An apparatus and method for analyzing the liquid bridge suction force and fracture distance between irregular particles

Abstract

The present invention discloses a device and a method for analyzing the liquid bridge suction force and the breaking distance between irregular particles. The device includes an upper mounting rod, a lower mounting rod, a micrometer, a microbalance and a camera. The device of the present invention is used for analyzing the liquid bridge suction force and the breaking distance between irregular particles, and can accurately measure the particle shape, the solid-liquid-gas three-phase contact angle, the liquid bridge volume, and their influence on the liquid bridge suction force and the breaking distance of irregular particles.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical testing, and particularly to a device and method for analyzing the liquid bridge suction and fracture distance between irregular particles. Background Art

[0002] In nature, the geometric shapes of granular materials are often complex and diverse, and extremely irregular. For granular geotechnical dispersive materials, the geometric shape of particles is not only a key control factor for their basic physical and mechanical properties (porosity, static angle of repose), but also directly affects the development of the strength and deformation properties of geotechnical bodies. Due to the influence of groundwater level changes, subgrades, natural slopes, etc. in geotechnical engineering are in an unsaturated state for a long time, and the fillers and rockfill bodies therein belong to typical unsaturated granular media. The geometric shape of particles will not only affect the contact action between unsaturated geotechnical particles, but also change the distribution of the liquid phase between pores, making the action effects of water pressure and surface tension on granular materials change.

[0003] For unsaturated granular materials, their states can be classified according to different saturations:

[0004] (I) Pendular regime: The water content of the granular material is low, and there is only a single liquid bridge between two particles;

[0005] (II) Funicular regime: The liquid exists in a clump form and contacts three or more particles simultaneously;

[0006] (III) Capillary regime: The pores are completely filled with liquid, and the gas is suspended in the liquid.

[0007] The geometric shape of the liquid bridge surface between particles is often described by the well-known Young-Laplace equation, which shows that the mean curvature of the liquid bridge surface is constant, and the fracture distance and suction of the liquid bridge can be obtained by solving the Young-Laplace equation. A large number of experiments have verified the accuracy and reliability of the Young-Laplace equation in describing the properties of liquid bridges.

[0008] Currently, the liquid bridge model between regular spherical particles has been widely studied. The common methods for measuring the liquid bridge fracture distance and suction include the following four:

[0009] (I) Indoor physical experiments. The liquid bridge fracture distance and suction can be directly measured, but it is expensive and has high technical difficulty due to the influence of gravity and particle surface roughness;

[0010] (II) Numerical solution of the non-linear Young-Laplace equation. The properties of the liquid bridge can be accurately described, but it requires a high degree of discretization fineness, the solution process is cumbersome and time-consuming, and the calculation efficiency is low;

[0011] (III) Based on the curve fitting of a large number of numerical solutions of the Young-Laplace equation. The fitting expression obtained by this method can quickly and accurately calculate the properties of the liquid bridge with different liquid bridge volumes and interparticle distances. However, the parameters in this expression do not have clear physical meanings, and the number of fitting parameters to be calibrated is large, and the calibration process is complex;

[0012] (IV) Establishing an analytical solution of the Young-Laplace equation with clear physical meanings. However, due to certain assumptions involved in the process of establishing the analytical solution, the obtained analytical solution is only applicable to a limited range.

[0013] For the liquid bridge model between irregular particles, the particles are irregular, the three-phase boundary line of solid-liquid-gas is no longer a circle, and the axisymmetric property of the boundary line is no longer applicable, that is, the boundary conditions of the Young-Laplace equation become complex and difficult to determine. Therefore, the properties of the liquid bridge between irregular particles cannot be directly determined by the analytical solution or numerical solution of the Young-Laplace equation, and a database of solutions of the Young-Laplace equation available for curve fitting has not been established yet. Summary of the Invention

[0014] The present invention is mainly used to analyze the liquid bridge shape, fracture distance and the suction force generated by the liquid bridge between particles in the suspension state.

[0015] To solve the above existing problems, the present invention provides a set of experimental devices for obtaining the change of the liquid bridge suction force between irregular particles with the change of the particle spacing and the corresponding liquid bridge fracture distance, laying a foundation for the construction of the liquid bridge model between irregular particles.

[0016] A device for analyzing the liquid bridge suction force and fracture distance between irregular particles, comprising:

[0017] An upper mounting rod, vertically arranged, and the bottom is used to mount one of the irregular particles;

[0018] A lower mounting rod, vertically arranged, and the top is used to mount another irregular particle. The upper mounting rod and the lower mounting rod are arranged in a straight line vertically. After the two irregular particles are respectively mounted on the upper mounting rod and the lower mounting rod, the irregular particles are close to each other;

[0019] A micrometer, connected to the upper mounting rod and used to drive the upper mounting rod to move vertically;

[0020] A microbalance, the top surface of which has a weighing plate, and the lower mounting rod is arranged on the weighing plate;

[0021] A camera, which can rotate horizontally around the upper mounting rod and the lower mounting rod and is used to take pictures of the two irregular particles at different angles.

[0022] The camera can be a high-resolution camera, such as: BASLER acA4600 10μ, 4608px×3288px, and continuously take pictures at a frequency of 10 frames per second.

[0023] Preferably, the precision of the microbalance is 0.01 mg. For example, the microbalance can be selected as: artoriusMCE225P-100-DU Cubis Model. The microbalance has a wind shield, and the top surface of the wind shield is provided with the micrometer.

[0024] On the side of the camera facing away from the upper mounting rod and the lower mounting rod, there is an LED backlight, and the LED backlight can also rotate horizontally around the upper mounting rod and the lower mounting rod.

[0025] The present invention also provides a method for analyzing the liquid bridge suction force and the fracture distance between irregular particles, including the following steps:

[0026] (1) Prepare irregular particles;

[0027] (2) Use the device to detect a pair of irregular particles prepared in step (1). During the detection, the two irregular particles are respectively installed on the upper mounting rod and the lower mounting rod. Zero the reading of the microbalance. Inject distilled water between the two irregular particles to establish a liquid bridge. The microbalance measures the mass m of the liquid bridge, and the liquid bridge suction force F cap can be calculated from m, ρ w 、V w are the density and volume of distilled water respectively, and g represents the acceleration due to gravity. Then

[0028] F cap =mg - ρ w V w g;

[0029] (3) Adjust the distance between the two irregular particles through the micrometer. Calculate different liquid bridge suction force values by measuring the mass of the liquid bridge with the microbalance until the liquid bridge breaks;

[0030] (4) When measuring the liquid bridge suction force in steps (2) and (3), simultaneously take pictures through the camera. Based on the images, perform three-dimensional reconstruction to reconstruct the images at different angles into a 3D view. Determine the spherical coordinate origins of the two irregular particles, and calculate the distance between the spherical coordinate origins of the two irregular particles. The distance between the spherical coordinate origins of the two irregular particles corresponding to the liquid bridge fracture is the liquid bridge fracture distance.

[0031] In step (3), when adjusting the distance between the two irregular particles through the micrometer, increase the distance between the two irregular particles in the vertical direction with a step size of 0.01 mm.

[0032] Among them, when preparing irregular particles in step (1), an appropriate center point O is selected on the cross-section of the irregular particles, the contour of the irregular particles is described by a polar coordinate equation, the polar coordinate equation is Fourier-expanded to obtain Fourier descriptors for describing the shape of the irregular particles, and particles with different shapes and different average radii are randomly generated by setting the values of the Fourier descriptors;

[0033] Select three randomly generated 2D contour surfaces, and through uniform scaling, make their projected lengths on the same coordinate axis the same, satisfying the compatibility condition of the projection surface;

[0034] Interpolate the polar coordinate equations of the three uniformly scaled projection surfaces to obtain a spherical coordinate equation describing the 3D surface information of the irregular particles. According to the spherical coordinate equation, use 3D printing technology to make irregular particles.

[0035] Fourier expansion of the polar coordinate equation gives the equation:

[0036]

[0037] Then, the definition of the Fourier descriptor used to describe the particle shape is:

[0038]

[0039] Among them, r0 is the average radius; A n 、B n are the spectra of the nth harmonic; D n is the nth-order Fourier descriptor; N is the total number of harmonics, N > 8.

[0040] Set D n to have the following relationship with n:

[0041]

[0042]

[0043] By given β1, β2, D2, D3, D8, determine a set of Fourier descriptors D n to construct and obtain irregular particles.

[0044] Advantages of the present invention:

[0045] In view of the problems that existing test methods cannot consider the influence of the irregular geometric shape of particles on the properties of liquid bridges, it is difficult to measure the solid-liquid-gas three-phase contact angle of asymmetric liquid bridges (an important parameter for measuring the wetting performance of liquids on solid surfaces), and it is impossible to accurately obtain the liquid bridge fracture distance, etc., the present invention proposes a device and a test method for analyzing the liquid bridge suction force and fracture distance between irregular particles. Using this invention, the particle shape, the solid-liquid-gas three-phase contact angle, and the liquid bridge volume can be accurately measured, and the influence laws of these on the liquid bridge suction force and fracture distance of irregular particles can be quantitatively studied. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 : Diagram showing the influence of D2 on the particle shape, where D2 is 0 (left), 0.1 (middle), and 0.2 (right) respectively, D3 = 0, D8 = 0.

[0047] Figure 2 : Diagram showing the influence of D3 on the particle shape, where D3 is 0.05 (left), 0.10 (middle), and 0.15 (right) respectively, D2 = 0.3, D a = 0.

[0048] Figure 3 : Diagram showing the influence of D8 on the particle shape, where D8 is 0 (left), 0.015 (middle), and 0.030 (right) respectively, D2 = 0.2, D3 = 1.

[0049] Figure 4 : 3D view of typical irregularly shaped particles.

[0050] Figure 5 : Schematic structural diagram of the experimental device.

[0051] Figure 6 : 3D reconstruction view of a typical specimen processed based on image processing technology.

[0052] Figure 7 : Measurement results of the liquid bridge suction force varying with the inter-particle distance for different liquid bridge volumes.

[0053] Figure 8 : Measurement results of the liquid bridge suction force varying with the inter-particle distance for different contact angles.

[0054] Figure 9 : Measurement results of the liquid bridge suction force varying with the inter-particle distance for different particle shapes.

[0055] Reference numerals: upper mounting rod 1, lower mounting rod 2, micrometer 3, microbalance 4, weighing plate 5, wind shield 6, camera 7, LED backlight 8. DETAILED DESCRIPTION OF THE INVENTION

[0056] The following further describes the analysis process of the liquid bridge mechanical property model proposed by the present invention with reference to the drawings.

[0057] 1. Description and manufacturing method of irregular particle shapes

[0058] Based on the Fourier series method, the present invention constructs the polar coordinate equation r = r(α) of the 2D contour of an irregular particle, and generates a series of 2D outer contours of particles with irregular shapes based on this; performs scaling and interpolation processing on it to obtain the 3D surface spherical coordinate equation of the irregular particle

[0059] Select the center point O on the cross-section of the irregular particle. Then, the 2D particle outer contour can be described by the polar coordinate equation r = r(α). Perform Fourier expansion on this equation to obtain equation (1):

[0060]

[0061] Then, the Fourier descriptors used to describe the particle geometry are defined as shown in equation (2):

[0062]

[0063] where r0 is the average radius; A n and B n are the spectra of the nth harmonic; D n is the nth-order Fourier descriptor; N is the total number of harmonics. The larger N is, the more accurate the description of the particle shape. Generally, it is required that N > 8. In the present invention, N = 50

[0064] Due to the normalization process, D0 = 1. D1 describes the offset of the particle contour relative to the center point O. By selecting a suitable center point O, D1 can be made equal to 0. D2 describes the elongation rate of the particle and is a direct description of the overall shape of the particle; D3 - D8 are the characterization quantities of the particle roundness and describe the sharpness of the particle edges and corners, while the Fourier descriptors above the 8th order are used to describe the texture and roughness of the particle surface. In the present invention, it is assumed that D n and n satisfy the relationships shown in equations (3) and (4). When the corresponding parameter values of β1, β2, D2, D3, D8, and r0 are determined, the polar coordinate equation r(α) can be uniquely determined. The influence of different Fourier descriptors on the particle contour is as shown in Figure 1 , Figure 2 , Figure 3 shown

[0065]

[0066]

[0067] Determine a set of Fourier descriptors D n through equations (3) and (4), and based on this set of D nRandomly generate particles with different shapes and average radii. Select three 2D particle profile surfaces randomly generated by the above steps, and after uniform scaling, make their projected lengths on the same coordinate axis the same, so as to meet the compatibility conditions of the projection surface. Perform linear interpolation on the polar coordinate equations of the three uniformly scaled projection surfaces to obtain a spherical coordinate equation describing the 3D surface information of irregular particles. The 3D view of the particles constructed according to this method is as Figure 4 shown. Using 3D printing technology, the corresponding irregular particles can be fabricated.

[0068] 2. Test Equipment and Procedures

[0069] As Figure 5 shown, the present invention has developed a set of devices for measuring the liquid bridge suction force and fracture distance between irregular particles, including a microbalance 4, a high-resolution camera (camera 7), and a telecentric LED backlight (LED backlight 8). The precision of the microbalance 4 is 0.01 mg. For example, the microbalance 4 can be selected as: artorius MCE225P-100-DU Cubis Model. The top surface of the microbalance 4 has a weighing plate 5, and the microbalance 4 is equipped with a wind shield 6.

[0070] The device of the present invention further includes an upper mounting rod 1 and a lower mounting rod 2. The upper mounting rod 1 is vertically arranged, and the bottom is used to mount one of the irregular particles; the lower mounting rod 2 is vertically arranged, and the top is used to mount another irregular particle. The upper mounting rod 1 and the lower mounting rod 2 are arranged in a straight line vertically. After the two irregular particles are respectively mounted on the upper mounting rod 1 and the lower mounting rod 2, the irregular particles are close to each other.

[0071] The lower mounting rod 2 is arranged on the weighing plate 5. The top surface of the wind shield 6 is provided with a micrometer 3, and the upper mounting rod 1 is connected to the micrometer 3. The height of the irregular particle on the upper mounting rod 1 is adjusted by the micrometer 3 to adjust the distance between the two irregular particles.

[0072] Weld an aluminum rod with a connecting screw to the irregular particle, and screw the screw into the upper mounting rod 1 or the lower mounting rod 2 for fixation.

[0073] The camera 7 can rotate horizontally around the upper mounting rod 1 and the lower mounting rod 2 and is used to take pictures of the two irregular particles at different angles. The camera 7 can be selected as a high-resolution camera, such as: BASLER acA460010μ, 4608px×3288px, and continuously take pictures at a frequency of 10 frames per second. An LED backlight 8 is provided on the side of the camera 7 facing away from the upper mounting rod 1 and the lower mounting rod 2, and the LED backlight 8 can also rotate horizontally around the upper mounting rod 1 and the lower mounting rod 2.

[0074] The test specimen contains two irregular particles. Using a microsyringe, a small amount of distilled water is injected between the two particles to form a liquid bridge. The test specimen is illuminated by a telecentric LED backlight, and a high-resolution camera is used to continuously take pictures at a frequency of 10 frames per second. The backlight and the camera can rotate around the specimen in the horizontal plane to record the specimen images at different angles. Both the camera and the LED light are equipped with telecentric lenses to prevent image distortion and reflection. All geometric parameters are calculated in pixels and then converted to millimeters through a calibration slider with a precision of 0.01 mm. The lower particle is mounted on the plate of a microbalance with a precision of 0.01 mg. The upper particle is fixed on a micrometer, and the inter-particle distance d is increased in steps of 0.01 mm in the vertical direction.

[0075] At the beginning of each test, the surfaces of the particles are cleaned with ethanol with a concentration of 99%, and wait for a period of time for the ethanol to completely volatilize to avoid its mixing with the test liquid. Subsequently, distilled water is slowly injected onto the top of the lower particle. Before injecting the distilled water, the balance reading is zeroed. After the liquid bridge is established, the liquid bridge suction force F cap can be calculated using Equation (5) from the mass m value measured by the balance:

[0076] F cap = mg - ρ w V w g (5)

[0077] where ρ w , V w are the density and volume of distilled water respectively, and the acceleration due to gravity g = 9.81 m / S 2 . After each increase in the inter-particle distance, wait for a period of time until the liquid bridge reaches a new stable equilibrium, and then record the balance reading m and the specimen images at different angles again. When the liquid bridge breaks and leaves two droplets on the upper and lower particles, the test ends.

[0078] 3. Image processing technology

[0079] Based on the image-based 3D reconstruction and meshing algorithm, the specimen images at different angles can be reconstructed into a 3D view. The specific process includes three steps:

[0080] 1) Extract and match the feature points of the specimen images at different angles based on the scale-invariant feature transform matching algorithm and the nearest neighbor algorithm;

[0081] 2) Calculate the geometric constraints between the specimen images at different angles based on the random sample consensus algorithm.

[0082] 3) Based on the multi-view stereo vision algorithm, reconstruct the 2D feature points into a 3D mesh.

[0083] Image processing is performed on the reconstructed 3D view to obtain the distance d between irregular particles and the solid-liquid-gas three-phase contact angle θ, as Figure 6 shown. The specific process includes three steps:

[0084] 1) Determine the spherical coordinate origins o1 and o2 of two particles. The inter-particle distance d is the distance between points o1 and o2;

[0085] 2) Select ten contact points (ten points for each of the upper and lower particles, a total of twenty points) c1, c2,......, c 20 at equal intervals on the solid-liquid-gas three-phase boundary lines of the two particles respectively, and determine the coordinates of each contact point in combination with the spherical coordinate equation of the irregular particles.

[0086] 3) At each contact point c j (j is a natural number with a value from 1 to 20, the same below), draw the tangent v pj of the particle surface and the tangent v bj of the liquid bridge surface. The corresponding contact angle θ j is the included angle between v pj and v bj , and θ is the average value of θ j .

[0087] According to the above method, the variation of the liquid bridge suction force with the inter-particle distance is measured under the conditions of different liquid bridge volumes, different contact angles, and different particle shapes, as Figure 7 , Figure 8 , Figure 9 shown. The maximum inter-particle distance on the curve is the breaking distance of the liquid bridge in this case.

Claims

1. A method for analyzing the liquid bridge suction force and fracture distance between irregular particles, characterized in that, It includes the following steps: (1) Prepare irregular particles; (2) Use a device for analyzing the liquid bridge suction force and fracture distance between irregular particles to detect a pair of irregular particles prepared in step (1). The device includes: an upper mounting rod, which is vertically arranged, and the bottom is used to mount one of the irregular particles; a lower mounting rod, which is vertically arranged, and the top is used to mount the other irregular particle. The upper mounting rod and the lower mounting rod are arranged in a straight line vertically. After the two irregular particles are respectively mounted on the upper mounting rod and the lower mounting rod, the irregular particles are close to each other; a micrometer, which is connected to the upper mounting rod and is used to drive the upper mounting rod to move vertically; a microbalance, the top surface of which has a weighing plate, and the lower mounting rod is arranged on the weighing plate; a camera, which can rotate horizontally around the upper mounting rod and the lower mounting rod and is used to take pictures of the two irregular particles at different angles; During the detection, two irregular particles are respectively installed on the upper mounting rod and the lower mounting rod. The reading of the microbalance is adjusted to zero. Distilled water is injected between the two irregular particles to establish a liquid bridge. The mass m of the liquid bridge is measured by the microbalance, and the liquid bridge suction force F cap can be calculated from m, ρ w , V w are the density and volume of distilled water respectively, and g represents the acceleration due to gravity. Then: F cap = mg - ρ w V w g; (3) Adjust the distance between the two irregular particles through the micrometer, and measure the liquid bridge mass through the microbalance to calculate different liquid bridge suction force values until the liquid bridge breaks; (4) When measuring the liquid bridge suction force in steps (2) and (3), at the same time, use the camera to take real-time pictures of the particles and the liquid bridge during the measurement process; reconstruct the 3D view based on the image data obtained from the pictures, and determine the spherical coordinate origin positions of the two irregular particles; calculate the spherical coordinate origin distance between the two irregular particles, and the spherical coordinate origin distance between the two irregular particles corresponding to when the liquid bridge breaks is the liquid bridge fracture distance.

2. The method according to claim 1, wherein When preparing irregular particles in step (1), select the center point O of the cross-section of the irregular particle, and use the polar coordinate function to describe the outer contour of the irregular particle; perform Fourier series expansion on the outer contour polar coordinate function. The coefficients of each term in the Fourier expansion formula are collectively called Fourier descriptors, which are used to quantitatively characterize the irregular geometric shape of the prepared particles; By changing the parameter values of each Fourier descriptor, particles with different geometric shapes and average radii can be randomly generated; Select three 2D particle contour surfaces randomly generated based on the Fourier series method, and place them on three mutually perpendicular planes in the three-dimensional Cartesian coordinate system, namely the xy-plane, the yz-plane, and the xz-plane; uniformly scale the sizes of the contour surfaces so that the projected lengths on the same coordinate axis are the same, thereby meeting the compatibility conditions of the projection planes; Perform linear interpolation on the polar coordinate equations of the three uniformly scaled projection planes in three-dimensional space to obtain a spherical coordinate equation describing the 3D surface information of the irregular particle; based on the spherical coordinate information of the three-dimensional geometric shape of the obtained particle, use 3D printing technology to produce the corresponding irregular particle.

3. The method according to claim 2, wherein Perform Fourier expansion on the polar coordinate equation to obtain the equation: Then, the definition of the Fourier descriptor used to describe the particle shape is: where r0 is the average radius; A n , B n are the spectra of the nth harmonic; D n is the nth-order Fourier descriptor; N is the total number of harmonics, N > 8.

4. The method according to claim 3, wherein D n has the following relationship with n: Determine a set of Fourier descriptors D by given β1, β2, D2, D3, D8 n , so as to construct and obtain irregular particles.

5. The method according to claim 1, characterized in that The precision of the microbalance is 0.01 milligrams.

6. The method according to claim 1, wherein The microbalance is provided with a windproof cover, and the micrometer is arranged on the top surface of the windproof cover.

7. The method according to claim 1, wherein On the side of the camera facing away from the upper mounting rod and the lower mounting rod, there is an LED backlight, and the LED backlight can also rotate horizontally around the upper mounting rod and the lower mounting rod.

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