Dependency of Contact Angles on Three-Phase Contact Line: A Review

Round 1

Reviewer 1 Report

The author demonstrates a nice review that focuses on surface wettability. 

I only concern if there is no Figure or Image for demonstrating, could the authors get the clear meaning of this review.

Some new articles should be added to support the viewpoint of the review. 

 

Author Response

Reviewer # 1: The author demonstrates a nice review that focuses on surface wettability. I only concern if there is no Figure or Image for demonstrating, could the authors get the clear meaning of this review. Some new articles should be added to support the viewpoint of the review. 

Comments: I would like to thank to Reviewer # 1 for his/her constructive comments. I agree with the reviewer on the lack of figures and 4 new figures were added in the revised text: 1- Definition of contact angle (q) and other parameters are given in Figure 1 (in page 2, line 50-56); 2- the schematic of the measurement of “advancing” (q_a) and “receding” contact angles (q_r) on a substrate with the “syringe-needle” method is given in Figure 2 (in page 2, lines 62-66); 3- Schematic description of sessile droplets on patterned surfaces according to Wenzel and Cassie-Baxter states are given in Figure 3 (in page 4, lines 120-124); and 4- The distortions of the drop perimeter by showing the plan and side views of a water drop on MYLAR (polyester) surface and resultant contact angles in Figure 4 which was reproduced from Ref.4 (in page 8, lines 320-326) of the revised MS. Figs.1-3 are originally drawn and Fig.4 was reproduced from a published article (Ref.4) after obtaining the copyright permission.

Two articles which was published in 2020 are also added to support the viewpoint of the review as new references 87 and 88 in page 13, lines 537-550. All of the reference numbers are corrected accordingly.

      One of the reviewers asked me to divide section 3. Recent advances on the dependency of contact angles on three-phase contact line into several parts. I accepted and divided section 3 into four parts as given in the revised MS from page 10, line 411 to page 14, line 596. The subtitles are “3.1. Line energy-contact angle relationships”; “3.2. Stick-slip phenomenon of drops on solids”; “3.3. Direct testing of Wenzel and Cassie equations”; and “3.4. Thermodynamic investigations of contact angles on heterogeneous solids”, as requested by the Reviewer # 3.

Reviewer 2 Report

In Dependency of contact angles on three-phase contact line: a Review, HY Erbil summarizes the current arguments to reject the mixture model of Cassie and Wenzel.

I am not convinced of the usefulness of this review: Cassie and Wenzel mixture models have been proven wrong a over and over. Furthermore, I think this review is misleading and should not be published for the following reasons:

• the droplet geometry exhibits a hysteresis, and therefore the process by which it has reached its final shape is important in determining this shape (in thermodynamic terms, the apparent contact angle is not a state variable). Therefore, a contact angle with hysteresis cannot be found from local thermodynamic arguments alone, and the whole history of contact line motion should be known. When a droplet spreads over a surface and meets a defect (roughness, chemical heterogeneity), two situations may occur: either the defect is weak and can be overcome, then the contact line moves on; or the defect is strong and the contact line is pinned. Similarly to an optimization problem, the droplet free energy is the optimization function to minimize, and the pinning by strong defects is like a constraint. One could well assume an infinitely strong defect that would make the contact line energy infinite and would still obtain a finite contact angle because the contact line would be pinned there. Therefore, the authors should review the literature on the evolution of the contact line, including pinning and depinning. I especially advise them to check the paper by Joanny and De Gennes: A model for contact angle hysteresis -- J. Chem. Phys. 81, 552 (1984)
• According to the arguments above, a surface with a mixture of weak (non-pinning) defects would behave according to Cassie and Wenzel mixture laws. However, this law is indeed not relevant for most practical applications. In view of this complex situation, I would advise the authors to be more nuanced in their statements (mixture laws are not valid for most practical situations).
• My main concern is that, despite proving time and time again that mixture law are not always valid, the authors have not shown that the contact line energy determines the contact angle regardless of the contact line evolution before equilibrium. This is discussed again by De Gennes in the same 1984 paper "It is not easy to see, however, how this [contact line] energy could be detected in practice. Weak heterogeneities give small line energies and large heterogeneities are dominated by hysteretical effects, which we now begin to discuss."

Minor revisions:

• the concept of contact angle is distinct for the concept of droplet. For instance, the meniscus of water in a cup also exhibits a contact angle that obeys the same laws as the one of droplets. The authors should stress this point.
• the authors should add a figure in the introduction to show the contact angle, and how advancing and receding contact angles can be observed. The distribution of contact angles around the droplet is an interesting point and could also be graphically illustrated.

Author Response

Reviewer # 2: In “Dependency of contact angles on three-phase contact line: a Review”, HY Erbil summarizes the current arguments to reject the mixture model of Cassie and Wenzel. I am not convinced of the usefulness of this review: Cassie and Wenzel mixture models have been proven wrong a over and over. Furthermore, I think this review is misleading and should not be published for the following reasons:

Comments: I do not agree with the Reviewer # 2 that this review is misleading. Yes, “Cassie and Wenzel mixture models have been proven wrong over and over” as stated by the Reviewer # 2 in the past, but they are still under use by many scientists especially to evaluate the contact angles on patterned surfaces in the last 13 years, although these equations were shown to be erroneous experimentally in 2007. I tried to underline the point that these equations are wrong and should be abandoned and will not be used in future publications. Otherwise, many young scientists and newcomers to this field will continue to use them over and over.

 

The focus of this review article is on the important practical issue that the advancing, receding contact angles, and contact angle hysteresis of rough and chemically heterogeneous surfaces are determined by interactions of the liquid and the solid at the three-phase contact line alone and the interfacial area within the contact perimeter is irrelevant. On the other hand, this review article is not on the definition or investigation of “contact angle hysteresis” depending on line energy.

 

The droplet geometry exhibits a hysteresis, and therefore the process by which it has reached its final shape is important in determining this shape (in thermodynamic terms, the apparent contact angle is not a state variable). Therefore, a contact angle with hysteresis cannot be found from local thermodynamic arguments alone, and the whole history of contact line motion should be known. When a droplet spreads over a surface and meets a defect (roughness, chemical heterogeneity), two situations may occur: either the defect is weak and can be overcome, then the contact line moves on; or the defect is strong and the contact line is pinned. Similarly to an optimization problem, the droplet free energy is the optimization function to minimize, and the pinning by strong defects is like a constraint. One could well assume an infinitely strong defect that would make the contact line energy infinite and would still obtain a finite contact angle because the contact line would be pinned there. Therefore, the authors should review the literature on the evolution of the contact line, including pinning and depinning. I especially advise them to check the paper by Joanny and De Gennes: A model for contact angle hysteresis -- J. Chem. Phys. 81, 552 (1984).

 

Comments: The Reviewer # 2 is right to point that a contact angle with hysteresis cannot be found from local thermodynamic arguments alone, and the whole history of contact line motion should be known if possible, (unfortunately this is not possible in most of the practical cases). The defect (roughness, chemical heterogeneity) dependent contact angle hysteresis could be estimated according to the weakness or strongness of the defects (if their magnitudes were known) during the spreading of a droplet on a surface and this approach was well explained in the article by Joanny and De Gennes: A model for contact angle hysteresis, J. Chem. Phys. 81, 552 (1984).

 

However, our review article is not on the definition or investigation of “contact angle hysteresis”, and it is on the irrelevance of the interfacial area within the contact perimeter to the contact angle value. Moreover, Joanny and De Gennes paper was related with the situations where contact angles were small, but finite, and no arguments were given for contact angles which were larger than 90 degrees (sometimes larger than 150 degrees such as on patterned superhydrophobic surfaces). The irrelevance of the interfacial area within the contact perimeter to the contact angle value is a problem which is important both academically and industrially since wrong Wenzel and Cassie equations have been used to test or compare the measured advancing or receding contact angle values on the patterned surfaces such as superhydrophobic or superolephobic by using the contact areas of the patterns calculated from pattern geometry. There are about one hundred articles using this approach in the literature (sometimes in Q1 and Q2 journals) and the number of similar articles is expanding. We need to put an end to this false reasoning especially for the newcomers to the contact angle field. It is expected that this review will serve for this purpose.

 

However, I added statements describing the importance and analysis of contact angle hysteresis in page 7, lines 287-293 of the revised MS and cited the important paper of Joanny and De Gennes: A model for contact angle hysteresis, J. Chem. Phys. 81, 552 (1984) as reference 51 in the revised MS (reference numbers were arranged accordingly).

 

According to the arguments above, a surface with a mixture of weak (non-pinning) defects would behave according to Cassie and Wenzel mixture laws. However, this law is indeed not relevant for most practical applications. In view of this complex situation, I would advise the authors to be more nuanced in their statements (mixture laws are not valid for most practical situations).

 

Comments: I do not agree with the Reviewer # 2 that the contact angles on a surface with a mixture of weak (non-pinning) defects would obey to interfacial area dependent and erroneous Wenzel equation. There is no scientific evidence or proof for this statement.

 

However, it is possible that the contact angles on a surface with a mixture of weak (non-pinning) defects may obey to Cassie equation since it is a standard mixture model of the physical chemistry. We also accepted this fact in the original and also the revised MS. This fact was mentioned in page 6, lines 243-247 and page 10, lines 395-400 of the revised MS as advised by the Reviewer # 2.

 

My main concern is that, despite proving time and time again that mixture law are not always valid, the authors have not shown that the contact line energy determines the contact angle regardless of the contact line evolution before equilibrium. This is discussed again by De Gennes in the same 1984 paper "It is not easy to see, however, how this [contact line] energy could be detected in practice. Weak heterogeneities give small line energies and large heterogeneities are dominated by hysteretical effects, which we now begin to discuss."

 

Comments: We thank to Reviewer # 2 for this point. He/she is right to point out that the contact line energy determines the contact angle regardless of the contact line evolution before equilibrium and weak defects give small line energies and large defects are dominated by hysteretical effects. We added these comments in in page 7, lines 287-293 of the revised text.

 

Minor revisions: The concept of contact angle is distinct for the concept of droplet. For instance, the meniscus of water in a cup also exhibits a contact angle that obeys the same laws as the one of droplets. The authors should stress this point.

 

Comments: We thank to Reviewer # 2 for this point. We added the requested comments in page 2, lines 36, 37 of the revised text to remind the use of contact angles on the meniscus in a cup or tube.

 

The authors should add a figure in the introduction to show the contact angle, and how advancing and receding contact angles can be observed. The distribution of contact angles around the droplet is an interesting point and could also be graphically illustrated.

 

Comments: I agree with the reviewer on this point and 4 new figures were added in the revised text. 1- Definition of contact angle (q) and other parameters are given in Figure 1 (in page 2, line 50-56); 2- the schematic of the measurement of “advancing” (q_a) and “receding” contact angles (q_r) on a substrate with the “syringe-needle” method is given in Figure 2 (in page 2, lines 62-66); 3- Schematic description of sessile droplets on patterned surfaces according to Wenzel and Cassie-Baxter states are given in Figure 3 (in page 4, lines 120-124). Figs.1-3 are originally drawn.

 

I agree with the Reviewer # 2 that the distribution of contact angles around the droplet is an interesting point and should also be graphically illustrated; and I added Figure 4 showing the distortions of the drop perimeter by reporting the plan and side views of a water drop on MYLAR (polyester) surface and resultant contact angles (in page 8, lines 320-326) of the revised MS. Figure 4 was reproduced from Ref.4 after obtaining the copyright permission. I also added an explanation for Figure 4 in p.9, lines 327-333 of the revised MS.

Reviewer 3 Report

This manuscript mainly focuses on the dependency of contact angles on three-phase contact line. The author gave a review of debates in recent years on the relationship between the contact angle and surface roughness and chemical heterogeneity. Conclusions are given that the original Wenzel and Cassie equation are both wrong and should be abandoned, while the modified Cassie equation based on line fractions can be derived and used. The topic is interesting and has many applications in the industries. However, there are some questions before this manuscript can be published.

• First of all, I must ask the authors to add the representative figures in this manuscript. We cannot accept a review paper without any figures.
• I suggest the author to improve the structure of the article. In the part ” RECENT ADVANCES ON THE DEPENDENCY OF CONTACT ANGLES ON THREE-PHASE CONTACT LINE”, it is better to divide the text into several parts. For example “3.1 Stick-slip phenomenon”, “3.2  Effects of interactions between the liquid and solid at the triple contact line”, “3.3 ……”,”3.4 ……”, ……
• Please check the titles carefully. “5 conclusions” should be “4 conclusions”.
• I think the author might be arbitrary to give the conclusion that the original Wenzel equation and Cassie equation are both wrong. The concepts is acceptable and be used for more than 70 years. They can predict the contact angle in many cases. For example, the Wenzel equation can be accurate when the size of the drop is much larger compared with the scale of the roughness (Apparent contact angles on rough surfaces: the Wenzel equation revisited. A: Physicochemical and Engineering Aspects 156 (1999) 381–388).

Author Response

Reviewer 3: This manuscript mainly focuses on the dependency of contact angles on three-phase contact line. The author gave a review of debates in recent years on the relationship between the contact angle and surface roughness and chemical heterogeneity. Conclusions are given that the original Wenzel and Cassie equation are both wrong and should be abandoned, while the modified Cassie equation based on line fractions can be derived and used. The topic is interesting and has many applications in the industries. However, there are some questions before this manuscript can be published.

Comments: I thank to Reviewer # 3 for these constructive comments.

 

First of all, I must ask the authors to add the representative figures in this manuscript. We cannot accept a review paper without any figures.

 

Comments: I agree with the reviewer on this point and 4 new figures were added in the revised text. 1- Definition of contact angle (q) and other parameters are given in Figure 1 (in page 2, line 50-56); 2- the schematic of the measurement of “advancing” (q_a) and “receding” contact angles (q_r) on a substrate with the “syringe-needle” method is given in Figure 2 (in page 2, lines 62-66); 3- Schematic description of sessile droplets on patterned surfaces according to Wenzel and Cassie-Baxter states are given in Figure 3 (in page 4, lines 120-124); and 4- The distortions of the drop perimeter by showing the plan and side views of a water drop on MYLAR (polyester) surface and resultant contact angles in Figure 4 which was reproduced from Ref.4 (in page 8, lines 320-326) of the revised MS. Figs.1-3 are originally drawn and Fig.4 was reproduced from a published article (Ref.4) after obtaining the copyright permission.

 

 

I suggest the author to improve the structure of the article. In the part “RECENT ADVANCES ON THE DEPENDENCY OF CONTACT ANGLES ON THREE-PHASE CONTACT LINE”, it is better to divide the text into several parts. For example “3.1 Stick-slip phenomenon”, “3.2  Effects of interactions between the liquid and solid at the triple contact line”, “3.3 ……”,”3.4 ……”, ……

 

Comments: I agree with the Reviewer # 3 on this point and divided section 3. Recent advances on the dependency of contact angles on three-phase contact line, into four parts as given from page 10, line 411 to page 14, line 596 of the revised MS. The subtitles are “3.1. Line energy-contact angle relationships”; “3.2. Stick-slip phenomenon of drops on solids”; “3.3. Direct testing of Wenzel and Cassie equations”; and “3.4. Thermodynamic investigations of contact angles on heterogeneous solids”, as requested by the Reviewer # 3.

 

Please check the titles carefully. “5 conclusions” should be “4 conclusions”.

Comments: I thank to Reviewer # 3 for this correction. It is now “4. Conclusions” in page 14, line 598 of the revised MS.

 

I think the author might be arbitrary to give the conclusion that the original Wenzel equation and Cassie equation are both wrong. The concepts is acceptable and be used for more than 70 years. They can predict the contact angle in many cases. For example, the Wenzel equation can be accurate when the size of the drop is much larger compared with the scale of the roughness (Apparent contact angles on rough surfaces: the Wenzel equation revisited. A: Physicochemical and Engineering Aspects 156 (1999) 381–388).

 

Comments: As stated by one of the reviewers of this MS, “Cassie and Wenzel mixture models have been proven wrong over and over” and the articles which were giving the experimental proofs were cited in the reference list. Thus, it is not arbitrary to conclude that the original Wenzel equation and Cassie equation are both wrong for practical cases.  However, we discriminated between the visually useable “Wenzel and Cassie concepts” and wrong “Wenzel and Cassie equations” in the original and revised MS in page 7, lines 259-267.

 

For the second part of the comment of Reviewer # 3 on the validity of the Wenzel equation and the size of the droplet, it is known that the size of a drop should be extremely large in comparison with the roughness scale on a solid substrate and for practical cases such a very large drop can be easily distorted due to the gravity effect. However, the mathematical analysis given in the publication “Apparent contact angles on rough surfaces: the Wenzel equation revisited. A: Physicochemical and Engineering Aspects 156 (1999) 381–388, is also cited as reference 39 in the revised MS in page 6, lines 221-227 as an example of a theoretical case as requested by the Reviewer # 3.

 

Round 2

Reviewer 3 Report

More figures and texts summarizing the recent advances of the representative works must be carefully organized.