Device and method for measuring capillary acting force between floating particles and solid wall surface

Abstract

The invention relates to a device and method for measuring capillary acting force between floating particles and a solid wall surface, the device comprises a base, a background plate, a measuring cylinder, an overflow barrel, a camera, a light supplementing lamp, a water supplementing system, a probe fixing system and a wall surface fixing system, the overflow barrel is arranged on the plane base, the measuring cylinder is arranged in the overflow barrel, and the camera is arranged on the background plate. Water is supplemented to the measuring cylinder through a water supplementing pipe and a micro-flow valve of the water supplementing system, floating particles are fixed through the probe fixing system, illumination adjustment is conducted through a light supplementing lamp, and liquid bridge shape recognition is conducted through a camera and image recognition software. The method has the advantages of high measurement precision, simplicity and convenience in operation, wide application range and the like, and can be widely applied to the fields of environmental protection, industrial production and scientific research.

Description

Technical Field

[0001] This application relates to the field of ecological environment protection, and specifically to a device and method for measuring the capillary force between floating particles and a solid wall surface. Background Art

[0002] Floating particles widely exist in natural water bodies, especially in wetland ecosystems, lakes, rivers, and the ocean. The propagation process of floating particles has an important impact on aspects such as ecological restoration, water flow regulation, and species invasion. Floating particles usually include organic life forms such as plant seeds, fish eggs, larvae, and snails. Under the action of water flow, these particles are often driven and spread in different water areas. Studying the movement and settlement laws of floating particles not only helps to understand the migration process of substances and organisms in the ecosystem but also provides a theoretical basis for water ecological protection, wetland restoration, etc.

[0003] Capillarity, as a physical phenomenon commonly existing in nature, plays a crucial role in the interaction between floating particles and the wall surface. Capillary force is the mutual attraction formed between floating particles and the surrounding medium (such as the water surface, plant stems, other floating particles, etc.) due to the action of surface tension of the water. Specifically, the liquid surface between the solid side wall and the floating particles often presents a semi-circular arc shape. The capillary force in this arc-shaped liquid surface has both vertical and horizontal components. The horizontal component causes the floating particles to approach each other, while the vertical component balances the weight of the liquid, ensuring the floating stability of the particles. For hydrophilic floating particles (such as plant seeds, fish eggs, etc.), when their surfaces come into contact with the water surface, the capillary force will further cause the particles to approach the solid wall surface (such as stems, the shore, etc.), forming a clustering phenomenon.

[0004] However, the difficulty in measuring the capillary force lies in the complexity of the shape and morphology of floating particles. Floating particles in nature have various shapes, which may be spherical, ellipsoidal, disc-shaped, etc. This complex shape makes the calculation of the capillary force difficult. Traditionally, researchers often simplify the particles into standard shapes (such as spherical, ellipsoidal, or square) for analysis, but this method often has a large error and is difficult to accurately reflect the actual situation. For example, when irregularly shaped particles come into contact with the wall surface, the action mode of the capillary force is significantly different from that of particles with standard shapes.

[0005] Currently, the measurement of capillary force usually relies on experimental data or theoretical models. For irregularly shaped floating particles, there is a lack of a simple and reliable measurement method. Therefore, there is an urgent need for a technical solution that can adapt to floating particles of various shapes and sizes and accurately measure their capillary force. This technology can not only provide important data support for fields such as ecological restoration and water flow regulation but also provide key scientific bases for the management of non-native species invasion, species diffusion, and aquatic ecosystems.

[0006] In multiple fields such as ecology, climate change, and flow regulation, the research on the capillary force between floating particles and the wall will provide important theoretical support for understanding ecological processes, optimizing ecological restoration plans, and improving water treatment. With the in-depth research in this field, accurate measurement and analysis methods of capillary force will have broad application prospects, especially in the fields of ecological environment protection, agriculture, aquaculture, etc., helping us better understand and respond to the dynamic changes in the water ecosystem. Summary of the Invention

[0007] The purpose of the embodiments of this application is to provide a device and method for measuring the capillary force between floating particles and a solid wall, which can solve the problems of complex current capillary force measurement methods and insufficient engineering applications.

[0008] To achieve the above purpose, this application provides the following technical solutions:

[0009] In the first aspect, the embodiments of this application provide a device for measuring the capillary force between floating particles and a solid wall, including a base, a background board, a measuring cylinder, an overflow bucket, a camera, a fill light, a water replenishing system, a probe fixing system, and a wall fixing system. The overflow bucket is placed on the flat base, and the measuring cylinder is placed inside the overflow bucket. The measuring cylinder is replenished with water through the water supply pipe and microflow valve of the water replenishing system. The floating particles are fixed by the probe fixing system, the light is adjusted by the fill light, and the shape of the liquid bridge is recognized by the camera and image recognition software.

[0010] The base is used to fix the overflow bucket and the water supply pipe, and the structure of the base is designed as a frame-type bracket.

[0011] The background board is made of high-density polyethylene material and is light gray in color to ensure that there is no reflection in the background during the shooting process and avoid interfering with the image quality.

[0012] The diameter of the measuring cylinder is 15 - 25 cm, the height is 20 cm, the edge is designed with rounded corners, the part of the cylinder mouth is concave, the angle is 5° - 15°, and it is coated with a hydrophobic material to effectively prevent the liquid from spreading when it touches the cylinder mouth and ensure the formation of a stable convex liquid surface in the middle area of the measuring cylinder for easy observation and shooting.

[0013] The overflow bucket is fixed on the base, with a diameter of 40 cm, and is used to receive the water overflowing from the measuring cylinder to ensure the stability of the water level during the measurement process.

[0014] The water supply pipe of the water replenishing system conveys water through a PVC pipe with a diameter of 4 - 6 mm, and the microflow valve of the water replenishing system is precisely controlled by a PID control valve with an accuracy of ±1% to ensure the stable replenishment of water flow and keep the liquid level in the measuring cylinder stable.

[0015] The probe fixing system includes a probe needle, which is embedded in a slider. The slider moves freely along seven annular sliding rails to precisely control the position of floating particles.

[0016] The wall fixing system fixes the solid wall at the bottom of the measuring cylinder through a fixing frame. The fixing frame is made of square aluminum alloy, and there is an aluminum alloy bolt on each side to ensure that the wall is firmly fixed at the bottom of the measuring cylinder, simulating a vegetation or hard wall.

[0017] In a second aspect, an embodiment of the present application provides a method for measuring the capillary force between floating particles and a solid wall, including the following steps:

[0018] (1) Determine the simulated wall and floating particles: Use real particles, water-absorbing biological balls, wood, and polycarbonate materials as simulated particles. The solid wall is a vegetation or hard wall. The simulated vegetation is made of a soft material, and the hard wall is simulated using high-density polyethylene, metal, and plexiglass materials;

[0019] (2) Measurement needle arrangement and adjustment: Select a suitable measurement needle according to the maximum diameter of the floating particle. If the maximum diameter of the floating particle is less than 3 cm, select 3 inner measurement needles for measurement; if the maximum diameter of the floating particle is greater than 3 cm, gradually select 4 outer measurement needles. The measurement needles are fixed through a slider and rail system, and ensure that the distance between the measurement needle and the floating particle can be precisely adjusted during the measurement process;

[0020] (3) Water replenishment process and water level adjustment: Adjust the water flow through a PID control valve. First, raise the water level to 18 cm, and then slowly adjust the small valve opening to continue replenishing water, so that the water level gradually rises to the mouth of the measuring cylinder, and the liquid surface is slightly higher than the surface of the barrel mouth to ensure the stability of the liquid surface and avoid fluctuations affecting the formation of the liquid bridge;

[0021] (4) Place the floating particle and adjust the measurement needle: Slowly place the floating particle on the water surface, and use the measurement needle to adjust the position of the floating particle to gradually approach the solid wall. Each adjustment distance is about 5 mm. Observe the change in capillary force and use a fill light for illumination to ensure that the formation process of the liquid bridge is clearly visible;

[0022] (5) Liquid bridge formation and photographing record: When an obvious liquid bridge is formed between the floating particle and the solid wall, use a high-resolution camera to take a photo, record the formation process of the liquid bridge after each measurement needle adjustment, gradually reduce the distance between the floating particle and the wall, and take a photo after each adjustment to ensure a detailed record of the morphological changes of the liquid bridge;

[0023] (6) Image analysis and data processing: Use OpenCV software to process the captured images, identify the shape and geometric features of the liquid bridge. Through edge detection and contour analysis, extract the parameters of the liquid bridge, calculate the relationship between the capillary force and the distance, and obtain accurate capillary force data through statistical analysis of multiple measurement results.

[0024] The calculation formula for calculating the relationship between the capillary force and the distance is as follows:

[0025]

[0026] In the formula, Fc is the capillary force, dp is the equivalent diameter of the particle, ds is the equivalent diameter of the solid wall surface. The equivalent diameter is the diameter of a circle with the same size as the top-view area; α p is the contact angle between the particle and the liquid bridge; α s is the contact angle between the solid wall surface and the liquid bridge; φ p is the filling angle between the liquid bridge at the particle end and the horizontal line; φs is the filling angle between the liquid bridge at the solid wall surface end and the horizontal line; is the surface tension coefficient; L is the distance between the particle and the solid wall surface, q is the capillary force parameter, , is the liquid density, is the air density, g is the acceleration due to gravity.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows: Integrate a high-precision water level adjustment and fine-tuning system and a programmable probe positioning mechanism in the same device, which can accurately quantify the capillary force for irregularly shaped floating particles and various solid wall surfaces; simple operation, high repeatability, and wide application ranges for particle materials, sizes, and wall surface types; real-time collect the morphology of the liquid bridge through a high-resolution camera and image recognition software, significantly improving data reliability; the obtained experimental results can be directly used for optimizing wetland ecological restoration plans, screening superhydrophobic / superhydrophilic materials, improving microfluidic and membrane separation processes, and calibrating and validating numerical models of interfacial hydrodynamics, with broad engineering application and scientific research promotion value. In ecological restoration and water treatment, it can quantitatively evaluate the capillary force of floating particles (such as plant seeds, fish eggs, snails, etc.) in complex environments, providing technical support for wetland restoration, shore vegetation configuration, and pollutant interception; in microfluidics, bioseparation, and membrane separation processes, it can accurately characterize the mechanical parameters of the liquid bridge, guiding the screening of superhydrophobic / superhydrophilic materials and process optimization; in interfacial physics and multiphase flow research, the experimental data obtained by the present invention can be used to calibrate numerical simulation models such as CFD and DEM. Description of the Drawings

[0028] To more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings required for use in the embodiments of the present application. It should be understood that the following drawings only show some embodiments of the present application, and thus should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings.

[0029] Figure 1 It is the overall layout diagram of the experimental device

[0030] Figure 2 It is the design drawing of the bottom of the measuring cylinder

[0031] Figure 3 It is the sectional view of the measuring cylinder

[0032] Figure 4 Side view of the measurement process

[0033] Figure 5 It is the top view of the measurement process. Specific implementation manners

[0034] The following will describe the technical solutions in the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. It should be noted that: similar reference numerals and letters indicate similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0035] The term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or device including the said element.

[0036] Terms such as "first", "second", etc. are only used to distinguish one entity or operation from another entity or operation, and cannot be understood as indicating or implying relative importance, nor can it be understood as requiring or implying any such actual relationship or order between these entities or operations.

[0037] Please refer to Figure 1- 5, the present invention provides a device for measuring the capillary force between floating particles and a solid wall surface, including a base 1, a background plate 11, a measuring cylinder 3, an overflow bucket 2, a camera 13, a fill light 9, a water replenishing system, a probe fixing system, a wall surface fixing system 7, etc. The overflow bucket 2 is placed on the flat base 1, and the measuring cylinder 3 is placed inside the overflow bucket 2. The measuring cylinder 3 is replenished with water through the water replenishing pipe 4 and the microflow valve 5 of the water replenishing system. The floating particles 18 are fixed by the probe fixing system. The illumination is adjusted through the annular fill light strip of the fill light 9, and the annular fill light strip is fixed by the light strip fixing clip 10. The shape of the liquid bridge 19 is recognized by using the camera 13 and image recognition software.

[0038] The base 1 is used to fix the overflow bucket 2, the water replenishing pipe 4, etc. It is made of aluminum alloy, and the structural design is a frame-type support, which can stably fix the overflow bucket 2 and the water replenishing pipe 4, and is convenient for assembly and disassembly at the same time.

[0039] The background plate 11 is made of high-density polyethylene material and is light gray in color to ensure that there is no reflection in the background during the shooting process and avoid interfering with the image quality.

[0040] The measuring cylinder 3 has a diameter of 15 - 25 cm and a height of 20 cm. The edge is designed with rounded corners, and the part of the cylinder mouth is slightly concave, with an angle of 5° - 15°. It is coated with a hydrophobic material to effectively prevent the liquid from spreading when it touches the cylinder mouth, ensuring the formation of a stable convex liquid surface 8 in the middle area of the measuring cylinder 3, which is convenient for observation and shooting.

[0041] The overflow bucket 2 is fixed on the base 1 and has a diameter of 40 cm, which is used to receive the water overflowing from the measuring cylinder 3 to ensure the stability of the water level during the measurement process.

[0042] The water replenishing pipe 4 of the water replenishing system conveys water through a PVC pipe with a diameter of 4 - 6 mm, and the microflow valve 5 of the water replenishing system is precisely controlled by a PID control valve with an accuracy of ±1% to ensure the stable replenishment of water flow and maintain the smoothness of the liquid level in the measuring cylinder 3.

[0043] The probe fixing system includes a stainless steel probe 6 with a diameter of 3 mm and a length of 22 cm. The stainless steel probe 6 is embedded in the stainless steel slider 15. The width of the stainless steel slider 15 is 1 cm, and the stainless steel slider 15 moves freely along seven annular slide rails 17. The width of the annular slide rails 17 is 8 mm, which are fixedly installed on the upper surface of the measuring cylinder bottom plate 14. The distance between the 3 inner annular slide rails is 1 cm, and the distance between the 4 outer annular slide rails is 2 cm, ensuring the selection of a suitable track according to the size of the floating particles 18 to precisely control the position of the floating particles 18.

[0044] The wall fixing system 7 fixes the solid wall at the bottom of the measuring cylinder 3 through the fixing bracket 16. The fixing bracket is made of square aluminum alloy with a width of 2 cm, and an aluminum alloy bolt is provided on each side to ensure that the wall is firmly fixed at the bottom of the cylinder, simulating a vegetative or hard wall.

[0045] The camera 13 is fixedly installed through the camera bracket 12 mounted on the base 1. The camera 13 uses a zoom lens (24 - 70mm f / 2.8), has a 4K resolution, and is configured with computer control functions and software. The image recognition software uses OpenCV software to identify the liquid bridge 19 through threshold segmentation, contour detection, and morphological operations, uses edge detection to highlight the contour of the liquid bridge 19, and further screens and analyzes the characteristics of the liquid bridge 19 through parameters such as area, shape, and position.

[0046] A method for measuring the capillary force between floating particles and a solid wall, comprising the following steps:

[0047] (1) Determine the simulated wall and floating particles: The floating particles include plant seeds, fish eggs, other organisms, etc. Real particles, water-absorbing bio-balls, wood, polycarbonate, etc. can be used as simulated particles. The solid wall is generally a vegetative or hard wall. The simulated vegetation can be made of soft materials (such as cylinders or sheets made of polyethylene, artificial rubber, wood, etc.), and the hard wall can be simulated using materials such as high-density polyethylene, metal, and plexiglass.

[0048] (2) Measurement needle arrangement and adjustment: Select a suitable measurement needle according to the maximum diameter of the floating particles. If the maximum diameter of the floating particles is less than 3 cm, then select 3 inner measurement needles for measurement; if the maximum diameter of the floating particles is greater than 3 cm, then gradually select 4 outer measurement needles. The measurement needles are fixed through a slider and rail system, and ensure that the distance between the measurement needles and the floating particles can be precisely adjusted during the measurement process.

[0049] (3) Water replenishment process and water level adjustment: Regulate the water flow through the PID control valve. First, raise the water level to 18 cm, and then slowly adjust the small valve opening to continue replenishing water, so that the water level gradually rises to the mouth of the measuring cylinder, and the liquid level is slightly higher than the surface of the barrel mouth. Ensure the stability of the liquid level and avoid fluctuations affecting the formation of the liquid bridge.

[0050] (4) Placement of floating particles and adjustment of measurement needles: Slowly place the floating particles on the water surface, and use the measurement needles to adjust the position of the floating particles to gradually approach the solid wall. Each time the adjustment distance is about 5 mm, observe the change in capillary force and use a supplementary light for illumination to ensure that the formation process of the liquid bridge is clearly visible.

[0051] (5) Liquid bridge formation and recording: After an obvious liquid bridge is formed between the floating particle and the solid wall, use a high-resolution camera to take pictures. Record the formation process of the liquid bridge after each probe adjustment. Gradually reduce the distance between the floating particle and the wall, and take pictures after each adjustment to ensure a detailed record of the morphological changes of the liquid bridge.

[0052] (6) Image recognition and data analysis. Use OpenCV software for image processing and analysis to read the shape parameters of the liquid bridge. The software can automatically identify the liquid bridge in the image and extract relevant geometric features through algorithms such as edge detection, morphological transformation, and contour analysis. Combine image processing algorithms with an accurate pixel coordinate system to further quantify the mechanical characteristics of the liquid bridge and provide data support for subsequent calculation of capillary forces. Through the statistics and analysis of multiple measurement data, give the functional relationship between the capillary force and the distance. The specific analysis content includes indicators such as the width, morphology, contact angle, and filling angle of the liquid bridge. The calculation formula for the relationship between the capillary force and the distance is as follows:

[0053]

[0054] In the formula, Fc is the capillary force, dp is the equivalent diameter of the particle, ds is the equivalent diameter of the solid wall, and the equivalent diameter is the diameter of a circle with the same size as the top view area; α p is the contact angle between the particle and the liquid bridge; α s is the contact angle between the solid wall and the liquid bridge; φ p is the filling angle between the liquid bridge at the particle end and the horizontal line; φs is the filling angle between the liquid bridge at the solid wall end and the horizontal line; is the surface tension coefficient; L is the distance between the particle and the solid wall, q is the capillary force parameter, , ρ w is the liquid density, ρ a is the air density, and g is the acceleration due to gravity.

[0055] The values of the capillary tension are as described in the following table.

[0056]

[0057] The above are only the embodiments of the present application and are not used to limit the protection scope of the present application. For those skilled in the art, various changes and modifications can be made to the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. An apparatus for measuring the capillary force between a floating particle and a solid wall, characterized in that, It includes a base, a background board, a measuring cylinder, an overflow bucket, a camera, a fill light, a water replenishing system, a probe fixing system and a wall fixing system. The overflow bucket is placed on the flat base, and the measuring cylinder is placed inside the overflow bucket. The measuring cylinder is replenished with water through the water replenishing pipe and the microflow valve of the water replenishing system. The floating particles are fixed by the probe fixing system. The light is adjusted by the fill light, and the shape of the liquid bridge is recognized by the camera and the image recognition software.

2. The device for measuring the capillary force between floating particles and a solid wall surface according to claim 1, characterized in that The base is used to fix the overflow bucket and the water replenishing pipe, and the structure of the base is designed as a frame-type support.

3. The device for measuring the capillary force between floating particles and a solid wall surface according to claim 1, wherein The background board is made of high-density polyethylene material and is light gray in color to ensure that there is no reflection in the background during shooting and to avoid interfering with the image quality.

4. The device for measuring the capillary force between floating particles and a solid wall surface according to claim 1, characterized in that, The measuring cylinder has a diameter of 15 - 25 cm and a height of 20 cm. The edge is designed with rounded corners, and the part of the cylinder mouth is concave, with an angle of 5° - 15°. It is coated with a hydrophobic material to effectively prevent the liquid from spreading when it touches the cylinder mouth, ensuring the formation of a stable convex liquid surface in the middle area of the measuring cylinder for easy observation and shooting.

5. The device for measuring the capillary force between floating particles and a solid wall surface according to claim 1, wherein The overflow bucket is fixed on the base and has a diameter of 40 cm. It is used to receive the water overflowing from the measuring cylinder to ensure the stability of the water level during the measurement process.

6. The device for measuring the capillary force between floating particles and a solid wall surface according to claim 1, wherein The water replenishing pipe of the water replenishing system conveys water through a PVC pipe with a diameter of 4 - 6 mm, and the microflow valve of the water replenishing system is precisely controlled by a PID control valve with an accuracy of ±1% to ensure the stable replenishment of water flow and maintain the smoothness of the liquid surface in the measuring cylinder.

7. The device for measuring the capillary force between floating particles and a solid wall surface according to claim 1, wherein The probe fixing system includes a measuring needle. The measuring needle is embedded on the slider, and the slider moves freely along seven circular slide rails to precisely control the position of the floating particles.

8. The device for measuring the capillary force between floating particles and a solid wall surface according to claim 1, wherein The wall fixing system fixes the solid wall at the bottom of the measuring cylinder through a fixing frame. The fixing frame is made of square aluminum alloy, and there is an aluminum alloy bolt on each side to ensure that the wall is firmly fixed at the bottom of the measuring cylinder to simulate a vegetation or a hard wall.

9. A method for measuring the capillary force between a floating particle and a solid wall, characterized in that, It includes the following steps: (1) Determine the simulated wall and floating particles: Use real particles, water-absorbing bio-balls, wood, and polycarbonate materials as simulated particles. The solid wall is a vegetation or a hard wall. The simulated vegetation is made of a soft material, and the hard wall is simulated with high-density polyethylene, metal, and plexiglass materials; (2) Arrangement and adjustment of the measuring needles: Select a suitable measuring needle according to the maximum diameter of the floating particles. If the maximum diameter of the floating particles is less than 3 cm, then select 3 inner measuring needles for measurement; if the maximum diameter of the floating particles is greater than 3 cm, then gradually select 4 outer measuring needles. The measuring needles are fixed through the slider and the slide rail system, and ensure that the distance between the measuring needle and the floating particles can be precisely adjusted during the measurement process; (3) Water replenishing process and water level adjustment: Adjust the water flow through the PID control valve. First, raise the water level to 18 cm, and then slowly adjust the small valve opening to continue replenishing water, so that the water level gradually rises to the mouth of the measuring cylinder, and the liquid surface is slightly higher than the surface of the bucket mouth to ensure the stability of the liquid surface and avoid fluctuations from affecting the formation of the liquid bridge; (4)Placement of floating particles and adjustment of the measuring needle: Slowly place the floating particles on the water surface and use the measuring needle to adjust the position of the floating particles to gradually approach the solid wall surface. The distance of each adjustment is about 5 mm. Observe the change of capillary force and use a fill light for illumination to ensure the clear visibility of the liquid bridge formation process; (5)Liquid bridge formation and photography recording: After an obvious liquid bridge is formed between the floating particle and the solid wall surface, use a high-resolution camera to take pictures and record the liquid bridge formation process after each adjustment of the measuring needle. Gradually reduce the distance between the floating particle and the wall surface and take pictures after each adjustment to ensure the detailed recording of the morphological changes of the liquid bridge; (6)Image analysis and data processing: Use OpenCV software to process the taken images, identify the shape and geometric features of the liquid bridge, extract the parameters of the liquid bridge through edge detection and contour analysis, and calculate the relationship between the capillary force and the distance. Through the statistical analysis of multiple measurement results, accurate capillary force data can be obtained.

10. A method for measuring the capillary force between a floating particle and a solid wall surface according to claim 9, wherein, The calculation formula for calculating the relationship between the capillary force and the distance is as follows: ， where Fc is the capillary force, dp is the equivalent diameter of the particle, ds is the equivalent diameter of the solid wall, and the equivalent diameter is the diameter of a circle with the same size as the top view area; α p is the contact angle between the particle and the liquid bridge; α s is the contact angle between the solid wall and the liquid bridge; φ p is the filling angle between the liquid bridge at the particle end and the horizontal line; φs is the filling angle between the liquid bridge at the solid wall end and the horizontal line; is the surface tension coefficient; L is the distance between the particle and the solid wall, q is the capillary force parameter, , is the liquid density, is the air density, is the acceleration due to gravity.

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