, the validity of Young's equation itself has been scrutinized, and the debate has not subsided (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, E. N., et al., Uni-Directional Liquid Spreading on Asymmetric Nanostructured Surfaces. Nature materials 2010, 9 (5), 413-417), (see Demirel, M. C., 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).

[0048] In particular, regarding the relationship between gravity and the Young's contact angle, it has been found through microgravity experiments in both drop towers and parabolic arc flights that gravity actually significantly contributes to the contact angle up to a 5 μL droplet (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 Reduced Gravity. 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 Solid Substrates. Microgravity Sci. Technol. 2012, 24 (3), 181-188), (see Calvimontes, A. The Measurement of the Surface Energy of Solids by Sessile Drop Accelerometry. Microgravity Sci. Technol. 2018, 30 (3), 277-293).

[0049] Even for a microdroplet of about 1 μL with an analytical small-gradient solution,

Number

[0050] In fact, in order to apply the knowledge related to the moving contact line, the conditions of a smooth, flat, and chemically homogeneous surface must be maintained until the life of the accelerometer ends, which would impose an excessive burden on both the manufacturer and the user (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 hurdles, what is disclosed herein is a material system that completely wets the interior of the display surface, where θ = 0. This allows calculations related to stress singularities and contact line pinning to be ignored, substantially making the display surface less prone to corrosion over its service life and enabling the use of inexpensive chemically inhomogeneous materials.

[0051] To provide an equilibrium state that can be interpreted as a display, it is useful to identify potential sources of force that balance gravity. Some of these sources of force that can be used to balance gravity include van der Waals interactions, including short-range electromagnetic forces between molecules and / or atoms, electrical double-layer overlap, including electrical interactions due to the overlap of electrical double layers around particles having only neutral charges, steric interactions of adsorbed polymers, including short-range interactions due to the overlap of adsorbed polymer layers on particles, ridge forces, including the formation of polymer binders and / or surfactant bridges between particles, hydration forces, including the overlap of hydrogen-bonded water molecules on hydrophilic surfaces of particles, and depletion, including negative absorption of solutes and polymers due to a lower affinity of the solvent for the surface than for the bulk (see Hosokawa M, Naito M, Nogi K, Yokoyama T. Nanoparticle Technology Handbook [Internet]. Saint Louis, NETHERLANDS, THE: Elsevier; 2012).

[0052] Table 2 below shows some examples of the basic categories of possible adaptation mechanisms. While these categories may be available for display by themselves, the most ideal solutions are likely to involve combinations of these categories. For example, in this embodiment, the solution focuses only on the inner surface, but by suspending quantum dots in a liquid that fills the corners, a more improved display can be achieved. In such a scenario, the quantum dots provide visual feedback for display and introduce additional surface forces and mass available to the system, as well as additional phenomena that can be used for measurement purposes such as electrostatic aggregation. The categories in Table 2 can be clearly mixed and matched to find solutions, but it should also be noted that in some categories, multiple mechanisms are already essentially employed, so implementation may not be easy. For example, gravity perception in biology can utilize mechanical membrane strain as a stimulus for membrane ion transport and serve as an indicator for cells. In both examples, adding quantum dots to corner flow or biological cell membranes poses the challenge of complexity. As complexity increases, it becomes difficult to theoretically elucidate composite mechanisms. In the face of such difficulties, the solution would rely on an empirical approach, but since the empirical approach also has scalability limitations, it is not suitable for adaptive design.

Table 2

[0053] An ideal system is highly sensitive, adaptable, operates in real-time, is robust, has a long lifespan, is inexpensive, requires no maintenance, and is simple. Mechanical gravity monitoring systems include ceramics, quartz, springs, MEMS, etc. Electromagnetic gravity monitoring systems include superconducting materials, levitation, magnetic fluids, cold atom interferometers, piezoresistors, superconducting materials, etc. Thermal / electrostatic / dynamic gravity monitoring systems include temperature-controlled surface tension, phase separation, sedimentation. Internal surface gravity monitoring systems include wetting and capillary applications. External surface gravity monitoring systems include particles. Quantum gravity monitoring systems include atom interferometers, phonons in zero-temperature superfluids, etc. Optical gravity monitoring systems include pressure-sensitive materials and reflective oblique deposition films. Living body gravity monitoring systems include gravity perception in flagellates and plants, membrane ion channels, adaptation of the cytoskeleton and exoskeleton, etc.

[0054] The internal surface gravity monitoring system meets the conditions of being highly sensitive, adaptable, operating in real-time, being robust, having a long lifespan, being inexpensive, requiring no maintenance, and being simple.

[0055] The mechanical spring accelerometer with the reference mass connected via a spring is perhaps the most intuitively starting example. It is a theoretically simple and already proven concept, and is a concretization in one embodiment of the Italian Spring Accelerometer (ISA). Its high accuracy reaches up to 3×10 -8 (m / s 2 ) and is shown by the ability to characterize the interior of exoplanets through gravity anomalies (see Santoli, F., et al., ISA, a High Sensitivity Accelerometer in the Interplanetary Space. Space Sci Rev 2020, 216 (8), 145).

[0056] The prior research is extensive. Historically, regarding capillary flow, a numerical approach has been emphasized for contrast with the non - numerical aggregation method presented by Weislogel (see Weislogel, M. M.; Ross, H. D. Surface Settling in Partially Filled Containers upon Step Reduction in Gravity, 1990). P.S. Ayyaswamy et al. studied the laminar flow in grooves and constructed the basis of capillary flow in negligible - gravity corners by solving the friction coefficient (see Ayyaswamy, P. S., et al., Capillary Flow in Triangular Grooves. Journal of Applied Mechanics 1974, 41 (2), 332 - 336). Dong et al. investigated the capillary rise at the corners based on Ayyaswamy's research as a function of liquid viscosity, surface tension, contact angle, the size of the whole tube, and the roundness of the corners (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). The study of non - circular porous flow has also contributed. In particular, Ransohoff and Radke applied the Galerkin finite - element method to quantify the dimensionless flow resistance and obtained an application value similar to the friction coefficient (see Ransohoff, T. C., 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 influence of this initial research has been demonstrated by the application of the flow resistance value in the reverse case of bubbles rising in a liquid-filled prism, as studied by Bico and Quere (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 study of non-circular pores using the flow resistance value was carried out by A.R. Kovscek et al., where gravity was included in the calculation as a term giving a simple pressure gradient (see Kovscek, A. R., 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).

[0057] Finally, the research paper by Weislogel laid the foundation for corner ascent in a gravity-free state in 1996 and was applied to the present disclosure (see Weislogel, M. M. Capillary Flow in an Interior Corner, NASA Technical Memorandum 107364, 1996). Further, in 1998, Weislogel and Litcher, and in 2009, Rame and Weislogel contributed to this model (see Weislogel, M. M.; Lichter, S. Capillary Flow in an Interior Corner. Journal of Fluid Mechanics 1998, 373, 349-378), (see Rame, E.; Weislogel, M. M. Gravity Effects on Capillary Flows in Sharp Corners. Physics of Fluids 2009, 21 (4), 042106). Closed-form dimensionless analytical solutions for the liquid column tip position and velocity are generated. These solutions, especially those for a constant volume, can be directly adopted for the display under negligible gravity.

[0058] Referring now to the drawings in detail, like reference numerals designate like parts or elements throughout the several views, and in various embodiments, presented herein is a system and method for a corner flow accelerometer for low gravity applications.

[0059] According to one or more embodiments of the present invention, there is provided a container with a sealed boundary forming a lumen of finite dimensions having at least one solid surface and a lumen containing at least one fluid or suspension fluid including particles having at least one material element with inherent material properties responsive to gravity.

[0060] Figures 1A-1B illustrate an exemplary capillary-based corner flow accelerometer device 100 for microgravity applications, according to some embodiments. It is an exemplary design of a corner flow accelerometer comprising a capillary tube 101 (e.g., with a number of corners N = 4, etc.) (e.g., made of acrylic, etc.) partially filled with a liquid 102 (e.g., silicone oil, etc.), but any suitable shape, volume, and / or number of corners N 104 can be utilized. In some embodiments, the capillary tube 101 is shown to be fixed to an optional weight 107 inside an optional gyroscope body 106 and is configured to align the capillary tube 101 with the center of gravity in the vicinity. The capillary tube 101 within the gyroscope body 106 can be configured similar to a floating compass where the capillary tube 101 is disposed inside the gyroscope body 106. The gyroscope body 106 can be of any suitable type including a classical gyroscope body having three circular frames and three sets of hinges, a gyroscope such as a compass as shown in FIG. 1A, and / or a sphere filled with liquid. In some embodiments, the friction of the gyroscope hinges needs to be weakened in proportion to the weight of the liquid and the gravitational force to be detected. As used herein, "corner" and "edge" are used interchangeably to describe embodiments of the corner flow accelerometer device, with "edge" being used to describe the shape of the device and "corner" being able to be used to describe the inner portion of the edge shape where an increase in capillary action occurs.

[0061] In some embodiments, the microgravity corner flow accelerometer device 100 includes a sealed capillary tube 101 having a first end and a second end and a long portion therebetween, the capillary tube 101 forming a lumen having at least one inner surface 105, the capillary tube 101 being partially filled with a capillary fluid 102, and the capillary tube 101 including at least one corner 104 extending along at least a portion of the long portion at an end of at least one inner surface 105 configured to facilitate a capillary flow 103.

[0062] In some embodiments, at least one corner 104 is at an intersection between two or more inner surfaces 105. In some embodiments, the capillary tube 101 is fixed to a pendulum within a gyroscope body. In some embodiments, the capillary tube 101 is transparent or translucent. In some embodiments, the inner surface 105 includes a display surface. In some embodiments, the device 100 further includes at least one wedge or fin attached to the inner surface 105. In some embodiments, the at least one corner 104 is in the range of 1 to 1000 corners.

[0063] In some embodiments, the capillary tube 101 includes an n-sided prism, a square prism, a prism, a triangular prism, a pentagonal prism, a hexagonal prism, an octagonal prism, a trapezoidal prism, or a polygonal prism, any enclosed bounded volume, or any other suitable shape, or combinations thereof. In some embodiments, the capillary tube 101 includes a cylinder or sphere having a triangular wall. In some embodiments, the capillary tube 101 includes a sphere having ribbed or wedge-shaped walls. In some embodiments, the capillary tube 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 tube 101 includes a wedge-shaped surface. In some embodiments, the cross-section of the lumen of the capillary tube 101 includes a square, rectangle, parallelogram, diamond, trapezoid, rhombus, triangle, curved triangle, teardrop, crescent, pentagon, polygon, or any other suitable shape, or combinations thereof. Further exemplary cross-sections are shown in FIG. 1B, the example of which is detailed in Weislogel et al. (see Weislogel MM. Compound capillary rise. Journal of Fluid Mechanics. 2012 Oct;709:622-47). In some embodiments, the capillary tube 101 includes a ceramic having high intrinsic wetting properties, a glass ceramic having adjustable wetting properties (contact angle < 90 degrees) (e.g., borosilicate glass, titanium dioxide, silica, etc.), a polymer having high intrinsic wetting properties, or a polymer having adjustable wetting properties (contact angle < 90 degrees) (acrylic, epoxy, polyethylene, polystyrene, polyvinyl chloride, polytetrafluoroethylene, polydimethylsiloxane, polyester, polyurethane, etc.).In some embodiments, the capillary tube 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 10 L.

[0064] In some embodiments, the capillary tube 101 includes a container surrounded by a sphere having wedge-shaped walls and / or walls divided into flat surfaces with corners therebetween. This is a 3D shape that can exhibit gravity without the need for a gyroscope body. As shown in FIG. 2, the same principle applies to the sphere as the liquid rises along the corners as the gravitational acceleration decreases, and the bubbles move further away from the walls 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]). When the contact angle is 0 (θ = 0, completely wet surface), the droplet spreads infinitely along the rounded or sharp interior 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 sealed container, a floating surface that is not angled with respect to the wall can be used as the space of the minimum distance between the floating surface and the container wall that rises due to the liquid (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 assist in the display of microgravity can be found in Weislogel et al. Some embodiments include floating walls and / or floating shapes such as spheres and polygons. Examples include a tapered rectangular container (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), regular n-gons, rectangles, combinations of rounded rectangles, optionally equal-edge liquid contact parts, combinations of sharp corners and rounded corners, re-entrant parts, vane structures, and irregular polygons (see Weislogel MM. Compound capillary rise. Journal of Fluid Mechanics. 2012 Oct; 709: 622-47).

[0065] In some embodiments, the capillary fluid 102 includes either a polar liquid (e.g., water, ethanol) or a non-polar liquid (e.g., silicone oil). In some embodiments, the capillary fluid includes a volume of 1 μL to 10 L. In some embodiments, the capillary tube 101 and the capillary fluid 102 include any suitable combination of solids and liquids that create a liquid contact surface.

[0066] In some embodiments, a corner flow accelerometer system for microgravity includes the above-described corner flow accelerometer device 100, at least one sensor proximate to the corner flow accelerometer device configured to measure the height of a fluid or the meniscus curvature due to capillary flow within the corner flow accelerometer device 100, and a computing system communicatively coupled to the at least one sensor, the computing system including a processor and a non-transitory computer-readable medium storing instructions, which when executed by the processor, perform steps of calculating a dimensionless Bond number based on the measured height of the fluid or the meniscus curvature, the dimensionless Bond number including a ratio between gravity and surface forces, and calculating gravity based on the Bond number. In some embodiments, the at least one sensor includes an electrical sensor or an optical sensor. In some embodiments, the system is configured to measure gravitational acceleration in the range of 0 g to 5 g (g = 9.8 m / sec 2 ).

[0067] In some embodiments, a gravitational acceleration monitoring method includes providing a corner flow accelerometer device 100 as described above, measuring the height of a fluid or the meniscus curvature due to capillary flow, calculating a dimensionless Bond number based on the measured height of the fluid or the meniscus curvature, the dimensionless Bond number including a ratio between gravity and surface forces, and calculating gravity based on the Bond number. In some embodiments, the height of the fluid 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.

[0068] In some embodiments, the Bond number is defined by the following equation.

Equation

Equation

Equation

[0069] In some embodiments, the Bond number of the system can be adjusted to adjust to an appropriate acceleration range. A large Bond number (B o > 1) characterizes a high gravity, such that the system is configured to show a high gravity, as characterized by a flat liquid surface (e.g., low curvature of the liquid surface) and minimization of rise to the corners, while a small Bond number (B o < 1) results in a liquid that rises at the corners (e.g., low curvature of the liquid surface). Variables such as surface tension and characteristic length can be selected such that the ratio B o ~ 1 acts, giving the opportunity for the ratio to become greater than or less than 1 during gravity variations. In some embodiments, to reach the desired Bond number, the gravity environment (g) and size (H) can be selected, searched in a material library to select the preferred surface tension of the liquid, and then a solid material that is completely wetted by the liquid can be selected.

[0070] Corner 104 enables significant capillary flow 103 on the solid surface and has a dimensionless closed-form solution for the fully wetting (θ = 0) case applied to create a map for optimal design. The following governing equation (Equation (2)) includes height, time, and a friction component (see Weislogel, M. M. Capillary Flow in an Interior Corner, 1996).

Number

[0071] The dimensionless Bond number is the ratio of gravity to surface force and can be directly incorporated into the above Equation (2).

Number

[0072] In some embodiments, for a design with α = 30°, D = 22.6 mm, and μ = 2 cS, when moving from g to μg, the induced acceleration changes because it reaches a new equilibrium position in 0.25 s. The liquid length can be easily predicted as follows.

Number

[0073] The meniscus curvature is the driving force for the rise of the liquid surface height (h´) and can be geometrically adjusted by changing the number of sides (N) of the tube (see Weislogel 1998).

Number

[0074] To easily understand how the capillary flow accelerometer 100 functions, water can be placed in a square or rectangular container with a hydrophilic surface. Since gravity is dominant, most of the meniscus is flat (B 0≫1). To see how the meniscus curvature increases to meet the contact angle condition, the edges can be examined. When these edges meet at the corner 104, the curvature becomes even greater, and the liquid tip 103 rises higher than a flat meniscus or the liquid along the edge, resulting in an increased influence of surface tension. This can be interpreted as the contact angle strengthening the pressure gradient through the meniscus curvature that balances the hydrostatic pressure. If this tabletop experiment were conducted in an environment with reduced gravity, the balance due to hydrostatic pressure would decrease, and the liquid would rise further at the corner 104. Concus and Finn mathematically treated the large capillary flow inside the corner (Concus, P.; Finn, R. On the behavior of a capillary surface in a wedge. Proc Natl Acad Sci U S A 1969, 63 (2), 292 - 299). For a surface to be constrained by the contact angle, the condition of Equation (6) must be satisfied. Otherwise, the surface will either become unconstrained or simply cease to exist (see Concus, P.; Finn, R. On Capillary Free Surfaces in a Gravitational Field. Acta Mathematica 1974, 132 (none), 207 - 223), (see Concus, P.; Finn, R. On Capillary Free Surfaces in the Absence of Gravity. Acta Mathematica 1974, 132 (none), 177 - 198).

Number

[0075] To provide general design requirements to the reader, the dimensionless governing equations shown by Weislogel in his first doctoral thesis and subsequent joint research with Lichter are used (see Weislogel 1998), (see Weislogel 1996). And his research has spread from sharp corners to rounded corner shapes, revealing how they are related to capillary flow under microgravity conditions (see Rame), (see Weislogel, M. M. 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). Furthermore, shapes where the system includes multiple wedges, such as polygonal flows and compound flows, are also addressed (see Weislogel, M. Capillary Flow in Containers of Polygonal Section: Theory and Experiment. Theory and Experiment 2001, 26), (see Weislogel, M. M. Compound Capillary Rise. Journal of Fluid Mechanics 2012, 709, 622 - 647). For such complex shapes, numerical data of the friction coefficient is generally required. To reduce the dependence on such data, his research includes a nondimensionalization scheme (see Weislogel, M. M.; 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, his derived values have been checked against experiments conducted in a microgravity environment, which is the environment in which a capillary flow accelerometer might 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). As the curvature of the interface increases, a pressure gradient along the corners occurs in the wetting liquid (see Weislogel 1996).

[0076] The internal corner flow is based on the related research of capillary flows in wedges, edges, grooves, and pores under microgravity (see Kovscek, A. R.; Radke, C. J. 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), (Concus, P. & Finn, R. 1990 Capillary surfaces in microgravity. In Low-Gravity Fluid Dynamics and Transport Phenomena. (ed. J. N. Koster & R. L. Sani), (Progress in Astronautics and Aeronautics, Vol. 130, pp. 183-204. AIAA), (Mason, G. & Morrow, N. 1991 Capillary behavior of a perfectly wetting liquid in irregular triangular tubes. J. Colloid Interface Sci. 141, 262-274), (Langbein, D. 1990 The shape and stability of liquid menisci at solid edges. J. Fluid Mech. 213, 251-265), (Wong, H., Morris, S. & Radke, C. J. 1992 Three-dimensional menisci in polygonal capillaries. J. Colloid Interface Sci. 148, 317-336).

[0077] Initial studies established an approach to solve capillary problems, but it was only applicable to small, slow-flowing vessels because of the assumptions of parallel flow, negligible inertia, and streamline curvature (see Ransohoff 1988), (see Ransohoff, T. C., Gauglitz, P. A. & Radke, C. J. 1987 Snap-off of gas bubbles in smoothly constricted noncircular capillaries. AIChE J. 33, 753-765). By introducing the dimensionless Bond number (Bo) and Suratman number (Su), these initial assumptions were directly addressed.

Number

Number

Table 3

[0078] Table 3 shows a dimensionless approach to solving the corner flow problem while relating the general characteristic interface dimensions obtained from equations (7) and (8) to the meniscus height with respect to the x-axis. As explained in the dimensionless approach, the prime symbol is used to represent dimensional terms. The velocity terms incorporate the geometry (along with α) through the balance of pressure and viscosity. An inert upper film and a no-slip condition are employed to determine the position and time of the meniscus along the yz plane (see Weislogel 1996). Next, the dimensionless parameters in Table 3 are applied to the Navier–Stokes equations and the continuity equation. Further, as a supplement to the analysis, the velocity, pressure, and the position of the meniscus along the yz plane are asymptotically obtained with respect to the aspect ratio. The curvature of the interface represented by the magnitude of f serves the role of the capillary driving force as shown in equation (9), depends on α and θ, where θ is related to δ,

Number

[0079] To proceed with the above steps, the conditions that it is symmetric about y = 0 and that the curvature is constant (R´ = fh´, where R´ is the radius of curvature) are used. The most important thing is to use the conditions of a thin column and a small curvature, which must be maintained during the design. A small curvature in the X-axis direction is ensured for ε 2 when f ≪ 1. On the other hand, a thin column is for ε 2Defined as in [1] (see Weislogel 1996). Such an approach is complemented since the conditions of slender columns are also adopted for film profile flows in the case of rising liquid film flows and moving film accelerations, particularly solved using the Navier-Stokes method at low to moderate Reynolds numbers (see Kheshgi, H. S. Profile Equations for Film Flows at Moderate Reynolds Numbers. AIChE Journal 1989, 35 (10), 1719-1727).

Number

Number

[0080] The range of use of this function is

Number

Number

[0081] The resulting dominant equations (11) and (12) indicate that the liquid velocity depends on the meniscus slope (see Weislogel 1996). Consistent with the above solution and from experiments on square capillaries, it was noted that the liquid velocity is also proportional to the square root of the tube size (see Dong 1995). More generally, the structure of equations (11) and (12) can also be applied to non-linear unsteady heat fluxes by conduction (see Mayer, F. J.; McGrath, J. F.; Steele, J. W. A Class of Similarity Solutions for the Nonlinear Thermal Conduction Problem. J. Phys. A: Math. Gen. 1983, 16 (14), 3393-3400).

Number

Number

Number

[0082] The meniscus height h(t,z) is both a focus of the governing equations and one of the important measurement criteria useful for representation. Since the zonal flow resistance (F i ) was also the focus of the numerical approach to solving such problems, its role has become clear. The solution by Ransohoff and Radke of the dimensionless flow resistance (β) and the equations (13) and (14) of Ayyaswamy's dimensionless friction coefficient (K) can be used.

Number

Number

[0083] Mathematical estimations by scaling the two-dimensional Laplace operator also exist with an error of 3% to 7% for the strip friction coefficient in the case of laminar flow with rectangular, triangular, and trapezoidal cross-sections (see Weislogel 2008). Supplementary asymptotic solutions for the strip friction coefficient exist as follows,

Number

[0084] When the bubble is axisymmetric, its shape is independent of θ. The transition of bubble symmetry is at Ca ~ 0.1 (see Kolb, W. B.; Cerro, R. L. 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 scale ratio of the restoring force of surface tension to viscosity. When high-frequency disturbances are a problem, Oh becomes an effective design indicator, and Oh 2 ≪ 1. The system becomes underdamped, and Oh 2 ≫ 1 is damped by viscous forces (see Weislogel 1996).

Number

Number

Number

[0085] The dimensionless Busseinesq viscosity (Bo η ) represents surface viscous dissipation. At small angles, viscous forces are dominant (see Ransohoff).

Number

[0086] The design parameters include surface tension, viscosity, liquid density, number of wedges, radius of the container, and height. The flow resistance is a function of surface viscosity, corner angle, contact angle, and corner roundness. The surface viscosity increases the flow resistance by up to four times. Reducing the surface flow area increases the flow resistance. For example, increasing the corner roundness increases the flow resistance (see Ransohoff). Small systems are less affected by inertial disturbances. In some embodiments, an additional inner curved wall is used to make it round while ensuring the state of a thin column.

[0087] If there is a large reservoir, a solution with a similar tendency to the classical experiment of immersing the tip of a capillary tube in a liquid pool will be obtained. In these experiments, the assumption of infinite volume can be applied, and the results show that its size changes. On the other hand, changing from infinite volume to finite volume introduces a geometric shape, and as a result, the designed reservoir will function as a competing capillary. One approach to solving the reservoir problem can be carried out as a whole using the equations shown here, but it can also be divided into two problems. Since the reservoir does not need to function as an indicator, it is not limited to a completely wet gas / liquid / solid system, and since the requirements of a thin column do not apply, the degree of freedom in design increases. In the case of zero gravity, the two capillary forces are directly related to the liquid length at the contact angle, but in the case of gravity, the hydraulic pressure gradient caused by gravity must be considered, and the reservoir connection position also needs to be considered. As the simplest case, when a large reservoir with a large single spherical hydrophobic surface is located at the bottom (a position closer to the center of gravity), the length of the liquid column should be consistent with the aforementioned classical results. This is consistent with the existing research on the friction coefficient, and the shape of the accelerometer container and the liquid-to-vapor ratio discussed here can be adjusted to be easily interpretable by the naked eye without fundamentally sacrificing the function as long as the available surface area for the liquid to rise is constant.

[0088] An important convenience is that both the use and potential manufacture of such an indicator are simple. Electrical sensors or optical sensors can be attached to this device. The phenomenon of surface tension that balances the pressures of the liquid and gas can be miniaturized and is expected to function better on a smaller scale.

[0089] The surface sedimentation time is proportional to the response time. In some embodiments, the maximum response time from g to μg is about 4 seconds.

Number

Number

[0090] In some embodiments, the oil contains PDMS-EO diblock copolymer surfactant - poly(dimethylsiloxane-b-ethylene oxide) (bcp) 0.0 Conc. bcp mmol / L in water with a mass ratio of ethylene to the oil of 50 / 50 or 40 / 60.

Number

[0091] Inertial perturbations can potentially split a single gas-phase bubble. This begins by ensuring a wetted surface to prevent the bubble from "sticking" through the contact line and preferably exploiting the anti-foaming properties of silicone (Aziz, T., et al. Modified Silicone Oil Types, Mechanical Properties and Applications. Polym. Bull. 2019, 76 (4), 2129-2145). In geometric designs, it is necessary to avoid constrictions in the liquid path because snap-off of a gas thread (elongated bubble) can occur (see Kovscek). However, such cases can occur when the device is large enough and two or more bubbles in local equilibrium positions are separated from each other. In a state where gravity can be ignored, even a single bubble should recover. From a design perspective, corner flow shapes such as smooth square capillary tubes essentially assist in the high-speed transport of bubbles by ensuring a thick liquid film between the gas and the solid surface (see Bico, J.; Quere, 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.; Quere, D. Rough Wetting. EPL 2001, 55 (2), 214). In the case of a sealed square capillary filled with silicone oil, the experimental results show agreement with geometrically adjusted Poiseuille's law.

Number

[0092] However, V b, ρ, g, and η are the bubble velocity, liquid density, gravitational acceleration, and liquid viscosity, respectively. When there is not enough energy for the interface between the liquid and gas to deform from an ideal spherical shape and proceed, the bubble velocity becomes zero. To gain an intuition for when a bubble is trapped, refer to the example of the classical cylindrical capillary tube solved by Bretherton (see Bretherton, Francis Patton. The motion of long bubbles in tubes. Journal of Fluid Mechanics 1961, 10 (2) 166 - 188).

Number

Number

Number

[0093] In other embodiments, an accelerometer device for microgravity comprises a sealed-bounded container forming a lumen having at least one solid surface and at least one fluid within the lumen, the fluid including suspended particles, and at least one of the fluid and the suspended particles having intrinsic material properties that respond to gravity.

[0094] In one embodiment, the intrinsic material property that responds to gravity is surface energy. In one embodiment, the intrinsic material property that responds to gravity is electrostatic properties. In one embodiment, the solid, fluid, and / or suspended material forming the gravity measurement system is a dielectric, and the fluid includes particles sized in a range where surface-dominated electrostatic forces are greater than mass-proportional inertial forces that favor particle aggregation in proportion to the microgravity environment. In one embodiment, the suspended particles include dielectric particles including semiconductor quantum dot material of nanoscale dimensions, whereby particle aggregation in the microgravity environment promotes quenching of quantum dot photoluminescence.

[0095] ​​​In conclusion, the microgravity corner flow display is basically remarkable, rapid, and passive. The overall design in the future may be reduced and integrated into a digital system. Since a substrate of such a shape already exists, wedges or fins may be included in the future display surface. Most importantly, it is the design of a 360-degree display surface that does not require a gyroscope body, which is the ideal next step.

[0096] Experimental Examples Next, the present invention will be 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 examples. Rather, it is intended to encompass any variations that become apparent as a result of the teachings in these examples.

[0097] Although further description is omitted, those skilled in the art would think that they can manufacture and utilize the present invention and implement the claimed method using the above description and the following exemplary examples. Therefore, the following 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 sense.

[0098] A device similar to the one shown in FIG. 1 was prototyped. The operation of positioning the accelerometer to read gravity was performed through a double-walled transparent gyro body. A transparent lubricant was placed between the walls to facilitate movement. Once placed, the silicone oil reaches a new equilibrium position and is ready to start displaying. In the design of this prototype, the depth of the wall is 6.1 mm, the moving length of the column is 16 mm, and the silicone oil with a viscosity of 5 cS fills this chamber. When this accelerometer enters free fall, it will exhibit an unsteady state in about 2 seconds, similar to the experiment in the drop tower. This is consistent with both the theory shown here and the drop tower experiment. The error between the theory and the experiment is always less than 10%. The 2 seconds is because the liquid column first reaches the equilibrium height in an unsteady state, and then there may be a vibrating behavior damped by viscosity before reaching the steady state at the 16 mm point.

[0099] FIG. 2 is a diagram showing the gravity dependence of the general capillary characteristic geometric response (H) according to some embodiments. Note the magnitude of the high gradient when gravity decreases. This is an ideal mechanism for microgravity applications.

[0100] FIG. 3 is a diagram showing that according to some embodiments, the corners result in a significant reaction to classical capillary action.

[0101] The initial geometric flexibility was examined with variations in the number N of sides. As a result, the cross-sectional shape of the tube is biaxially symmetric and polygonal according to the requirements of the current theoretical model. Due to such constraints, in the current model, the number of sides controls the angle of the corner. As the number of corners increases, the cross-section of the tube becomes circular, and as a result, it becomes a classical capillary tube (FIG. 3). At the design stage, the dimensional characteristic height under the condition of constant height can be calculated by Equation (25).

Number

[0102] The chamber shape is the mean meniscus curvature (

Number

Number

[0103] When N approaches infinity, equations (25) - (26) represent a capillary tube. In this case, the mean meniscus curvature is simplified and described by equation (27).

Number

[0104] Figure 3 shows a comparison of the liquid column length over time in the case of an infinite reservoir, demonstrating the advantage of using a rectangular tube instead of a circular tube. Currently, the wedge is not fully integrated into the theoretical model, but some basic research has been conducted and is sufficient to show the advantages of using the wedge. To explain the advantages, the case of an infinite reservoir was chosen to check the capillary rise in a known circular tube, which has historically been implemented by immersing a long capillary column in a large pool.

[0105] The comparison with classical capillary devices is made to show the specific advantages of how the corners are beneficial, but more interesting is the time response of the liquid under a constant volume. When the acceleration changes stepwise, the modeling for the liquid to settle to a new equilibrium position is described in both dimensionless and dimensional forms in equations (28) - (29), and the latter is constructed by an empirical correlation.

Number

Number

[0106] The above equation applies exactly to a cylindrical container without corners and completely wet (θ = 0), but provides insights into the response time of a design with corners. As can be seen in Figure 3, a cornered design provides insights because it is amplified relative to a cylindrical design without changing the nature of the response.

[0107] The characteristic reaction shown in Figure 2 is a function of the square root of the surface tension divided by the density and gravity. The characteristic response was based on polydimethylsiloxane (PDMS, silicone oil) provided by Dow Corning, with μ = 5 sC, ρ = 913 kg / ml 3 and γ = 0.0197 N / m. Except for the specific materials used, the points in Figure 2 show that the corner flow accelerometer becomes essentially sensitive to gravity once gravity decreases. This is an example of the scaling of the characteristic height by the capillary length. To obtain more specific insights about the liquid length response (dimension along the z-axis) rather than the general characteristics (nondimensional along the x-axis), the similar solutions of Wieslogel and Litcher can be referred to. The similar solutions are derived from the governing equation (11), and with the implementation of a constant volume condition and a step change to negligible gravity at t = 0, the results are shown in the following equation (30). Referring to the drop tower experiment conducted by Wieslogel and Litcher shows how equation (30) is applied.

Equation

[0108] In the results of Wieslogel and Litcher, the meniscus displaces between an initial flat state and a steady state, and also shows a damping effect due to an increase in viscosity. At low viscosities, it shows oscillatory behavior before reaching the steady state, and at high viscosities, it is too damped and requires more time to converge to the steady value.

[0109] When the gravity changes stepwise, the surface settles into a new equilibrium position. However, when gravity can be ignored, the solution for a semi-infinite column does not converge. In the case of a finite column where gravity can be ignored, the liquid rises to the roof of the chamber and then distributes to the corners perpendicular to the z-axis. Conclusively, the liquid isolates the gas from the wall. Therefore, in the case of negligible gravity, it is also valuable to view this problem from the perspective of gas bubbles.

[0110] Turbulence due to inertia can split a single gas-phase bubble, and it is necessary to manage this. This begins with ensuring the liquid-gas interface to prevent the bubbles from "sticking" through the contact line and preferably utilizing the defoaming properties of silicone.

[94] In geometric design, it is necessary to avoid narrowing of the liquid path because long and thin bubbles may bend.

[84] However, such a case may occur when the device is large enough and two or more bubbles at local equilibrium positions are at separated locations. In the range where gravity can be ignored, the surface showing the bubbles is not a problem, but when gravity is applied, a single bubble should recover. From a design perspective, a corner flow shape such as a smooth square capillary tube essentially aids in the high-speed transport of bubbles by ensuring a thick 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 are consistent with the adjusted Poiseuille's law as described in Equation (22).

[0111] From the above model, it was identified that the design control parameters are the surface tension, density, viscosity, reduced surface viscosity of the liquid, and the dimensions of the chamber such as the angle of the corner, the length of the side, and the height. The contact angle is not included in the list because the fully wet state is utilized. Under such conditions, the calculation of the moving contact line and the contact line interacting with the inhomogeneous surface of the wall can be omitted. In principle, it is also possible to apply a homogeneous surface and the contact angle as an additional control parameter, but such requirements would impose a burden on the manufacturer and be transferred to the user through a price increase. Furthermore, maintaining a homogeneous surface would increase the maintenance burden and shorten the lifespan of the accelerometer. Also, when the contact line moves, the surface will be exposed to bubbles. On the other hand, in the case of total wetting, more theories are available and more reliance can be placed on empirical experiments. In order to satisfy both the condition of total wetting and low cost, an acrylic chamber filled with silicone oil was used.

[0112] When using silicone oil, its surface tension can be manipulated with additives such as surfactants. The surface tension emphasizes the meniscus equilibrium curvature as shown in Equation (26) regarding the mean meniscus curvature. This parameter also directly affects the Bond number that governs Equation (26). When the surface tension increases, the height of the equilibrium position of the liquid increases, and vice versa. Ultimately, the surface tension acts against gravity. On the other hand, density acts with gravity due to the gravity acting on the mass. Both ultimately act to establish the pressure gradient that determines the equilibrium state. The surface tension of the solid is not included due to total wetting.

[0113] Viscosity plays an important role in the attenuation of the liquid's position response, and an increase in viscosity increases the degree of attenuation. For the reduced surface viscosity rate known as the Boussinesq surface, the shear viscosity rate is necessary for a dimensionless approach to the problem.

[0114] The angle of the corner is controlled here by the number of sides N and is an important indicator. Figure 4 shows that the corner angle directly affects both the curvature and the cross-sectional area. The curvature dominates the reaction intensity, and the cross-sectional area dominates the response speed. This is because the larger the cross-sectional area, the greater the flow velocity along the flow path. This is important not only for the system but also for the display ability of the accelerometer. In this study, the increment of the possible corner angle is fixed by an N-sided polygon with a biaxial symmetry condition, but in the future, by improving the curvature model of the liquid, more flexible responses will be possible. Since basic research already exists for wedges, rounded corners, fins, and other irregular shapes, this is not a distant dream.

[0115] The length of the flow path determines the display distance. Keeping all else constant, increasing the length enables a display with reduced gravity. Together with the wall depth (the length of the wall measured from corner to corner), these two parameters determine the size of the accelerometer. As the size of the accelerometer increases, inertial forces become dominant, and as it decreases, surface forces become dominant.

[0116] Figure 4 is a diagram showing the geometric dependence of the corner driving force according to several embodiments. The curvature function (f) and the cross-sectional flow function (F A ) when the shape of the corner is changed from the upper surface to the lower surface to α = 72°, 60°, 45°, 30°, 15°, and 10°. The dotted line indicates the limits of both functions according to the conditions used (see Weislogel 1996).

[0117] Computing Environment In one aspect of the present invention, the software that executes the instructions provided herein can be stored in a non-transitory computer-readable medium, and when this software is executed on a processor, it executes some or all of the steps of the present invention.

[0118] One aspect of the present invention relates to an algorithm executed by computer software. Certain embodiments may be described as being described by a particular computer program or as being executed on a particular operating system or computing platform, but it should be understood that the systems and methods of the present invention are not limited to a particular computing language, platform, or combination thereof. The software that executes the algorithms described herein can be described in any compiled or interpreted 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. Further, it is understood that the elements of the present invention can 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 system known in the art.

[0119] Part of the present invention is described as software operating on a computing system. Although the software described herein may be disclosed as operating on a particular computing system (e.g., a dedicated server or workstation), in the art, software is inherently portable and it is understood that most software operating on a dedicated server is also executable. Although it may be disclosed as operating on a dedicated server or workstation, software is inherently portable, and for the purposes of the present invention, most software operating on a dedicated server can also operate on any of a wide range of devices including desktop or mobile devices, laptops, tablets, smartphones, watches, wearable electronics or other wireless digital / cellular phones, televisions, cloud instances, embedded microcontrollers, client devices, or any other suitable computing system known in the art.

[0120] Similarly, various parts of the present invention are described as communicating via various wireless or wired computer networks. For the purposes of the present invention, the terms "network", "networked", and "networking" are understood to include 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®, Bluetooth® Low Energy (BLE), or Zigbee® communication links, or any other means by which one electronic device can communicate with another. In some embodiments, elements of the networked portions of the present invention can be implemented via a virtual private network (VPN).

[0121] FIG. 5 and the following description are intended to provide a brief and general description of a suitable computing environment in which the invention may be implemented. The invention is described in the general context of program modules that execute with application programs on an operating system on a computer, but those skilled in the art will recognize that the invention may also be implemented in combination with other program modules.

[0122] In general, program modules include routines, programs, components, data structures, and other types of structures that perform particular tasks or implement particular abstract data types. Further, those skilled in the art will understand that the invention may be implemented in other computer system configurations including handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers, and the like. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0123] FIG. 5 illustrates an exemplary computer architecture of a computer 500 for implementing various embodiments of the invention. The computer architecture shown in FIG. 5 depicts a conventional personal computer including a central processing unit 550 (the "CPU"), a system memory 505 including random access memory 510 (the "RAM") and read-only memory (the "ROM") 515, and a system bus 535 coupling the system memory 505 to the CPU 550. The basic input / output system containing basic routines that help transfer information between elements within the computer, such as during startup, is stored in the ROM 515. The computer 500 further includes a storage device 520 for storing an operating system 525, applications / programs 530, and data.

[0124] The memory device 520 is connected to the CPU 550 via a memory controller (not shown) connected to the bus 535. The memory device 520 and the associated computer-readable medium provide a non-volatile memory device for the computer 500. Although the description of the computer-readable medium included herein refers to a memory device such as a hard disk or a CD-ROM drive, those skilled in the art should understand that the computer-readable medium can be any available medium accessible by the computer 500.

[0125] In this embodiment, by way of non-limiting example, the computer-readable medium can include a computer storage medium. Computer storage media includes 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 includes, but is not limited to, RAM, ROM, EPROM, EEPROM, flash (registered trademark) memory or other semiconductor memory technologies, CD-ROM, DVD or other optical storage devices, magnetic cassettes, magnetic tape, magnetic disk storage devices or other magnetic storage devices, or other media that can be used to store the desired information and that are accessible by a computer.

[0126] According to various embodiments of the present invention, the computer 500 can operate in a network environment using a logical connection to a remote computer via a network 540 such as a TCP / IP network such as the Internet or an intranet. The computer 500 can be connected to the network 540 via a network interface unit 545 connected to the bus 535. It should be understood that the network interface unit 545 can also be used for connections to other types of networks and remote computer systems.

[0127] Computer 500 can also include an input / output controller 555 for receiving and processing inputs from a number 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 can provide outputs to a display screen, printer, speaker, or other types of output devices. Computer 500 can be connected to the input / output devices 560 via wired connections including, but not limited to, fiber optic, Ethernet®, copper wire, or wireless means including, but not limited to, Bluetooth®, Near Field Communication (NFC), infrared, or other suitable wired or wireless connections.

[0128] As briefly described above, the storage device 520 and the RAM 510 of the computer 500 can store a number of program modules and data files, including an operating system 525 suitable for controlling the operation of a network-connected computer. The storage device 520 and the RAM 510 can also store one or more applications / programs 530. In particular, the storage device 520 and the RAM 510 can store applications / programs 530 for providing various functionality to the user. For example, the applications / programs 530 can include many types of programs such as a word processing application, a spreadsheet application, a desktop publishing application, a database application, a game application, an Internet browsing application, an email application, a messaging application, and the like. According to one embodiment of the present invention, the applications / programs 530 are composed of a multi-functional software application for providing a word processing function, a slide presentation function, a spreadsheet function, a database function, and the like.

[0129] In some embodiments, computer 500 can include various sensors 565 for monitoring the environment surrounding computer 500 and the environment inside computer 500. These sensors 565 can include a global positioning system (GPS) sensor, a light sensor, a gyroscope, a magnetometer, a thermometer, a proximity sensor, an accelerometer, a microphone, a biosensor, a barometer, a humidity sensor, a radiation sensor, or any other suitable sensor.

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[0131] The disclosures of each patent, patent application, and publication cited herein are hereby incorporated by reference in their entirety. Although the invention has been disclosed with reference to specific embodiments, it is apparent that other embodiments and variations of the invention may be devised by those skilled in the art without departing from the true spirit and scope of the invention.

Claims

1. An accelerometer device for microgravity applications, A sealed capillary tube having a first end, a second end, and a long section therebetween, the capillary tube comprising a capillary forming a lumen with at least one inner surface, The capillary tube is partially filled with a capillary fluid, The capillary tube includes at least one corner extending along at least a portion of the long section at an end of at least one inner surface configured to facilitate capillary flow, Device.

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

3. The device according to claim 1, wherein the capillary tube is fixed to a pendulum within a gyroscope body.

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

5. The device according to claim 1, wherein the inner surface comprises a display surface.

6. The device according to claim 1, further comprising at least one wedge or fin attached to the inner 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 tube includes an n-sided prism, a square prism, a 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 diamond, a 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 containing water or ethanol, or a non-polar liquid containing silicone oil.

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

12. The capillary tube of the apparatus according to claim 1 includes at least one of ceramics having high intrinsic wetting properties, glass ceramics having adjustable wetting properties, borosilicate glass, titanium dioxide, silica, polymers having high intrinsic wetting properties, polymers having adjustable wetting properties, acrylic, epoxy, polyethylene, polystyrene, polyvinyl chloride, polytetrafluoroethylene, polydimethylsiloxane, polyester, and polyurethane.

13. The capillary tube of the apparatus according to claim 1 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 10 L.

14. An accelerometer system for microgravity applications, the accelerometer device according to claim 1, at least one sensor adjacent to the accelerometer device, the sensor being configured to measure the height of a fluid or the meniscus curvature due to capillary flow within the accelerometer device, a computing system communicatively connected to the at least one sensor, the computing system including a processor and a non-transitory computer-readable medium storing instructions, and when executed by the processor, calculating a dimensionless Bond number based on the measured height of the fluid or the meniscus curvature, the dimensionless Bond number including a ratio between gravity and surface forces, calculating gravity based on the Bond number, a computing system that performs a system comprising.

15. The system according to claim 14, wherein the at least one sensor includes an electrical sensor or an optical sensor.

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

17. A method for monitoring gravitational acceleration, providing the accelerometer device according to claim 1, measuring the height of a fluid or the meniscus curvature due to capillary flow, calculating a dimensionless Bond number based on the measured height of the fluid or the meniscus curvature, the dimensionless Bond number including a ratio between gravity and surface forces, calculating gravity based on the Bond number, a method comprising.

18. The method according to claim 17, wherein the height of the fluid or the meniscus curvature is measured via at least one sensor adjacent 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 bond number is 【Number 1】 defined 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, the method according to claim 17.

21. An accelerometer device for microgravity applications, a container with a sealed boundary forming a lumen having at least one solid surface, and at least one fluid within the lumen, wherein the fluid contains suspended particles, and at least one of the fluid and the suspended particles has an inherent material property that responds to gravity. Device.

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

23. The device according to claim 21, wherein the inherent material property that responds to gravity is electrostatic properties.

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