Accurate measurement method of contact angle within a small angle

The wetting phenomenon of liquid on a solid surface is a fundamental natural phenomenon in nature. It has a significant impact on people’s production and life. This paper solves the problem that small-angle wetting cannot be accurately measured by changing the imaging direction and complete auxiliary methods.


Introduction
Wettability is one of the fundamental properties of solid surfaces.It plays a vital role in industrial and agricultural production and people's daily lives, encompassing oil extraction, pesticide spraying, fabric waterproofing, and washing.Surface wettability mainly hinges on surface roughness and surface free energy, which is usually measured by the contact angle between the droplet and the solid surface.In the equilibrium state, the tangent lines to the solid and liquid surfaces are drawn at the junction of the three phases of solid, liquid, and gas, respectively.The angle formed by two tangent lines inside the liquid is the contact angle.There are usually three methods for measuring the wetting angle [1][2][3]: Wilhelmy plate, session drop, and capacitive bubble.The larger the contact angle is, the better the wettability will be.The surface can be completely dripped to the ground, showing good wettability, indicating that the surface is completely covered by a substance.The smaller the contact angle is, the worse the wettability of the substance is, and the surface cannot be completely dropped by the liquid.Therefore, the contact angle is also widely used for wettability experimental research and surface control.The precise measurement of contact angle plays an essential role in the research of related fields.
Contact angle measuring instrument is a vital equipment for measuring contact angle.At the moment, the commonly used contact angle measurement is to image from the side and read the contact angle directly [4][5], as shown in Figure 1: The characteristic of the mentioned measurement method is that the frame is taken directly along the horizontal direction of the specimen surface.There is no theoretical error in the test method.It has become the primary method for contact angle measurement at present.However, when the contact angle is small and the droplet diameter is large, the depth of field at the edge of the droplet increases as the droplet radius increases (as shown in Figure 2).In addition, due to the limited height of the liquid, it is unable to provide enough light reflection, and the droplet edge imaging will generate a large error, resulting in a doubling of the final measurement error [6].Building upon the above reasons, the current contact angle test equipment will produce a relatively large error when the contact angle is below 10.The smaller the contact angle is, the greater the measurement error will be.When the accuracy requirements are not stringent and the contact angle is less than 5-7℃, researchers often assume that the liquid is thoroughly wetted [7], and further investigations are typically not pursued.In reality, many liquids, despite having small contact angles, still exhibit variations in their wetting capabilities.It is crucial to select the most suitable liquid among approximate candidates, differentiate the optimal wetting medium on specific surfaces, and research areas such as wetting on superhydrophilic surfaces.However, these endeavors require more advanced and high-precision measurement methods for support.Although current testing institutions have made unremitting efforts in the fields of light sources, testing methods, and platform stability, due to the limitations of testing methods, the accurate evaluation of small contact angles is still an insurmountable worldwide problem [8][9][10].To alleviate the mentioned problems, an accurate evaluation of a small contact angle is the main motivation of this paper.

Framing direction settings
Given the above existing problems, the testing principle is improved and designed, commencing from side imaging to the top imaging of samples, to easily obtain a top-down view of the entire droplet after the droplet has spread.Then, the area of the droplet is used to solve the problem.This design solves the problem that small contact angles cannot accurately image.The specific framing direction is shown in Figure 3: This testing method differs from conventional contact angle tests by imaging from above the specimen rather than from the side, eliminating the influence of depth of field on imaging.This modification facilitates obtaining the entire droplet shape after spreading, allowing for precise characterization of the wetting state of small-angle wetting droplets.

Principle and design of light source irradiation method
When the reagent drops on the sample, most of the droplets are transparent, similar in the color of the sample, and cannot be clearly imaged.During the experiment, a surface light source is provided to cover the entire sample.The droplets and the sample reflect light at different angles, resulting in a clear image in the camera.The schematic diagram is shown in Figure 4.In Figure 4, θ and θ′ are the incident angle and reflection angle.

Wetting experiment operation method
A digital imaging device is placed at the camera lens of Figure 4 to obtain the wetting status of the liquid on the sample surface.Since this experiment requires continuous shooting, the camera equipment should have an automatic timing shooting function, and the pixels should meet the requirements for clear imaging (pixels greater than 2 million).With the development of digital equipment, there are many related equipment.For example, general-purpose single lens reflex (SLR) cameras and dedicated digital imaging equipment can achieve such functions.By focusing parallel light on the sample surface, the surface color of the wet sample is nearly consistent after being photographed (when the tolerance is less than 20 in Photoshop, the background color of all samples can be extracted), as shown in Figure 5.If examining the wetting state at a specific moment, capturing a single photograph is sufficient.However, if investigating the dynamic wetting process of a droplet on the specimen surface, multiple photos need to be taken at regular intervals.When studying the dynamic wetting process, the observation time should exceed 1 minute, and the number of captured photos should be no less than 5.

Extraction of droplet wetted area
In Photoshop, the following method can be used to remove the area outside the droplets: (1) Areas other than the non-wetted sample are manually selected and removed; (2) All areas of the wetted sample are selected and removed using a magic wand tool with a tolerance of 20.The droplets' shape after differentiation is shown in Figure 6:

Calculation method of contact angle
The calculation of the contact angle involves the following steps: 1) The pixel value of the length of the wetted sample in the picture in Figure 6 is measured using the ruler function in the PS software, and the total pixels of the wetted sample are calculated using length*width.
2) The actual length and width of the wetted sample are measured and the actual area of the sample is calculated.
3) The histogram module in the PS software is opened, droplets are selected, and the total pixel values of the four droplets in Figure 6 are read.
4) The area of four droplets is calculated through the pixel ratio of the droplet to the sample and the area of four droplets is divided by 4 to get the average area of each droplet.
5) the droplet radius r is derived according to the area equation of a circle: A = πr , and the actual radius value is calculated from the ratio of radius to piece length.
Substituting the radius r into the equation yields: The contact angle of the reagent on the sample surface can be obtained.
In Equation (1), v is the droplet volume, representing the average value of the volume of each droplet in previous experiments, r is the radius of the droplet, and θ is the contact angle.
Since Equation ( 1) is a linear equation with one unknown, an appropriate method is required to calculate the solution of the equation.For example, this can be achieved using the single-variable solution method in Excel or programming calculations.

Validation of the small contact angle testing
A contact angle wetting experiment is conducted using butanoic acid on the surface of silicon carbide ceramics due to its superior wetting effect.

Experimental environment
Since the experiment is not only oriented to a single experimental target, the surface tension and spread of organic chemical reagents on solid surfaces are different under different temperature conditions.In order to reduce the deviation caused by temperature on the measurement results of the wetting experiment and ensure that the experimental data is true and reliable, the test temperature must be constant.In the experiment, the experimental site and reagent temperatures are artificially set at 25°.Under the same temperature conditions, different reagents can show better compatibility.The imaging equipment utilized is the Canon 700D DSLR camera, assisted by the JGW-360r contact angle testing platform and a microinjection system.The lighting source employed is a three-stage adjustable LED light source.

Experimental process and results
The auxiliary information recorded through Photoshop is shown in Table 1 As can be seen from Table 2, the wetting of n-butanol on the silicon carbide ceramic surface continues to decrease from the initial 4.95 degrees to 2.9 degrees and remains stable as time increases.It should be emphasized that in this experiment, the final stable contact angle on the silicon carbide ceramic surface was 2.9 degrees, which cannot be measured with a traditional contact angle tester.Since this article uses a top-down view for measurement, the larger the wetted area is and the smaller the contact angle is, the higher the measurement accuracy will be, which makes up for the shortcomings of the traditional contact angle measurement method.
Moreover, theoretically, contact angle measurements should be conducted when the wetting liquid is stable.However, different wetting liquids may take varying amounts of time to reach a stable state.In this study, a timed measurement method was employed, allowing for the identification of a stable wetting state through the changing wetting process.This approach avoids prolonged waiting times and variations in contact angle due to liquid evaporation, thereby enhancing measurement accuracy.

Conclusion 1)
Conventional wetting angle measurement devices often face challenges in accurately measuring small contact angles due to excessive depth of field, leading to difficulties or even impossibility in conducting precise measurement experiments.The top-down view measurement method proves effective in detecting the wetting conditions of small contact angles, offering higher detection accuracy.
2) The data corresponding to the top-down framing method in this article can be quantified by using the proportion of pixels in the wetted area to the entire area.Then, the wetting angle can be calculated through the equation =3tan( )+tan ( ).
3) The wetting angle test method for top-down framing is suitable for accurate measurement of small-angle wetting angles, especially for wetting angles below 7° that are difficult to measure with conventional wetting angle devices.

Figure 1 .
Figure 1.Framing direction settings for commonly used contact angle test.

Figure 2 .
Figure 2. Variation of the detected depth of field in the contact angle with droplet radius.

Figure 3 .
Figure 3. Framing direction of contact angle.

Table 1 .
: Auxiliary information for contact angle calculation.

Table 2 .
Contact angle calculation information table.