Influence and Correction of Refraction Phenomenon in Liquid Contact Angle Measurement in Capillary Tube

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have presented a novel approach for measuring contact angles, offering a potential alternative to the widely adopted sessile droplet method. While their work provides valuable insights into this area, a few points need to be addressed to strengthen the study further.

1. The authors are requested to clarify how the calibration of the instrument is performed and the level of difficulty involved in the calibration process. Further details on this aspect would help in understanding the accuracy and reliability of the proposed method.
2. The sessile droplet method is a commonly used and well-accepted technique in the research community for measuring contact angles. The authors need to incorporate a comparison of the newly proposed method with the sessile droplet method in terms of accuracy and other relevant factors.
3. To evaluate the accuracy of the proposed method more effectively, the authors are requested to include a comparison of the contact angle values measured by both the sessile droplet method and the proposed method.
4. The authors need to address whether it is possible to measure contact angle hysteresis using the proposed method. This would provide valuable insight and add depth to the understanding of surface behavior.
5. While the proposed method can predict static contact angles, the authors are requested to explore whether it can also be extended to predict dynamic contact angles.
6. It would be beneficial for the authors to include information on the reproducibility and robustness of the proposed method. Are the measurements consistent across different trials and varying surface conditions? The authors should provide data or examples demonstrating the reliability of the method under various experimental setups. Additionally, contact angle values with error bars need to be incorporated into the manuscript.
7. The authors are encouraged to discuss any potential limitations or scenarios where the proposed method might not perform as well compared to existing techniques.
8. The authors are requested to provide a discussion on the practical aspects of implementing the proposed method in real-world applications. This should include equipment requirements, ease of use, and potential challenges in translating the method to industrial or laboratory settings, to provide a clearer perspective on its feasibility.
9. Aside from the sessile droplet method, the authors may need to briefly compare the proposed method with other popular techniques for contact angle measurement, such as the advancing/receding drop method or the tilting plate method, to provide a more comprehensive understanding of its relative advantages.
10. The authors are requested to clarify how the proposed method handles variations in surface roughness. Does it account for or correct the effects of roughness on contact angle measurements? Since surface roughness can significantly influence results.

Author Response

Comments 1:The authors are requested to clarify how the calibration of the instrument is performed and the level of difficulty involved in the calibration process. Further details on this aspect would help in understanding the accuracy and reliability of the proposed method.

Response 1:Thanks for the reviewer’s comments. This study used a Canon 1DX Mark II camera (21.5 million pixels, 50 frames per second) to directly record the meniscus morphology of liquid droplets in capillary tube. The vapor-liquid interface contour was captured, and measurement coordinate points were extracted based on image analysis software (such as ImageJ) and contact angles were measured using angle measurement tool in the software. Since the core of this method is to obtain vapor-liquid interface lines through a digital camera, and the camera operates under fixed focal length and lighting conditions, no additional instrument calibration is required. To ensure measurement accuracy, we have taken the following measures: (1) Focus calibration of the camera before the experiment to ensure that the imaging plane is perpendicular to the capillary axis; (2) Use standard scales to ensure accurate conversion of geometric dimensions; (3) Verify the repeatability of measurement results through repeated experiments. This method avoids the systematic errors of complex instruments and relies on direct analysis of high-resolution images, simplifying the experimental process while ensuring reliability.

Comments 2: The sessile droplet method is a commonly used and well-accepted technique in the research community for measuring contact angles. The authors need to incorporate a comparison of the newly proposed method with the sessile droplet method in terms of accuracy and other relevant factors.

Response 2: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 3:To evaluate the accuracy of the proposed method more effectively, the authors are requested to include a comparison of the contact angle values measured by both the sessile droplet method and the proposed method.

Response 3:Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 4:The authors need to address whether it is possible to measure contact angle hysteresis using the proposed method. This would provide valuable insight and add depth to the understanding of surface behavior.

Response 4:Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 5:While the proposed method can predict static contact angles, the authors are requested to explore whether it can also be extended to predict dynamic contact angles.

Response 5:Thanks for the reviewer’s comments. At present, only the proposed method has been used to measure the contact angle of the working fluid when droplet in a stationary state. The dynamic contact angle includes the forward contact angle and the backward contact angle. The visualized experimental platform built can accurately control the volume of liquid in the capillary tube through a syringe. During the flow of liquid, the forward contact angle and backward contact angle can be measured.

Comments 6:It would be beneficial for the authors to include information on the reproducibility and robustness of the proposed method. Are the measurements consistent across different trials and varying surface conditions? The authors should provide data or examples demonstrating the reliability of the method under various experimental setups. Additionally, contact angle values with error bars need to be incorporated into the manuscript.

Response 6:

• Thanks for the reviewer’s comments. We have measured three sets of upper and lower contact angles of the liquid surface during quasi-static conditions (a total of six sets of data), as well as six sets of upper and lower contact angles of the droplet during the initial heating stage without activation (a total of twelve sets of data). Among the 18 sets of measured data, the difference range between the measured value and the actual value of the static contact angle is [1.84, 5.61], indicating that the proposed method has repeatability.
• Thanks for the reviewer’s comments. We have added error bars in Fig. 10.

Comments 7: The authors are encouraged to discuss any potential limitations or scenarios where the proposed method might not perform as well compared to existing techniques.

Response 7:Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 8:The authors are requested to provide a discussion on the practical aspects of implementing the proposed method in real-world applications. This should include equipment requirements, ease of use, and potential challenges in translating the method to industrial or laboratory settings, to provide a clearer perspective on its feasibility.

Response 8: 

• Thanks for the reviewer’s comments. In the laboratory, the wettability of surfaces can be evaluated by contact angle. The larger the contact angle between the surface and water, the worse the wettability of water on the surface.
• The equipment required for the contact angle measurement method proposed by us in capillary tubes is relatively simple and easy to obtain, mainly including capillary tube, high-resolution digital camera, and software for selecting measurement coordinate points and measuring contact angles. These devices are already available and easy to configure in most laboratory or industrial environments, therefore, the infrastructure threshold for implementing this method is relatively low. From the perspective of usability, our method emphasizes the simplicity and repeatability of operation. The experimental steps include vacuuming the capillary tube, injecting an appropriate amount of working fluid into the capillary tube, capturing clear vapor-liquid interface lines with a camera, selecting measurement coordinate points using software, calculating actual coordinate points using the proposed method, and finally fitting the actual vapor-liquid interface lines and measuring the contact angle using angle measurement tools in the software. Each step is easy to operate.

Comments 9: Aside from the sessile droplet method, the authors may need to briefly compare the proposed method with other popular techniques for contact angle measurement, such as the advancing/receding drop method or the tilting plate method, to provide a more comprehensive understanding of its relative advantages.

Response 9: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 10: The authors are requested to clarify how the proposed method handles variations in surface roughness. Does it account for or correct the effects of roughness on contact angle measurements? Since surface roughness can significantly influence results.

Response 10: Thanks for the reviewer’s comments. The static contact angle measurement method proposed in this study for capillary tube mainly involves optical measurement and geometric correction of vapor-liquid interface lines. The main objective of this study is to establish a method for measuring contact angle in capillary tubes by considering the optical refraction effects caused by the material and thickness of the tube wall. This method is suitable for measuring the contact angle of fluids in capillaries with different roughness.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors proposed a method to measure the static contact angle within a capillary tube by considering light refraction. I personally find the idea novel. However, I have the following concerns before recommending it for publication.
  
  1. In Figure 9, the left and right sides of the liquid-gas interface are not symmetric with respect to x=0. What is the reason for this asymmetry? According to the energy minimization principle, the liquid-gas interface should form part of a sphere or circle, which differs from the experimental results shown in Figure 9.
  
  Furthermore, error bars should be added in Figure 9.
  
  2.  It seems that the measured contact angle refers to the local microscopic contact angle rather than the macroscopic apparent contact angle. I wonder if the authors could measure the macroscopic contact angle using the base radius and the height of the meniscus.
  
  3. The authors only demonstrate the applicability of the method for the hydrophilic case. For the hydrophobic case, the double light refraction differs from that in the hydrophilic scenario.
  
  4. The up-to-date Young's law, Phys. Rev. Lett. 132, 126202 (2024), should be introduced in the introduction.
  
  5. Some grammar problems: line 165, The side length should be the side length, etc.

Comments on the Quality of English Language

see 5.

Author Response

Comments 1: In Figure 9, the left and right sides of the liquid-gas interface are not symmetric with respect to x=0. What is the reason for this asymmetry? According to the energy minimization principle, the liquid-gas interface should form part of a sphere or circle, which differs from the experimental results shown in Figure 9.

Furthermore, error bars should be added in Figure 9.

Response 1: 

• Thanks for the reviewer’s comments. This asymmetry is mainly due to the small errors caused by manual point selection during the experimental process, as well as the possible nanoscale local non-uniformity on the surface of the capillary. Although theoretically the vapor-liquid interface in equilibrium state should exhibit a perfect symmetrical shape, in practical experiments, there are microscopic differences in the distribution of capillary surface energy, slight vibrations of the liquid, and inevitable subjectivity in the manual point selection process. Ultimately, it may lead to asymmetric morphology at the vapor-liquid interface.
• Thanks for the reviewer’s comments. We have added error bars in Fig. 10.

Comments 2: It seems that the measured contact angle refers to the local microscopic contact angle rather than the macroscopic apparent contact angle. I wonder if the authors could measure the macroscopic contact angle using the base radius and the height of the meniscus.

Response 2:  Thanks for the reviewer’s comments. The contact angle measured in the paper is the contact angle in a capillary tube with an inner diameter of 3 mm, which can be measured using the base radius and meniscus height. But the focus of this paper is that the proposed contact angle measurement method takes into account the light refraction effect of the pipe wall material and thickness on the contact angle, and optimizes the contact angle measurement method in capillary tube.

Comments 3: The authors only demonstrate the applicability of the method for the hydrophilic case. For the hydrophobic case, the double light refraction differs from that in the hydrophilic scenario.

Response 3: Thanks for the reviewer’s comments. The contact angle measurement method in capillary tube indicates that there is a phenomenon of optical refraction in the measurement of contact angle. This phenomenon of light refraction causes deviation in the measurement of contact angle (measured value & actual value). Therefore, this measurement method is applicable for both hydrophobic and hydrophilic working fluids.

Comments 4: The up-to-date Young's law, Phys. Rev. Lett. 132, 126202 (2024), should be introduced in the introduction.

Response 4: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 5: Some grammar problems: line 165, The side length should be the side length, etc.

Response 5: Thanks for the reviewer’s comments. We have made modifications in the article.

Reviewer 3 Report

Comments and Suggestions for Authors

Shi et al. examine the effect of refraction on measurement of contact angles of water in a pulse heated capillary system.  Snell’s law for refraction along with geometric analysis leads to a correction in the shape of the vapor-liquid interface for different levels of heating.  Significant differences in the values for the contact angles are obtained.

Results of the study are interesting and of potential value to those using capillary tubes for determination of contact angles.  The presentation of their analysis is thorough and well-presented apart from the omission of the equation for DAC which can be found from Angle DAC = pi/2 - Angle OAC - Angle EAD.  Overall though, the manuscript lacks sufficient information on experimental details and on results for the reader.  

The description of the experimental system is not clear and needs further elaboration.  What is the purpose of the pulsed heating system?  No explanation is provided for its use nor is there a citation of a precedence for its use.   The temperature of the contact angle measurements has not been given.  Figure 1 is inconsistent with Figure 2 which shows an inlet and outlet at the top and bottom of the loop.   Operating conditions of the jacketed cooling system have not been described.  The heating component as represented in Figure 1 appears to mirror the cooling system rather than a resistance heating unit as shown in Figure 3. 

The methodology section indicates the interface line was fit with an equation and software was then used to determine the contact angle.   Explain the underlying theories employed by the software to find the contact angle.  Why were the upper and lower contact angles so different?  Were the effects of hydrostatic pressure taken into account? 

Discuss errors in determining contact angles by this method.    The correction for refraction is expected to improve the accuracy.    However, it seems precision can be worse on looking at the results in Table 2.  How does this method affect precision?

Captions of figures should explain the purpose of the figure and describe to the reader what it shows.   

Ln 2: Study the influence of refraction phenomenon on static contact angle measurement of liquid in a capillary tube   [The effect is on the measurement, not the contact angle.]

Ln. 18: a difference in the range of

Fig. 1:   Filling port for working fluid

Ln 75-77:   This description and the basis for Equation (1) are not clear. 

Ln 97 and Table 1: saturation temperature of 101.325 kPa?

Fig. 5:  The spherical shape does not match the structures shown in the photos.

Ln 163:   ∆ORB

Ln 166: ...is L_AE = R
Ln 169: …has been obtained,  can be found:
Ln 173:  supplementary angles, not complementary angles
Ln 179: where L_AD = r.
Ln 182: supplement
Ln 200-201: “The size of the measurement coordinates X_i increases from left to right and Y_i decreases from bottom to tip, as shown in Fig. 7.” Values given in the table of Fig. 7 don’t follow the stated trend.  Two sets of points appear in the figure.  What are these? 
Ln 213---: This belongs in the methodology section.
Ln 233---: This belongs in the methodology section.   And elsewhere.
Ln 248-250:  Sentence is not clear.

 

 

 

Author Response

Comments 1: The description of the experimental system is not clear and needs further elaboration. What is the purpose of the pulsed heating system? No explanation is provided for its use nor is there a citation of a precedence for its use. The temperature of the contact angle measurements has not been given. Figure 1 is inconsistent with Figure 2 which shows an inlet and outlet at the top and bottom of the loop. Operating conditions of the jacketed cooling system have not been described. The heating component as represented in Figure 1 appears to mirror the cooling system rather than a resistance heating unit as shown in Figure 3.

Response 1: 

• Thanks for the reviewer’s comments. The visualization experimental system mainly consists of quartz glass capillaries, vacuum and liquid filling devices, heating system, cooling system, data acquisition system, digital camera, and LED lights. Please refer to the manuscript for a detailed explanation:

“The pulsating heat pipe is vertically placed, and its bottom is wound with a nickel-chromium resistance wire for heating. The heating power is adjusted by regulating the input voltage through a transformer. At the same time, a T-type thermocouple is arranged at the bottom to collect the instantaneous temperature. The top of the pulsating heat pipe specimen is cooled by using a cooling water tank, and the cooling water is provided by a low-temperature constant temperature bath and maintained at 10℃. A Canon 1DX-Mark Ⅱ digital camera is used for shooting and recording. The total pixel of the camera is about 21.5 million, and it can take 50 photos continuously per second. The distance between the camera position and the center of the experimental system is 18 cm.

Arrange LED light with uniform illumination intensity around the pulsating heat pipe, and use LED light to create a contrast between the liquid and the background. By using this method, the vapor-liquid interface of the liquid column is clearly displayed, as shown in Fig. 3.”

• The heating system of the pulsating heat pipe is located at the bottom of the capillary tube, and heat is input to the capillary tube by adjusting the transformer. Figure 9 investigates the static contact angle during the initial heating stage. The temperature during static contact angle measurement is around 20℃ at room temperature. We have added an outlet branch in Figure 1 to ensure consistency between Figure 1 and Figure 2.
• Please refer to the manuscript for the operating description of the cooling system:

“The top of the pulsating heat pipe specimen is cooled by using a cooling water tank, and the cooling water is provided by a low-temperature constant temperature bath and maintained at 10℃.”

• In Figure 3, the bottom of the capillary tube is wrapped with a heating wire, and the bottom is the heating system. The upper part of the capillary tube is cooled by an acrylic plate water tank, which serves as the cooling system. So the heating and cooling ends expressed in Figure 1 are consistent with Figure 3.

Comments 2: The methodology section indicates the interface line was fit with an equation and software was then used to determine the contact angle. Explain the underlying theories employed by the software to find the contact angle. Why were the upper and lower contact angles so different? Were the effects of hydrostatic pressure taken into account?

Response 2: 

• Thanks for the reviewer’s comments. The measurement steps for the static contact angle of liquid in the proposed capillary tube are as follows: the camera captures a clear vapor-liquid interface line, the measurement coordinate points are selected using software, the actual coordinate points are calculated using the proposed method, and finally the actual vapor-liquid interface line is fitted and the contact angle is measured using the angle measurement tool in the software. In the process of angle measurement, the solid-liquid line and vapor-liquid line are manually selected to obtain the static contact angle of the liquid. The influence of hydrostatic pressure was not taken into account in the measurement, and images were collected based on the actual distribution state of the fluid for analysis.
• From the droplet image selected in Figure 10, it can be seen that the upper liquid surface is flatter than the lower liquid surface, resulting in a larger static contact angle value for the upper liquid surface than for the lower liquid surface.
• Thank you very much for your suggestion. We have supplemented the manuscript with the asymmetric phenomenon of liquid surface and the difference in contact angle between the upper and lower liquid surfaces of droplets.

Comments 3: Discuss errors in determining contact angles by this method. The correction for refraction is expected to improve the accuracy. However, it seems precision can be worse on looking at the results in Table 2. How does this method affect precision?

Response 3: Thanks for the reviewer’s comments. The comparison in Table 2 shows the difference between the measured and actual values of the static contact angle in the capillary tube. The focus is not on improving the accuracy of the contact angle measurement, but on pointing out that the presence of light refraction phenomenon leads to a difference between the measured value of the static contact angle (direct measurement) and the actual value (corrected for the influence of light refraction phenomenon).

Comments 4: Ln 2: Study the influence of refraction phenomenon on static contact angle measurement of liquid in a capillary tube [The effect is on the measurement, not the contact angle.]

Response 4: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 5: Ln. 18: a difference in the range of.

Response 5: Thanks for the reviewer’s comments. In the paper, three sets of upper and lower contact angles of the liquid surface were measured under quasi-static conditions (a total of six sets of data), as well as six sets of upper and lower contact angles of the droplet during the initial heating stage without startup (a total of twelve sets of data). The difference range between the measured value and the actual value of the static contact angle in the 18 sets of measured data is [1.84, 5.61].

Comments 6: Fig. 1: Filling port for working fluid

Response 6: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 7: Ln 75-77: This description and the basis for Equation (1) are not clear.

Response 7: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 8: Ln 97 and Table 1: saturation temperature of 101.325 kPa?

Response 8: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 9: The spherical shape does not match the structures shown in the photos.

Response 9: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 10:

• Ln 163: ∆ORB
• Ln 166: ...is LAE= R
• Ln 169: …has been obtained, can be found:
• Ln 173: supplementary angles, not complementary angles.

Response 10: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 11: Ln 179: where LAD= r.

Response 11: Thanks for the reviewer’s comments. Yes, L_AD = r. But in the derivation process of the formula, we uniformly represent the side length. If you feel that the expression is not clear, we will replace L_AD with r.

Comments 12: Ln 182: supplement

Response 12: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 13: Ln 200-201: “The size of the measurement coordinates Xi increases from left to right and Yi decreases from bottom to tip, as shown in Fig. 7.” Values given in the table of Fig. 7 don’t follow the stated trend. Two sets of points appear in the figure. What are these?

Response 13: 

• Thanks for the reviewer’s comments. We have made modifications in the article. When X1=2.282, it can be seen from Figure 7 that the X values from X1 to X10 show an increasing trend from left to right, and the X values from X21 to X11 also show an increasing trend from left to right. Therefore, the size of the measured coordinates Xi increases from left to right. When Y1=3.889, it can be seen from Figure 7 that the Y value from Y1 to Y10 shows a decreasing trend from bottom to top, and the X value from Y21 to Y11 also shows a decreasing trend from bottom to top.
• The data in Figure 7 (Xi, Yi) mainly refers to the last two columns (X, Y), which represent the coordinates of the measurement coordinate points.

Comments 14:

•  Ln 213---: This belongs in the methodology section.
• Ln 233---: This belongs in the methodology section.   And elsewhere.

Response 14: Thanks for the reviewer’s comments. The methodology section mainly proposes a method for measuring and converting the contact angle in capillary tube after considering the phenomenon of light refraction. Ln 213 and Ln 233 are used to select measurement targets for the contact angle in capillary tube. After selecting the measurement targets, the static contact angle measurement values and actual values are obtained through measurement and calculation, and the measurement results are discussed.

Comments 15: Ln 248-250:  Sentence is not clear.

Response 15: Thanks for the reviewer’s comments. We have made modifications in the article.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

publish as is.

Author Response

Thanks for the reviewer’s comments！

Reviewer 3 Report

Comments and Suggestions for Authors

The strength of this paper is in a method to correct errors in the perceived location of the liquid-vapor interface in capillaries due to refraction.  This work merits its publication for that contribution. 

The addition of references 18 and 19 in the revision helps one understand the functioning of the pulsating heating pipe system.  However, these articles make clear that this apparatus is not suitable as a general method for measuring contact angles.   The contact angle values measured apply only for the very specific conditions of their heated pipe system.  Differences in the structure of the vapor liquid interfaces in Figure 10 (of the response) clearly show that more than the interfacial energies between the vapor, liquid and solid are involved.  To further this point, contact angles are presented in Figure 10 of the revision as a function of heating power, not temperature. Heating rate is a property of their constructed apparatus and its operation which is of little value to others.

Pulsating/oscillating heated pipe systems tend to be dynamic with change in pressure from the condenser to the evaporator.  There tends to be motion. Yin et al. (reference 18 in the revision) state “The pressure difference between the evaporator and condenser with a vapor spring constant between them generates the oscillation motion in the system.”.   In addition, there are hydrostatic contributions in the vertically oriented loop which are not accounted for.  Their apparatus does serve the authors’ purpose of demonstrating the value of their analysis of errors due to refraction.  A revision needs to be substantially modified (abstract, introduction, discussion, conclusion) to emphasize the valuable contribution on refraction and de-emphasizing this as a general method for determining contact angles.  A title along the lines of “Correcting Refraction Errors in Contact Angle Measurements in Capillary Tubes” would better reflect the value of this submission.

In your response, you indicate that the temperature is about 20oC.  This information does not appear to be in the paper. 

Add the equation for angle DAC .

Author Response

Comments 1: The addition of references 18 and 19 in the revision helps one understand the functioning of the pulsating heating pipe system.  However, these articles make clear that this apparatus is not suitable as a general method for measuring contact angles.   The contact angle values measured apply only for the very specific conditions of their heated pipe system.

Response 1: Thanks for the reviewer’s comments. References 18 and 19 both focus on explaining the source of equation (1) in the manuscript. In the field of flow and heat transfer research on pulsating heat pipe, this equation is a universal equation used to calculate the inner diameter size of capillary specimens. The research on pulsating heat pipe is divided into theory and experiment. And experiments are generally divided into numerical simulations and visualization experiments. Reference 18 is a theoretical study on the heat transfer limit of pulsating heat pipe. Reference 19 established a vapor-liquid phase transition model and experimentally studied the effects of design and operating parameters on pulsating heat pipe. The capillary tube used in the experiment was bent from a copper tube with an inner diameter of 3 mm and a wall thickness of 0.5 mm. The capillary used in the manuscript is a quartz glass tube with an inner diameter of 3 mm and a wall thickness of 1.5 mm, as shown in Figure 2, which can visually observe the distribution of vapor and liquid columns in the capillary tube. Therefore, the device meets the conditions for measuring contact angle. The contact angle measurement method proposed in the manuscript is applicable to both static and dynamic contact angle measurements.

Comments 2: Differences in the structure of the vapor liquid interfaces in Figure 10 (of the response) clearly show that more than the interfacial energies between the vapor, liquid and solid are involved.  To further this point, contact angles are presented in Figure 10 of the revision as a function of heating power, not temperature. Heating rate is a property of their constructed apparatus and its operation which is of little value to others.

Response 2:  Thanks for the reviewer’s comments.  Fig. 10 shows the static contact angle of the working fluid without flow under different heating conditions. This figure indicates that the static contact angle tends to be consistent under different operating conditions.

Comments 3: Pulsating/oscillating heated pipe systems tend to be dynamic with change in pressure from the condenser to the evaporator.  There tends to be motion. Yin et al. (reference 18 in the revision) state “The pressure difference between the evaporator and condenser with a vapor spring constant between them generates the oscillation motion in the system.”.   In addition, there are hydrostatic contributions in the vertically oriented loop which are not accounted for.

Response 3: Thanks for the reviewer’s comments. The contact angle measured in the manuscript refers to the state where the pulsating heat pipe is in a stationary state (unheated) and in the initial heating stage but the gas and liquid columns inside the pulsating heat pipe are not moving. The selected ones are all in the inactive state of pulsating heat pipe, therefore, non pulsating/oscillating heating pipeline systems often dynamically change with pressure changes from the condenser to the evaporator. In measurement, the fluid mainly forms vapor-liquid plug distribution under the action of surface tension.

Comments 4: Their apparatus does serve the authors’ purpose of demonstrating the value of their analysis of errors due to refraction.  A revision needs to be substantially modified (abstract, introduction, discussion, conclusion) to emphasize the valuable contribution on refraction and de-emphasizing this as a general method for determining contact angles.  A title along the lines of “Correcting Refraction Errors in Contact Angle Measurements in Capillary Tubes” would better reflect the value of this submission.

Response 4: Thanks for the reviewer’s comments. The title, abstract, introduction, discussion, and conclusion have been revised. The focus of the manuscript is to propose a new method for measuring contact angle in capillary tube, and to consider the influence of refraction phenomenon on the measurement of contact angle in capillaries. At present, the measurement methods for contact angle include fixed droplet method, forward/backward droplet method, inclined plate method, capillary rise method, etc. However, these contact angle measurement methods directly select the local contour of the liquid to measure the contact angle during measurement. For contact angle measurement in capillary tube, they do not consider the light refraction phenomenon caused by the material and thickness of the tube wall, resulting in a deviation between the measured value (direct measurement) and the actual value (corrected for the influence of light refraction phenomenon) of the contact angle. For a comparison of contact angle measurement methods, please refer to the introduction.

Comments 5: In your response, you indicate that the temperature is about 20oC.  This information does not appear to be in the paper.

Response 5: Thanks for the reviewer’s comments. We have made modifications in the article.

Comments 6: Add the equation for angle DAC .

Response 6: Thanks for the reviewer’s comments. We have made modifications in the article. See equation (19) for detail.