Unevenness of Thin Liquid Layer by Contact Angle Variation of Substrate during Coating Process

Round  1

Reviewer 1 Report

Review on the paper

Unevenness on thin liquid layer by contact angle variation of substrate during coating process

by Na Kyong Kim et al.

This paper reports numerical simulations of a coating liquid surface right after its application on the surface. The study presents the liquid retraction due to capillary effect and discusses the effect of the contact angle. This work may be of interest for the journal but I can not recommend this paper for publication under the present form.

Before recommending the paper for publication, I need to be convinced that the simulations are correct. In fact, the presentation of the numeric induces some doubt that the authors are really understanding the method they are using.  What is the code name? References? How has it been validated for configurations close to this one: unsteady capillary waves, unsteady wetting, weeting in a corner, .... Why the author are considering the velocity of the control volume u_g, Are the fluid compressible? Eq. 7 is not correct. Line 89 the unit is not correct. What is the mesh used for the study? What is the time step? Have they conducted some test for both the grid and time convergence?

How is managed the capillary term on the corner? This is one of the key point for the simulation and this need to be described and validated.

Initial condition: How can be obtained this condition in practice? What is the effect of the initial condition on the results and conclusions of the study?

Results are discussed by plotting the interface shape at different time. There is no discussion on the surface wave velocity? It needs to be measured and compared to literature, in particular to the Taylor-Culick velocity?

The satellite drop formation is interesting. What are the velocity (magnitude and direction), size of the drops? What is the grid size effect?

Table 1, 2: n is used for surface tension while it is s in the text.

Author Response

This paper reports numerical simulations of a coating liquid surface right after its application on the surface. The study presents the liquid retraction due to capillary effect and discusses the effect of the contact angle. This work may be of interest for the journal but I can not recommend this paper for publication under the present form. Before recommending the paper for publication, I need to be convinced that the simulations are correct. In fact, the presentation of the numeric induces some doubt that the authors are really understanding the method they are using.

What is the code name? References?

• We used the commercial code (CFD-ACE) which is developed by ESI group. For more information to readers, the sentence “Numerical simulations were performed to analyze the unevenness of the coating fluid in terms of the surface contact angle of the substrate using the VOF mode in CFD-ACE+ (ESI group) software.” is added at the section of 2.1. Volume of fluid.

How has it been validated for configurations close to this one: unsteady capillary waves, unsteady wetting, wetting in a corner, ....

• To validate the numerical model, we compared the contact angles on a silicon wafer substrate with the results of the surface contact angle simulation. Experimentally, the contact angles of water sessile droplets were measured on the silicon wafer substrate using 4 μl droplets at an ambient temperature. Digital images were obtained using a charge coupled device camera. The silicon wafer substrate showed the average static contact angle of 66.2°. To compare this result, numerical simulations were conducted using 4 μl at the ambient temperature condition. The water has a density of 1000 kg/m³, a dynamic viscosity of 0.001 kg/ms, and a surface tension of 0.0725 N/m. It was assumed that the coating fluid and substrate were surrounded by gas (air) at room temperature (25 °C) and ambient pressure (101,325 Pa). The gas density was 1.1614 kg/m³, and its dynamic viscosity was 1.846 × 10^-5 kg/ms. Figure SI.2 shows the comparison between the static contact angle of the silicon wafer and the simulation result of the contact angle. The contact angle of simulation results was 64.9°. These results show that the simulation is in reasonable agreement with the experiment data. Therefore, our numerical model is considered accurate enough to examine the coating fluid surface in terms of the substrate contact angle. In addition, a short comment of “In addition, validation was conducted experimentally using the contact angle data on a silicon wafer as shown in Figure SI.2.” is added at the section of 3.1. Validation of the numerical model.

Why the authors are considering the velocity of the control volume ug, Are the fluid compressible?

• We assumed the that coating fluid was incompressible during unevenness of coating fluid simulation. As pointed out by referee, the eqs.1 & 2 are corrected and a term of u_g (velocity of the control volume) is deleted.

Equation (7) is not correct. Line 89 the unit is not correct.

• The explanation of Equation (7) at the line 82 is corrected as the surface tension force. The unit of σ (surface tension coefficient) is also corrected as “N/m” at the section of 2.1 Volume of fluid. In this point, we added the reference of the surface tension force “[41] Brackbill, J.U.; Kothe, D.B.; Zemach, C. A continuum method for modeling surface tension. J. Comput. Phys. 1992, 100, 335–354.”

What is the mesh used for the study? What is the time step? Have they conducted some test for both the grid and time convergence?

What is the grid size effect?

• The structured grid was used for the simulation. The time step was 0.1 µs.

• The time and grid convergence test was checked by Courant–Friedrichs–Lewy (CFL) number.

The CFL number indicates that the distance of information travels during the time step should be lower than the distance between the mesh element. In this point, CFL number should be lower than 1,

Where “a” is the velocity magnitude [m/s], “∆t” is the computational time step [s], and “∆x” is the distance between mesh elements [m]. In our simulation model, the time step was 0.1 µs and the distance between mesh element was 2 μm. The maximum velocity magnitude under the same wetting condition of 90° was 0.855 m/s at 100 μs. In our simulation case, CFL condition number was 0.04275. Therefore, our numerical simulation model and grid is satisfied to grid and time convergence test.

We added the reference of CFL condition number “[42] Hirsch, C. Numerical Computation of Internal and External Flows. 2nd ed.; John Wiley & Sons: Oxford, UK, 2007; pp.291-292, ISBN 978-0-471-92452-4.”

• Grid size effect is especially important in the VOF method. The grid independence test was performed on our simulation models. Numerical simulations with the mesh numbers of 3040, 4332, 5050, 7200, 9918, 12606, 18400, 25803, 28028, 40533, 50490, and 79431 were performed, respectively. The static contact angle of substrate surface and sides was 90°. To investigate the grid independence, the maximum height (h) of the surface unevenness was measured at 20 μs. This measured value was divided by the initial height of the coating fluid (h_o) to express the values as dimensionless variables. When the grid number was larger than 25803, the results of maximum height converged. Therefore, the grid number of 28028 was chosen in our numerical simulation.

• A short comment “For the numerical simulation, the time step was 0.1 µs and the structured grid was used. The grid independence and the convergence test were proceeded, as shown in Figure SI.1. [42]” is added at the section of 2.2. Simulation model and conditions.

How is managed the capillary term on the corner? This is one of the key point for the simulation and this need to be described and validated.

• The relation between the surface tension and the surface energy on the corner is especially important. Because the behavior of coating fluid is affected by the surface tension and surface energy. To investigate this relation, we assumed the surface tension is a constant and managed the surface energy by the control of surface contact angle.

• As mentioned above, we validated our numerical simulation model by the theoretical and the experimental data. These results show that the simulation is in reasonable agreement with the experiment and theoretical data. Therefore, our numerical model is considered accurate enough to examine the coating fluid surface in terms of the substrate contact angle.

Initial condition: How can be obtained this condition in practice? What is the effect of the initial condition on the results and conclusions of the study?

• Spray coating technology can evenly deposit the thin film on the entire surface. It is reasonable to approach the ideal initial state of the coating fluid since the very thin film of coating liquid was assumed to be applied to a substrate such as a silicon wafer using the spray coating technology. We investigated the surface unevenness caused by the surface tension and the surface contact angle in the initial coating fluid, which has certain thickness.

Results are discussed by plotting the interface shape at different time. There is no discussion on the surface wave velocity? It needs to be measured and compared to literature, in particular to the Taylor-Culick velocity?

• Surface waves were generated to balance the energy in the ideal coating fluid. However, it is difficult to express the typical velocity of the surface wave. By the reason, the surface wave velocity is not discussed.

The satellite drop formation is interesting. What are the velocity (magnitude and direction), size of the drops?

• The satellite droplets create due to the high fluid inertia force that can break the surface tension force. When the substrate has the surface contact angle of 15° and a side contact angle of 180°, the satellite droplets have an average diameter of 5 μm and the velocity magnitude of 1.86 m/s. The satellite droplets move to the outside of the liquid film and fall down due to the gravity.

When the substrate surface contact angle ranges from 30 to 75° and the side contact angle is 180°, satellite droplets occur in all the analysis cases. The satellite droplets also formed and have similar average diameter of 5 μm and velocity magnitude of 1.75 m/s to that observed when the contact angle of 15°.

In case of the surface contact angle of 90° and the side contact angle of 180°, satellite droplets have average diameter of 16 μm and velocity magnitude of 1.55 m/s. These satellite droplets are 5.3 times larger in diameter and 1.2 times lower in velocity than the satellite droplet formed at the low contact angles (15-75°).

And some sentences “These satellite droplets have an average diameter of 5 μm and the velocity magnitude of 1.86 m/s. The satellite droplets move to the outside of the liquid film and fall down due to the gravity.”, “In addition, the satellite droplets also formed and have similar average diameter of 5 μm and velocity magnitude of 1.75 m/s to that observed when the angle is 15°.”, and “These satellite droplets have average diameter of 16 μm and velocity magnitude of 1.55 m/s. The satellite droplets are 5.3 times larger in diameter and 1.2 times lower in velocity than the satellite droplet formed at the low contact angles (15-75°).” are added at the section of 3.3. Different Wetting Condition.

Table 1, 2: n is used for surface tension while it is s in the text.

• As pointed out by referee, ν used for surface tension in the table 1, 2 is corrected as σ, which is used in the text.

Author Response File: Author Response.docx

Reviewer 2 Report

1.       A minor English improvement is needed. The manuscript is well-written but a second proofread will increase the quality of the paper after publication.

2.       There are many different coating techniques that can be used in the protection of parts and surface treatment. These processes include sol-gel, CVD, PVD, micro-arc oxidation, anodization, etc. These processes are available in the literature. The following articles are strongly recommended to be used in your manuscript to introduce these coating techniques. Please consider the following papers:

https://nrs.org/journal/pnrs/browse-the-journal/volume-2/sol-gel-process-applications-a-mini-review#history

https://etd.ohiolink.edu/pg_10?0::NO:10:P10_ACCESSION_NUM:toledo1525475381922659

https://www.sciencedirect.com/science/article/pii/S175161611500449X

3.       The numerical results are well-presented. There is a section in numerical results that says validation of the numerical results but validation is mostly done with experimental results, not other numerical results. did you do any experiments to present the results? if yes, please include the experimental results in the manuscript.

4.       In conclusion, please make the findings in bullet points to make it easier for the readers in order to get the gist of the paper and findings after reading the conclusion part.

Author Response

We appreciate the referee for her/his helpful and stimulating comments. We have prepared a revised manuscript in accord with the comments of the referee. Several new sentences have been inserted into the text. Please see the revised manuscript.

As to the specific responses in the revised paper, we would like to note the following modifications.

1. A minor English improvement is needed. The manuscript is well-written but a second proofread will increase the quality of the paper after publication.

• As suggested by referee, English is checked and some typos are corrected in whole manuscript.

2. There are many different coating techniques that can be used in the protection of parts and surface treatment. These processes include sol-gel, CVD, PVD, micro-arc oxidation, anodization, etc. These processes are available in the literature. The following articles are strongly recommended to be used in your manuscript to introduce these coating techniques. Please consider the following papers:

https://nrs.org/journal/pnrs/browse-the-journal/volume-2/sol-gel-process-applications-a-mini-review#history

https://etd.ohiolink.edu/pg_10?0::NO:10:P10_ACCESSION_NUM:toledo1525475381922659

https://www.sciencedirect.com/science/article/pii/S175161611500449X

• As suggested by referee, many coating techniques are introduced at the revised manuscript. The sentence “There are many coating techniques such as spray processes, dip coating, sol-gel, CVD, PVD, micro-arc oxidation, anodization.” is added at the section of introduction. And the references ‘[12] Asri, R.I.M.; Harun, W.S.W.; Hassan, M.A.; Ghani, S.A.C.; Buyong, Z. A review of hydroxyapatite-based coating techniques: Sol–gel and electrochemical depositions on biocompatible metals. J. Mech. Behav. Biomed. Mater. 2016, 57, 95-108,’ ‘[13] Dehghanghadikolaei, A.; Ansary, J.; Ghoreishi, R. Sol-gel process applications: A mini-review. Proc. Nat. Res. Soc. 2018, 2, 02008,’ are added in the revised manuscript.

3. The numerical results are well-presented. There is a section in numerical results that says validation of the numerical results but validation is mostly done with experimental results, not other numerical results. did you do any experiments to present the results? if yes, please include the experimental results in the manuscript.

• As indicated by referee, the validation is mostly done with experimental results. To validate the numerical model, we compared the contact angles on a silicon wafer substrate with the results of the surface contact angle simulation. Water contact angles of the sessile droplets were measured on the silicon wafer substrate using 4 μl droplets at an ambient temperature. Digital images were obtained using a charge coupled device camera. The silicon wafer substrate showed the average static contact angle of 66.2°. To compare this result, numerical simulations were conducted using 4 μl at the ambient temperature condition. The water has a density of 1000 kg/m³, a dynamic viscosity of 0.001 kg/ms, and a surface tension of 0.0725 N/m. It was assumed that the coating fluid and substrate were surrounded by gas (air) at room temperature (25 °C) and ambient pressure (101,325 Pa). The gas density was 1.1614 kg/m³, and its dynamic viscosity was 1.846 × 10^-5 kg/ms. The time step was 0.1 µs. Figure SI.2 shows the comparison between the static contact angle of the silicon wafer and the simulation result of the contact angle. The contact angle of simulation results was 64.9°. These results show that the simulation is in reasonable agreement with the experiment data. Therefore, our numerical model is considered accurate enough to examine the coating fluid surface in terms of the substrate contact angle.

As suggested by referee, a short comment of “In addition, validation was conducted experimentally using the contact angle data on a silicon wafer as shown in Figure SI.2.” is added at the section of 3.1. Validation of the numerical model.

4. In conclusion, please make the findings in bullet points to make it easier for the readers in order to get the gist of the paper and findings after reading the conclusion part.

• As suggested by referee, we made the findings in bullet form to make it easier for the readers in order to get the gist of the findings after reading the conclusion part.

We feel that the comments of the referee was helpful and productive. These led to the improvements in the revised paper. We are appreciative of the comments of the referee.

Author Response File: Author Response.docx

Reviewer 3 Report

--see attached file----

Comments for author File: Comments.pdf

Author Response

We appreciate the referee for her/his helpful and stimulating comments. We have prepared a revised manuscript in accord with the comments of the referee. Several new sentences have been inserted into the text. Please see the revised manuscript.

As to the specific responses in the revised paper, we would like to note the following modifications.

This paper treats the application of CFD simulations for coating purposes. Namely, the volume-of fluid method has been used to calculate the behavior of a thin film in the vicinity of a 90° edge as a function of the contact angle.

To some extent, a standard CFD approach for the simulation of free surfaces has been applied, but, nevertheless, the results are interesting for a number of people that are dealing with paint material development as well as application techniques.

However, there are a number of questions and remarks that should be treated and considered in the final version of the contribution.

1. It should be clearly pointed out, that the results are only valid for a Newtonian liquid with constant liquid viscosity. Moreover, evaporation is not considered which might influence viscosity and surface tension (-> contact angle) as well.

This is in fact an important shortcoming of this paper, as the selective evaporation of solvent mixtures significantly influences the temporal evolution of the surface tension. This mechanism is used by the paint manufacturers,

• As indicated by referee, our results are only valid for a Newtonian liquid with constant liquid viscosity. The sentence of “The coating fluid was assumed as a Newtonian fluid, with constant liquid viscosity.” is added at the section of 2.2. Simulation model and conditions.

• A short comment of “Any evaporation, which might influence viscosity and surface tension, was ignored during the thin film application process.” is added at the section of 2.2. Simulation model and conditions.

2. It should be also pointed out, that the calculations consider the “static contact angle” only, i.e. the shape of the liquid front is only driven by surface tension without any additional dynamic flow effects.

• As indicated by referee, our calculations only considered the static contact angle without any additional dynamic flow effects. The sentences are corrected “The contact angle between the substrate and the coating fluid was set to wetting (15, 30, 45, 60, 75, and 90°) conditions.” as “The static contact angle between the substrate and the coating fluid was set to wetting (15, 30, 45, 60, 75, and 90°) conditions i.e. the shape of the coating fluid front was only driven by surface tension without any additional dynamic flow effects.”.

3. The description of the numerical is too superficial and needs some further explanations. More details should be given with respect to

o The dimensionality. It can be only guessed that the simulations are made in 2-D only. In connection to this, the authors should add some comments if this 2-D modeling implements further restrictions and constraints.

• Due to the axisymmetric condition of the numerical model, the simulation was conducted in 2D. A short comment of “Due to the axisymmetric condition of the numerical model, the simulation was conducted in 2D.” is added at the section of 2.2. Simulation model and conditions section.

o The used numerical code. There is no need to hide the code that is used in the investigations.

• We used the commercial code (CFD-ACE) which is developed by ESI group. For more information to readers, the sentence “Numerical simulations were performed to analyze the unevenness of the coating fluid in terms of the surface contact angle of the substrate using the VOF mode in CFD-ACE+ (ESI group) software.” is added at the section of 2.1. Volume of fluid.

o Further details of the grid. Grid size, resolution and shape of the elements represent essential information for a further verification of the results. This is especially important in the region where the contact angle plays a major role. Usually, grid size independence has to be verified.

o Further details on computational details, such as calculation time etc.

• As indicated by referee, grid size is especially important in the region where the contact angle plays a major role. We discussed in more details of the gird and the grid independence test. The structured grid was used for the simulation. The independence test of the structured grid was carried out on the coating fluid model. Numerical simulations with the mesh numbers of 3040, 4332, 5050, 7200, 9918, 12606, 18400, 25803, 28028, 40533, 50490, and 79431 were performed, respectively. The time step was 0.1 µs. The static contact angle of substrate surface and sides was set 90°. To investigate the grid independence, the maximum height (h) of the surface unevenness was measured at 20 μs. This measured value was divided by the initial height of the coating fluid (h_o) to express the values as dimensionless variables. As shown in Figure SI.1, when the grid number was larger than 25803, the results of maximum height converged. Therefore, the grid number of 28028 was chosen in our numerical simulation.

As suggested by referee, a short comment “For the numerical simulation, the time step was 0.1 µs and the structured grid was used. The grid independence and the convergence test were proceeded, as shown in Figure SI.1. [42].” is added at the section of 2.2. Simulation model and conditions.

4. It is not clear if gravity is considered. Gravity is of specific important in cases where the material moves around the edge and wets the side wall.

• As indicated by referee, gravity is of specific important in cases where the material moves around the edge and wets the side wall. we considered the gravity, when simulating unevenness of coating fluid. The sentence is added as “The gravitational acceleration was set to -9.81 m/s² in the y-direction.” at the 2.2. Simulation model and conditions section.

5. Details of geometry. What is the exact geometry of the edge? Is any surface roughness considered?

• We assumed that the surface of the substrate was flat and then we ignored the surface roughness

We feel that the comments of the referee was helpful and productive. These led to the improvements in the revised paper. We are appreciative of the comments of the referee.

Author Response File: Author Response.docx

Round  2

Reviewer 2 Report

Thank you for addressing the comments.

The manuscript looks good now. Although I vote for accepting the paper, you have to wait for other reviewers and the editor of the journal for the final decision.

Best of luck.

Reviewer 3 Report

Thanks for considering my comments in your revised version. I have no further suggestions.