Method and device for estimating the surface tension of levitated droplets

Abstract

To provide a method and a device for estimating floating droplet surface tension, which enable accurate estimation of surface tension of a floating droplet using the flotation technique even when the floating droplet is not truly spherical due to an external force required for flotation.SOLUTION: A floating droplet surface tension estimation method for estimating surface tension of a floating droplet is provided, the method involving correcting surface tension derived on the basis of a vibration frequency of the floating droplet using a correction equation including variables based on an external force applied to the floating droplet.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for estimating the surface tension of a levitating droplet and an apparatus for estimating the surface tension of a levitating droplet. [Background technology]

[0002] The surface tension of molten metals is a physical property essential for materials development and the efficient smelting process. Because molten metals are generally high-temperature and highly reactive, measuring the surface tension using container-based methods is difficult. Therefore, containerless methods, such as the levitation method, have been developed. The levitation method generates levitated droplets by suspending molten metal as droplets. Known levitation methods include the gas jet levitation method, which levitates droplets by spraying a gas jet stream toward them, and the electromagnetic levitation method, which levitates droplets by applying a high-frequency magnetic field to them (Non-Patent Document 1). In measuring the surface tension of molten metals using this levitation method, the levitated droplets are assumed to be spherical, and the surface tension is calculated based on the vibration frequency of the levitated droplets. Furthermore, a simulation-based method using the SPH (Smoothed Particle Hydrodynamics) method and the MLS (Moving Least Square) method is known as a method for estimating the surface tension of high-temperature melts (Non-Patent Document 2). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Hidekazu Obata and 11 others, "Round Robin Test for Containerless Measurement of Surface Tension of Molten Platinum," 34th Symposium on Space Environment Utilization, 2019 [Non-patent document 2] Shungo Natsui and five others, "Numerical Analysis of High-Temperature Melt Interface and Dispersed Phase Behavior - Application of Smoothed Particle Hydrodynamics Method to Smelting Process Analysis -", ​​2019 The Mining and Materials Processing Institute of Japan, vol.135, No.8, 2019, pp.71-82 Summary of the Invention [Problem to be solved by the invention]

[0004] In the levitation method, the levitated droplets are assumed to be spherical and the surface tension of the droplets is estimated. However, because levitated droplets are subject to gravity, they are unlikely to become perfectly spherical. In particular, in the gas jet levitation method, which is one of the levitation methods, the levitated droplets are subjected to external forces from the gas jet airflow. Furthermore, the nozzle that sprays the gas jet airflow onto the levitated droplets obscures part of the levitated droplets, making it difficult to accurately grasp the overall shape of the levitated droplets. Therefore, an object of the present invention is to provide a surface tension estimation method and a surface tension estimation device that can accurately estimate the surface tension of levitated droplets using a levitation method, even when the shape of the levitated droplets is not spherical due to the external force required for levitation, as in the gas jet levitation method. [Means for solving the problem]

[0005] The inventors discovered that by correcting the surface tension calculated based on the vibration frequency of the levitating droplets using a correction formula based on the external force applied to the levitating droplets to levitate them, it is possible to accurately estimate the surface tension of the levitating droplets even if the shape of the levitating droplets cannot be accurately determined, and thus completed the present invention. Therefore, the present invention has the following aspects.

[0006] [1] A surface tension estimation method for estimating the surface tension of a levitated droplet that has been levitated by applying an external force to the droplet, wherein the surface tension calculated based on the vibration frequency of the levitated droplet is corrected using a correction formula based on the external force applied to the levitated droplet.

[0007] [2] The method for estimating the surface tension of levitated droplets according to [1], wherein the levitated droplets are levitated by a gas jet stream. [3] The method for estimating the surface tension of a levitated droplet according to [2], wherein the correction formula is an equation including the radius of curvature of the levitated droplet, the mass of the levitated droplet, the gravitational acceleration, and the surface area of ​​the levitated droplet to which the gas jet stream is applied. [4] A method for estimating the surface tension of a levitated droplet according to [3], wherein the surface area of ​​the levitated droplet is the area of ​​a portion of a cross section passing through the center of gravity of the levitated droplet that forms an arc with an angle of 80 to 85 degrees with the center of gravity as its vertex.

[0008] [5] A method for estimating the surface tension of a levitated droplet described in any one of [1] to [4], wherein the surface tension is a value calculated based on the vibration frequency of the levitated droplet measured by a vibration frequency measuring device. [6] A method for estimating the surface tension of a levitating droplet according to any one of [1] to [5], wherein the surface tension is a value calculated under conditions where the Bond number calculated by the following formula is 1 or less. Bond number = ρgL 2 / γ (where ρ is the density of the suspended droplets (unit: kg / m 3 ), g represents the gravitational acceleration (unit: N / kg), L represents the longest diameter of the levitating droplet (unit: m), and γ represents the surface tension of the levitating droplet (unit: N / m).

[0009] [7] A surface tension estimation device for levitated droplets, comprising: a levitated droplet formation unit that forms levitated droplets by applying an external force to the droplets; a vibration frequency measurement unit that measures the vibration frequency of the levitated droplets; and an estimation unit that calculates the surface tension based on the vibration frequency of the levitated droplets and corrects the obtained surface tension using a correction formula based on the external force applied to the droplets. [Effects of the Invention]

[0010] According to the present invention, it is possible to provide a surface tension estimation method and a surface tension estimation device that can accurately estimate the surface tension of a levitated droplet using a levitation method, even if the shape of the levitated droplet is not a perfect sphere due to the external force required for levitation. [Brief explanation of the drawings]

[0011] [Figure 1] These are conceptual diagrams illustrating the effects of external forces on levitated droplets. (a) is a conceptual diagram illustrating the effects of external forces on levitated droplets in a weightless state, and (b) is a conceptual diagram illustrating the effects on levitated droplets to which gravity and the fluid force of a gas jet stream are applied. [Figure 2] FIG. 1 is a conceptual diagram illustrating the state of the surface of a levitated droplet to which the fluid force of a gas jet airflow is applied in the gas jet levitation method. [Figure 3] 1 is a configuration diagram of a device for estimating the surface tension of a levitated droplet according to an embodiment of the present invention. [Figure 4] 1 is a cross-sectional view showing the vicinity of a nozzle of an apparatus for estimating the surface tension of a levitated droplet according to an embodiment of the present invention. [Figure 5] 1 is a graph showing the relationship between the surface tension of a levitating droplet (input value) and the surface tension of a levitating droplet (estimated value) in Example 1 and Reference Example 1. [Figure 6] 1 is a graph showing the relationship between the surface tension of a floating droplet (input value) and the relative error rate (Reference Example 1 / Example 1) of the estimated value of the surface tension (estimated value) in Example 1 and Reference Example 1. [Figure 7] 1 is a graph showing the relationship between the surface tension (input value) of a floating droplet and the relative error rate (Reference Example 1 / Example 1, Reference Example 2 / Example 2, Reference Example 3 / Example 3) of the estimated value of the surface tension (estimated value) in Examples 1 to 3 and Reference Examples 1 to 3. [Figure 8] 1 is a graph showing the relationship between the number of bonds and the relative error rate of the surface tension (estimated value) of the floating droplets in Examples 1 to 3 and Reference Examples 1 to 3 (Reference Example 1 / Example 1, Reference Example 2 / Example 2, Reference Example 3 / Example 3). [Figure 9] 10 is a graph showing the relationship between the surface tension of a levitating droplet (input value) and the relative error rate of the surface tension of a levitating droplet (estimated value) in Example 5 (Reference Example 2 / Example 5). [Figure 10] 10 is a graph showing the relationship between the surface tension of a levitating droplet (input value) and the relative error rate of the surface tension of a levitating droplet (estimated value) in Example 6 (Reference Example 1 / Example 6). [Figure 11] 10 is a graph showing the relationship between the surface tension of a levitating droplet (input value) and the relative error rate of the surface tension of a levitating droplet (estimated value) in Example 7 (Reference Example 3 / Example 7). [Figure 12] 10 is a graph showing the relationship between the surface tension of a levitating droplet (input value) and the surface tension of a levitating droplet (estimated value) in Reference Examples 1 and 4. [Figure 13] 10 is a graph showing the relationship between the surface tension of a levitating droplet (input value) and the relative error rate of the surface tension of a levitating droplet (estimated value) in Reference Examples 1 and 4. DETAILED DESCRIPTION OF THE INVENTION

[0012] An embodiment of the present invention will be described below with reference to the accompanying drawings. Note that the drawings used in the following description may show characteristic portions in an enlarged scale for the sake of convenience in order to make the characteristics easier to understand.

[0013] A surface tension estimation method according to one embodiment of the present invention uses a levitation method. Specifically, a substance whose surface tension is to be measured is levitated as droplets, and the surface tension of the levitated droplets is estimated. The substance to be measured is not particularly limited, and may be, for example, a metal, inorganic substance, or organic substance that forms droplets. The substance to be measured may also be a liquid such as water or oil, or a substance that forms droplets by melting with heat. Known levitation methods include gas jet levitation, electromagnetic levitation, electrostatic levitation, and acoustic levitation. In the following, this embodiment will be described using the gas jet levitation method as an example. In the gas jet levitation method, droplets are levitated by spraying a gas jet stream toward the droplets.

[0014] In this embodiment, the surface tension estimation method calculates the surface tension of the levitated droplet based on the vibration frequency of the levitated droplet, and then corrects the calculated surface tension using a correction formula that includes variables based on external forces applied to the levitated droplet. The external forces are gravity and the fluid force of the gas jet stream. The correction formula based on external forces includes, for example, the radius of curvature of the levitated droplet, the mass of the levitated droplet, the gravitational acceleration, and the surface area of ​​the levitated droplet to which the gas jet stream is applied. The correction formula will be described with reference to the accompanying drawings.

[0015] Figure 1 is a conceptual diagram illustrating the effect of external forces on levitated droplets. Figure 1(a) is a conceptual diagram illustrating the effect of external forces on levitated droplets in a weightless state, and Figure 1(b) is a conceptual diagram illustrating the effect on levitated droplets subjected to gravity and the pressure of a gas jet stream. As shown in FIGS. 1(a) and 1(b), a levitated droplet 1 is in a gas phase 2.

[0016] Surface tension is caused by the pressure difference between the curvature of the liquid phase (the suspended droplet) and the gas phase. This pressure difference between the two phases can be calculated using the Young-Laplace equation, shown below in equation (1). △P=γ(1 / r1+1 / r2) (1) Here, ΔP represents the pressure difference between the two phases, γ represents the surface tension of the liquid phase, and r1 and r2 represent the radii of curvature of the liquid phase. If the liquid phase is spherical, r1 = r2 = r.

[0017] As shown in (a) of FIG. 1, in a weightless state, the pressure P d and the pressure of gas phase 2, P0, is d >P0. Therefore, the pressure difference between the floating droplet 1 and the gas phase 2 in a weightless state is expressed by the following equation (2). △P=(P d -P0)=γ(2 / r) (2) Here, γ represents the surface tension of the levitated droplet 1 in a weightless state, and r represents the radius of curvature of the levitated droplet 1. The levitated droplet 1 in a weightless state is a sphere. Therefore, the surface tension γ of the levitated droplet 1 in a weightless state can be calculated based on the vibration frequency of the levitated droplet.

[0018] As shown in Figure 1(b), when gravity and the fluid force of the gas jet are applied, the force F applied from the gas phase 2 to the suspended droplet 1 by the gas jet is f is expressed by the following equation (3) based on the balance of vertical forces. F f =mg (3) Here, m represents the mass of the levitated droplet 1 and g represents the acceleration due to gravity.

[0019] The pressure P of the gas jet flow applied to the suspended droplet 1 f is expressed by the following equation (4). P f =F f / A f ···(4) where A f represents the area on which the fluid force of the gas jet stream acts strongly, that is, the surface area of ​​the suspended droplet 1 on which the fluid force of the gas jet stream is strongly applied.

[0020] Therefore, the pressure difference ΔP′ between the floating droplet 1 and the gas phase 2 when gravity and the fluid force of the gas jet stream are applied is expressed by the following equation (5). △P'=(P d -P0-P f )=γ'(2 / r) (5) Here, γ′ represents the surface tension of the levitating droplet 1 in the state where gravity and the fluid force of the gas jet stream are applied.

[0021] From the above equations (2) and (5), the relationship between the surface tension γ' of the levitating droplet 1 when subjected to the fluid forces of gravity and the gas jet airflow and the surface tension γ of the levitating droplet 1 when in a gravity-free state is expressed by the following equation (6). γ'=γ-P f (r / 2) (6)

[0022] In the gas jet levitation method, the estimated value of the surface tension obtained by assuming that the levitated droplet 1 is a sphere is considered to be the same as the surface tension γ of the levitated droplet 1 in a weightless state. Therefore, from the above equation (6), in order to improve the accuracy of the estimated value of the surface tension of the levitated droplet 1 in the gas jet levitation method, the surface tension γ obtained by assuming that the levitated droplet 1 is a sphere can be calculated by subtracting -P f It is clear that correction by (γ / 2) is necessary.

[0023] By substituting equations (3) and (4) into equation (6), equation (6) is expressed as equation (7) below. γ'=γ―rmg / A f ···(7)

[0024] From equation (7), the surface tension γ is calculated by the radius of curvature r of the levitated droplet 1, the mass m of the levitated droplet 1, the gravitational acceleration g, and the surface area A of the levitated droplet to which the fluid force of the gas jet stream is strongly applied. f Correction formula including (-rmg / A f ) is effective.

[0025] FIG. 2 is a conceptual diagram illustrating the state of the surface of a levitated droplet to which a strong fluid force of a gas jet airflow is applied in the gas jet levitation method. FIG. 2 is a cross-sectional view of a levitated droplet 1 passing through the center of gravity 1b of the levitated droplet 1. In FIG. 2, the portion of the levitated droplet 1 where the fluid force of the gas jet airflow is strongly exerted is shaded. The longer the shaded portion, the stronger the fluid force of the gas jet airflow is exerted. Note that FIG. 2 was obtained by analyzing the deformation of a levitated droplet to which the fluid force of the gas jet airflow is exerted, using the SPH (Smoothed Particle Hydrodynamics) method.

[0026] As shown in Figure 2, the portion where the fluid force of the gas jet stream is strongly exerted is within a range of 75 to 90 degrees when the angle θ is taken as the vertex at the center of gravity 1b (the dashed line from the center of gravity 1b to the circle in Figure 2 is the generatrix, and θ is the apex angle of the cone). In particular, the portion where the fluid force of the gas jet stream is strongly exerted is the surface (hereinafter also referred to as the correction surface) of the spherical portion (spherical crown) that forms an arc 1a within a range of 80 to 85 degrees at angle θ. Therefore, the correction formula (-rmg / A f ) Surface area A f It is preferable that the surface area of ​​the correction surface is a spherical portion formed by an arc 1a where the angle θ is in the range of 75 to 90 degrees (particularly in the range of 80 to 85 degrees).

[0027] The surface tension of the levitated droplet before correction (surface tension γ in equation (6)) is calculated based on the vibration frequency of the levitated droplet. The surface tension of the levitated droplet before correction can be calculated, for example, using equation (8) below. Surface tension of the levitated droplet before correction = 3Mω 2 / 32π (8) Here, M represents the mass of the levitated droplet (unit: g), and ω represents the angular frequency of the levitated droplet (unit: rad / s).

[0028] The vibration frequency of the floating droplets may be a value estimated by a simulation method. For example, a combination of the SPH (Smoothed Particle Hydrodynamics) method and the MLS (Moving Least Square) method can be used as the simulation method. In this embodiment, the influence of the external force applied to the droplets is corrected using a correction formula. Therefore, when estimating the drive frequency by the simulation method, it is not necessary to consider the influence of the external force applied to the droplets. The vibration frequency of the suspended droplets may be a value measured by a vibration frequency measuring device.

[0029] In the surface tension estimation method of this embodiment, it is preferable to calculate the surface tension under the condition that the Bond number (Bo) calculated by the following formula (9) is equal to or less than 1. Specifically, the longest diameter L of the floating droplet is adjusted so that the Bond number (Bo) is equal to or less than 1. Bond number = ρgL 2 / γ (9) where ρ is the density of the suspended droplets (unit: kg / m 3 ), and g represents the gravitational acceleration (unit: m / s 2 ), L represents the longest diameter of the levitated droplet (unit: m), and γ represents the surface tension of the levitated droplet (unit: N / m).

[0030] In the surface tension estimation method of this embodiment, the surface tension calculated based on the vibration frequency of the levitated droplet is corrected using a correction formula based on the external force applied to the levitated droplet. Therefore, the surface tension of a levitated droplet, which is levitated by applying an external force to the droplet, can be accurately estimated even if the shape of the levitated droplet cannot be accurately determined. Note that, although the gas jet levitation method has been described as the levitation method in this embodiment, it is not limited to this. Examples of levitation methods that can be used include electromagnetic levitation, electrostatic levitation, and acoustic levitation.

[0031] In the surface tension estimation method of this embodiment, the correction formula (-rmg / A f ) can be used to more accurately estimate the surface tension of a levitated droplet. f When the center of gravity angle (angle θ in Figure 2) forming the correction surface is in the range of 80 to 85 degrees, which is the area where the fluid force of the gas jet stream is particularly strong, the surface tension of the floating droplets can be estimated with even greater accuracy.

[0032] Furthermore, in the surface tension estimation method of this embodiment, the surface tension of a floating droplet can be estimated more accurately by performing calculations under conditions where the Bond number (Bo) calculated by the above equation (9) is 1 or less.

[0033] Next, a device for estimating the surface tension of a levitating droplet according to one embodiment of the present invention will be described. Fig. 3 is a configuration diagram of an apparatus for estimating the surface tension of a levitated droplet according to one embodiment of the present invention, and Fig. 4 is a cross-sectional view showing the vicinity of a nozzle 12 of the apparatus for estimating the surface tension of a levitated droplet according to one embodiment of the present invention.

[0034] As shown in FIGS. 3 and 4, the surface tension estimation device 100 for levitated droplets includes a levitated droplet formation unit 10, a vibration frequency measurement unit 30, and an estimation unit 40. The floating droplet forming unit 10 floats droplets to form floating droplets 1. The floating droplet forming unit 10 has a chamber 11. The chamber 11 has a nozzle 12 at the bottom. The flow path of the nozzle 12 is connected to a speaker 17. The speaker 17 is connected to a flow sensor 14 via a first valve 13a. The flow sensor 14 is connected to a supply source of an inert gas 15 via a second valve 13b. Any inert gas that does not react with the floating droplets can be used, such as argon gas. Furthermore, a rotary pump 18 for vacuum evacuation is disposed at the bottom of the chamber 11 via a third valve 13c. The chamber 11 also has an exhaust port 16, through which the inert gas introduced from the nozzle 12 is exhausted, via a fourth valve 13d.

[0035] The upper part of the chamber 11 is provided with a laser light inlet 19. Laser light 20a generated by a laser light generator 20 is reflected by a reflector (mirror) 21 and introduced into the laser light inlet 19. A temperature measurement opening 22 is also provided in the upper part of the chamber 11. A non-contact thermometer 23 measures the temperature of the floating droplets 1 through the temperature measurement opening 22.

[0036] A viewing window 24 for the levitated droplet 1 is arranged on the side of the chamber 11 . The vibration frequency measuring unit 30 measures the vibration frequency of the levitated droplet 1 . The vibration frequency measuring unit 30 has a high-sensitivity camera 31 and a lens 32. The high-sensitivity camera 31 is disposed at a position facing the observation window 24 with the lens 32 interposed therebetween.

[0037] The estimation unit 40 has a calculation unit 43 and a memory unit 42. The memory unit 42 stores a calculation formula and a correction formula for the surface tension. The calculation formula for the surface tension is a formula for calculating the surface tension based on the vibration frequency of the suspended droplet, for example, the formula for calculating the surface tension of the suspended droplet 1, and the correction formula is a correction formula based on the external force applied to the suspended droplet 1, for example, the correction formula (-rmg / A f The calculation unit 43 calculates the surface tension using the vibration frequency of the suspended droplets and a calculation formula for surface tension, and corrects the obtained surface tension using a correction formula.

[0038] The method for estimating the surface tension of a levitating droplet using the surface tension estimation device 100 can be performed as follows. After the third valve 13c is opened and the pressure inside the chamber 11 is reduced using the rotary pump 18, the first valve 13a and the second valve 13b are opened to introduce the inert gas 15 into the chamber 11 up to atmospheric pressure. Next, after closing the third valve 13c, the flow rate of the inert gas 15 is adjusted using the flow rate sensor 14 so that the metal will float, and the inert gas 15 is supplied. Also, while preventing the introduction of outside air, the fourth valve 13d at the exhaust port 16 is opened to exhaust the introduced inert gas so that the internal pressure of the chamber 11 does not increase and cause damage.

[0039] Next, the suspended metal is irradiated with laser light using a laser light generator 20 and a reflector 21. This melts the metal and generates suspended droplets 1. As shown in FIG. 4, a portion of the generated suspended droplets 1 is hidden by the opening 12a of the nozzle 12, making it difficult to accurately grasp the shape of the suspended droplets 1.

[0040] The speaker 17 is then activated to transmit sound waves into the supply gas, which causes the suspended droplets 1 to vibrate.

[0041] Next, the vibrating levitated droplet 1 is photographed using a high-sensitivity camera 31, and the photographed image is used to calculate the vibration frequency of the levitated droplet 1. The obtained vibration frequency of the levitated droplet 1 is sent to a calculation unit 43 of an estimation unit 40.

[0042] The calculation unit 43 calculates the surface tension of the levitated droplet 1 using the vibration frequency of the levitated droplet 1 and a calculation formula for surface tension stored in the memory unit 42. Next, the memory unit 42 corrects the obtained surface tension using the correction formula stored in the memory unit 42.

[0043] In the surface tension estimation device 100 for levitated droplets of this embodiment, the surface tension calculated based on the vibration frequency of the levitated droplets 1 is corrected using a correction formula based on the external force applied to the levitated droplets 1 by the inert gas flow from the nozzle 12. Therefore, even if the shape of the levitated droplets 1 cannot be accurately determined, the surface tension of the levitated droplets can be accurately estimated. [Example]

[0044] [Example 1] The surface tension of the levitated droplet was assumed to be 0.1 to 3.5 N / m, as measured using the gas jet levitation method. This surface tension was used as an input value and substituted into γ in the above equation (7) to calculate the surface tension (estimated value) γ' of the levitated droplet. The correction formula (-r mg / A f ) is r = 1.15 mm and m = 3.38 × 10 -2 g, g at 9.8 m / s 2 , surface area A f The correction value (0.0917 N / m) was obtained by setting the center of gravity angle (angle θ in Figure 2) forming the correction surface at 83 degrees.

[0045] [Reference example 1] Using a simulation method, levitated droplets with a surface tension of 0.1 to 3.0 N / m were generated by a gas jet levitation method, and the vibration frequency of the levitated droplets was calculated by the method described in (1) below. Next, the obtained vibration frequency was used to calculate the surface tension of the levitated droplets by the method described in (2) below. The simulation methods used were the SPH method and the MLS method. The SPH method is a calculation method that treats a continuum as an aggregate of many particles, and calculates a physical quantity at a certain coordinate in space using a weight function based on the physical quantities of nearby particles. The SPH method has a proven track record as a method for fluid analysis, and is capable of relatively stable analysis of systems with free surfaces and large surface deformations. For this reason, it was adopted as the analysis method for Reference Example 1. The MLS method is a method that applies a polynomial around a point of interest using the least squares method to correct the physical quantity at the point of interest. By introducing the MLS method into the SPH method, pressure vibrations can be suppressed, and disturbances to the droplet surface in the simulation can be reduced, so the simulation was performed by combining these methods.

[0046] (1) Calculation of the vibration frequency of the levitated droplet Levitated droplets with the following physical property values ​​(A) to (F) were assumed. Next, the predicted vibration frequency of the assumed levitated droplets when the surface tension of the droplets was the value (G) below was calculated as an estimated value using a simulation method that combined the SPH method and the MLS method, under the condition that gravity and the fluid force of the gas jet stream were applied as external forces. (Simulation conditions) (A) Size of floating droplets: 2.3 mm (a) Particle diameter of particles constituting suspended droplets: 0.1 mm (c) Number of particles constituting the suspended droplets: 8,468 (d) Arrangement of particles that make up the suspended droplet: Face-centered cubic lattice structure (FCC) (E) Density of suspended droplets: 5308 kg / m 3 (Assuming Cu2S) (F) Viscosity of suspended droplets: 4.9 mPas (G) Surface tension of floating droplets (input value): 0.1 to 3.0 N / m

[0047] (2) Calculation of the surface tension (estimated value) of the suspended droplet The vibration frequency obtained in (1) above and the mass of the suspended droplet, 3.38 × 10 -2 The estimated surface tension of the levitated droplet was calculated using the equations (g).

[0048] [evaluation] The relationship between the surface tension (input value) of the levitated droplets and the surface tension (estimated value) of the levitated droplets in Example 1 and Reference Example 1 is shown in the graph of FIG. 5. The surface tension (input value) of Example 1 is the surface tension used to calculate the surface tension (estimated value) of the levitated droplets, and the surface tension (input value) of Reference Example 1 is the surface tension used to calculate the vibration frequency of the levitated droplets (1). In FIG. 5, Example 1 is shown by a dashed line, and Reference Example 1 is shown by a dashed line. In addition, the relative error rate (Reference Example 1 / Example 1) of the surface tension (estimated value) of the levitated droplets in Reference Example 1 relative to the surface tension (estimated value) of the levitated droplets in Example 1 was calculated using the following formula (10). The results are shown in the graph of FIG. 6. Relative error rate (%) = Estimated surface tension of the floating droplet in Reference Example 1 / Estimated surface tension of the floating droplet in Example 1 × 100 (10)

[0049] 5 and 6, it can be seen that the surface tension (estimated value) of the levitated droplets obtained in Example 1 and the surface tension (estimated value) of the levitated droplets obtained in Comparative Example 1 are nearly identical, with a relative error rate of ±5% or less, when the surface tension is 0.2 N / m or more. By correcting the surface tension of the levitated droplets according to the present invention, the surface tension becomes nearly equal to the surface tension (estimated value) of the levitated droplets estimated by simulation, confirming that the correction is valid and that the situation can be accurately reproduced in the simulation.

[0050] [Example 2, Reference Example 2] In the second embodiment, the correction formula (-rmg / A f ) m to 1.27 × 10 -2 The surface tension (estimated value) of the levitated droplets was calculated in the same manner as in Example 1, except that the surface tension was set to 0.0345 N / m and the correction value was set to 0.0345 N / m. In Reference Example 2, in (1) calculating the vibration frequency of the levitated droplets, (e) the density of the levitated droplets was set to 2000 kg / m. 3 (Assuming magnesium), (2) In calculating the surface tension (estimated value) of the levitated droplet, the mass of the levitated droplet is 1.27 × 10 -2The surface tension (estimated value) of the suspended droplet was calculated in the same manner as in Reference Example 1, except that the surface tension was set to 1000 kJ / cm.

[0051] [Example 3, Reference Example 3] In the third embodiment, the correction formula (-rmg / A f ) m to 5.10 x 10 -2 The surface tension (estimated value) of the levitated droplets was calculated in the same manner as in Example 1, except that the surface tension was set to 0.0000 g and the correction value was set to 0.138 N / m. In Reference Example 3, in (1) calculating the vibration frequency of the levitated droplets, (e) the density of the levitated droplets was set to 8000 kg / m 3 (Assuming iron), (2) In calculating the surface tension (estimated value) of the levitated droplet, the mass of the levitated droplet is 5.10 × 10 -2 The surface tension (estimated value) of the suspended droplet was calculated in the same manner as in Reference Example 1, except that the surface tension was set to 1000 kJ / cm.

[0052] [evaluation] The relative error rate of the surface tension (estimated value) obtained in Reference Example 2 to the surface tension (estimated value) obtained in Example 2 (Reference Example 2 / Example 2), and the relative error rate of the surface tension (estimated value) obtained in Reference Example 3 to the surface tension (estimated value) obtained in Example 3 (Reference Example 3 / Example 3) were calculated in the same manner as the relative error rate of Reference Example 1 / Example 1. The results are shown in Figure 7 together with the relative error rate of Reference Example 1 / Example 1. In FIG. 7, the relative error rate for Reference Example 1 / Example 1 is shown by a dotted line, the relative error rate for Reference Example 2 / Example 2 is shown by a solid line, and the relative error rate for Reference Example 3 / Example 3 is shown by a dotted line. From the graph in FIG. 7, it can be seen that the relative error rates for Reference Example 1 / Example 1, Reference Example 2 / Example 2, and Reference Example 3 / Example 3 are all small, at ±5% or less, when the surface tension (input value) is 0.5 N / m or greater. However, when the density of the suspended droplets is low, the relative error rate is low even at very low surface tensions. However, as the density of the suspended droplets increases, the relative error rate at low surface tensions tends to increase. This may indicate that high-density suspended droplets are difficult to form and maintain when the surface tension is low.

[0053] To consider the above, we used the Bond number in equation (9), which represents the ratio of gravity to surface tension. Figure 8 is a graph showing the relationship between the bond number (Bo) and the relative error rate in Reference Examples 1 to 3. Each example is shown with the same line as in Figure 7. From the graph in Figure 8, it can be seen that when the bond number (Bo) is 1 or less, the relative error rate tends to be small, at ±10% or less. The large relative error rate when the Bond number exceeds 1 may actually indicate a difficult region for droplet levitation, which may lead to a measurement limit for gas jet levitation measurements. On the other hand, when the bond number is 1 or less, the relative error rate is very low, so the simulation may indicate the effectiveness of the correction by surface tension described in equation (7).

[0054] [Example 5] In Example 2, the correction formula (-rmg / A f ) surface area A f The surface tension (estimated value) of the levitated droplet was calculated in the same manner, except that the correction values ​​obtained were set using the center of gravity angle (angle θ in FIG. 2) forming the correction surface of 75 degrees, 80 degrees, 85 degrees, and 90 degrees. The relative error rate (Reference Example 2 / Example 5) of the surface tension (estimated value) of the levitated droplet obtained in Reference Example 2 relative to the surface tension (estimated value) of the levitated droplet was calculated. The results are shown in FIG. 9. In FIG. 9, 75 degrees is indicated by a solid line, 80 degrees by a chain line, 83 degrees by a dotted line, 85 degrees by a dashed line, and 90 degrees by a dashed line. FIG. 9 is a graph showing the relationship between the surface tension (input value) of the levitated droplet and the relative error rate (Reference Example 2 / Example 5) in Example 5.

[0055] [Example 6] In Example 1, the correction formula (-rmg / A f ) surface area A fThe surface tension (estimated value) of the levitated droplet was calculated in the same manner, except that the correction values ​​obtained were used when the center of gravity angle (angle θ in FIG. 2) forming the correction surface was set to 75 degrees, 80 degrees, 85 degrees, and 90 degrees. The relative error rate (Reference Example 1 / Example 6) of the surface tension (estimated value) of the levitated droplet obtained relative to the surface tension (estimated value) obtained in Reference Example 1 was calculated. The results are shown in FIG. 10. In FIG. 10, 75 degrees is indicated by a solid line, 80 degrees by a chain line, 83 degrees by a dotted line, 85 degrees by a dashed line, and 90 degrees by a dashed line. FIG. 10 is a graph showing the relationship between the surface tension (input value) of the levitated droplet and the relative error rate (Reference Example 1 / Example 6) in Example 6.

[0056] [Example 7] In Example 3, the correction formula (-rmg / A f ) surface area A f The surface tension (estimated value) of the levitated droplet was calculated in the same manner, except that the correction values ​​obtained were set using the center of gravity angle (angle θ in FIG. 2) forming the correction surface of 75 degrees, 80 degrees, 85 degrees, and 90 degrees. The relative error rate (Reference Example 3 / Example 7) of the surface tension (estimated value) of the levitated droplet obtained in Reference Example 3 relative to the surface tension (estimated value) of the levitated droplet was calculated. The results are shown in FIG. 11. In FIG. 11, 75 degrees is indicated by a solid line, 80 degrees by a chain line, 83 degrees by a dotted line, 85 degrees by a dashed line, and 90 degrees by a dashed line. FIG. 11 is a graph showing the relationship between the surface tension (input value) of the levitated droplet and the relative error rate (Reference Example 3 / Example 7) in Example 7.

[0057] 9 to 11, it can be seen that as the density of the suspended droplets increases, the relative error rate tends to decrease as the center of gravity angle forming the correction surface increases. Furthermore, by setting the center of gravity angle of the correction surface at 80 to 85 degrees, the overall relative error rate falls within ±8%, and it can be seen that by assuming that strong pressure from the gas jet airflow is applied to angles in this range and performing correction, it is possible to further reduce the relative error rate of the surface tension (estimated value) of the suspended droplets.

[0058] [Reference Example 4: Surface tension in zero gravity (estimated value)] Using a simulation method, the surface tension of the levitated droplets was calculated under conditions where no external force was applied (weightless state). That is, the estimated vibration frequency of the levitated droplets was calculated in the same manner as in Reference Example 1, except that in (1) Calculation of the vibration frequency of the levitated droplets, the conditions where no external force was applied (weightless state) were used, and the surface tension (estimated value) of the levitated droplets was calculated.

[0059] [evaluation] The surface tension (estimated value) of the levitated droplets in a gravity-free state obtained in Reference Example 4 is shown in Figure 12, along with the surface tension (estimated value) of the levitated droplets under conditions in which an external force is applied obtained in Reference Example 1. Also shown in Figure 12 is an ideal line, where the input value and estimated value of the surface tension of the levitated droplets are the same. In Figure 12, Reference Example 1 is shown as a solid line, Reference Example 4 as a dashed-dotted line, and the ideal line as a dotted line. Furthermore, the relative error rates of the surface tension (estimated value) of the levitated droplets in Reference Examples 1 and 4 relative to the surface tension (estimated value) of the levitated droplets on the ideal line were calculated using the following equation (11). The results are shown in the graph of Figure 13. Relative error rate (%) = Surface tension of the levitated droplets in Reference Examples 1 and 4 (estimated value) / Surface tension of the levitated droplets on the ideal line × 100 (11)

[0060] 12 and 13, it can be seen that in the weightless state of Reference Example 4, the relative error rate of the surface tension (estimated value) of the floating droplets is 10% or less when the input value of surface tension is in the range of 0.2 to 3.0 N / m, and that highly accurate surface tension (estimated value) can be obtained by using the simulation method. In contrast, in the state where an external force is applied in Reference Example 1, the relative error rate is as high as 10% when the input value of surface tension is 0.8 N / m, and it can be seen that correction is necessary to obtain highly accurate surface tension (estimated value). [Explanation of symbols]

[0061] 1. Levitating droplets 1a Arc 1b Center of gravity 2 Gas Phase 10. Floating droplet formation section 11 Chamber 12 nozzles 12a opening 13a First valve 13b Second valve 13c Third valve 13d 4th valve 14 Flow Sensor 15 Inert gas 16 Exhaust port 17 Speaker 18 Rotary Pump 19 Laser light inlet 20 Laser light generator 21 Reflective material 22 Temperature measurement opening 23 Non-contact thermometer 24 Observation window 30 Vibration frequency measurement unit 31 High-sensitivity camera 32 Lens 40 Estimation part 42 Storage section 43 Calculation section 100 Surface tension estimation device

Claims

1. A surface tension estimation method for estimating the surface tension of a levitated droplet that is levitated by applying an external force to the droplet, comprising: A method for estimating the surface tension of a levitating droplet, in which the surface tension calculated based on the vibration frequency of the levitating droplet is corrected using a correction formula based on the gravity acting on the levitating droplet and the surface area on which an external force applied to levitate the levitating droplet acts.

2. 2. The method for estimating the surface tension of a levitated droplet according to claim 1, wherein the levitated droplet is levitated by a gas jet stream.

3. 3. The method for estimating the surface tension of a levitated droplet according to claim 2, wherein the correction formula includes the radius of curvature of the levitated droplet, the mass of the levitated droplet, the gravitational acceleration, and the surface area of ​​the levitated droplet to which the gas jet stream is applied.

4. The surface area of ​​the levitating droplet is the area of ​​a portion of a cross section passing through the center of gravity of the levitating droplet, the portion forming an arc with an angle of 80 to 85 degrees with the center of gravity as its vertex. A method for estimating the surface tension of a levitating droplet according to claim 3.

5. The method for estimating the surface tension of a levitated droplet according to claim 1 , wherein the surface tension is a value calculated based on a vibration frequency of the levitated droplet measured by a vibration frequency measuring device.

6. The method for estimating the surface tension of a levitating droplet according to any one of claims 1 to 5, wherein the surface tension is a value calculated under the condition that the bond number calculated by the following formula is 1 or less. Bond number = ρgL ２ / γ (where ρ is the density of the suspended droplets (unit: kg / m ３ ), g represents the gravitational acceleration (unit: N / kg), L represents the longest diameter of the levitated droplet (unit: m), and γ represents the surface tension of the levitated droplet (unit: N / m).

7. a floating droplet forming unit that forms floating droplets by applying an external force to the droplets; a vibration frequency measuring unit for measuring the vibration frequency of the suspended droplets; and an estimation unit that calculates the surface tension based on the vibration frequency of the levitated droplets and corrects the obtained surface tension using a correction formula based on the gravity acting on the levitated droplets and the surface area on which an external force applied to levitate the levitated droplets acts.

Images