Investigation of Single and Binary of “Sandwich” Type Convex Liquid Capillary Bridges, Stretched between Two Flat Surfaces (Experimental Approach)

Round 1

Reviewer 1 Report

The authors investigate single and binary liquid capillary bridges using a relatively simple, yet well-thought, experimental set-up. The experiments are complemented by solid theoretical analysis.  The manuscript does not require a major revision but the authors should consider addressing the minor comments given below:

-         The authors use a general term ‘contact angle’ through the manuscript but since the bridges are being stretched upon retraction of two surfaces perhaps ‘receding contact angle’ is a more appropriate term;

-         line 184: the authors state ‘hold pre-washed glass plates 18x18 mm’ it should read either ‘hold pre-washed glass plates 18 mm x 18 mm’ or 'hold pre-washed glass plates 18x18 mm²'

-         line 189: the symbols seems to be replaced by some random characters;

-         line 191: the authors claim the measured  oil surface tension was 31.372  mN/m. I do not believe such accuracy in surface tension measurements is achievable and the accuracy to one decimal point is more realistic;

-         The authors are encouraged to be consistent and use either cedar oil or cedarwood oil through all the manuscript.

Author Response

Dear Reviewer,

Thank you very much for your review. We find your comments very helpful and we intend to implement them in the revised version of the manuscript. Please find below our answers to your comments:

Comment: "The authors use a general term ‘contact angle’ through the manuscript but since the bridges are being stretched upon retraction of two surfaces perhaps ‘receding contact angle’ is a more appropriate term"

Indeed the general term "contact angle" is not very much appropriate for our case. Despite that we already discussed this in paragraph 4.3 "Contact angle measurements", we will correct it on the appropriate places.

Comment:  "line 184: the authors state ‘hold pre-washed glass plates 18x18 mm’ it should read either ‘hold pre-washed glass plates 18 mm x 18 mm’ or 'hold pre-washed glass plates 18x18 mm²"

Yes, we will correct this 

Comment: "line 189: the symbols seems to be replaced by some random characters"

We will restore the original characters

Comment "line 191: the authors claim the measured  oil surface tension was 31.372  mN/m. I do not believe such accuracy in surface tension measurements is achievable and the accuracy to one decimal point is more realistic"

We provided the numerical accuracy which is not the one of the measurement. The number will be corrected. 

Comment: "The authors are encouraged to be consistent and use either cedar oil or cedarwood oil through all the manuscript"

We will make the designation of the oil consistent everywhere in the manuscript

Reviewer 2 Report

The authors present new theory in the effect of contact angle on vertical capillary bridges. Sections 2 and 3 provide a theoretical background on the nature of capillary bridges and current approaches to understanding the relationship between wetting phenomena and stretching behavior. Most importantly, a linear dependence between stretching and contact angle was determined for contact angles less than 45^o and partial linearity for contact angles 45^o < θ < 60^o. This was found to simplify analysis and allow modification or prediction of capillary bridge stretching and breakage characteristics, as shown in section 6. Furthermore, the authors present a relation to determine contact angle from easily determined macroscopic capillary bridge geometrical attributes.

            Despite the rigorous theoretical development and utility of the relations mentioned above, the authors did not provide confidence intervals or error analysis in their findings. Furthermore, with the low volumes, how might the time and length scales set forth by the camera affect determination of stretching phenomena. Specifically, is resolution fine enough and experimental error low enough to support the authors’ claim that the binary capillary bridge deviates from the monophasic capillary bridges shown in figure 8a? The authors mention the stretching was done in steps with 1-2 minutes of equilibration, is the step size small enough to accurately characterize the bridge breaking kinetics?  

Author Response

Dear Reviewer,

Thank you very much for the important remarks and comments. Indeed, any paper involving experimental research should include at least a paragraph involving uncertainty (error) analysis. I will include in my final version of the paper such paragraph, where we discuss the uncertainty and possible issues, related to fig 8a in the paper. Below I provide answers to your questions:

Question 1: “with the low volumes, how might the time and length scales set forth by the camera affect determination of stretching phenomena”

The experimental errors from the pictures are related to camera resolution, which is 24.39 mkm (distance between two pixel). The smallest dimensions in the series of analyzed pictures, is the initial CB height (pressed state), which is stated in the paper to be minimum around 21 times longer. I consider minimum 22 pixels height to be sufficient to reveal the highly pressed CBs geometry properties. As we look mainly in statics, the time dynamics is not accounted at low volumes (except for the breakage kinetics, which is discussed further).

Question 2 “is resolution fine enough and experimental error low enough to support the authors’ claim that the binary capillary bridge deviates from the monophasic capillary bridges shown in figure 8a?”

Indeed answer to this question requires uncertainty analysis, which we have. The variables in Figure 8a (CB’s height and contact radius) are scaled by CB’s neck. This requires calculation of two measured values ratio uncertainty. In addition, the independent variable is under “ln”. As a result the uncertainties for dependent variable are ~10-2. The "ln" of scaled independent variable shows uncertainty of ~10-5. Thus, even small deviations as these, observed in fig. 8a could be attributed to difference in their properties, not a result from experimental uncertainty.

Question 3: “The authors mention the stretching was done in steps with 1-2 minutes of equilibration, is the step size small enough to accurately characterize the bridge breaking kinetics?”

Unfortunately, we can not characterize the breakage kinetics in detail, because we do not possess a camera with a suitable capturing speed. Our current camera allows the speed 1/60 s. In our previous work (Petkov&Radoev, 2014) we found that there is a static limit for CB existence that is predictable during the stretching. In our report we look for this limit and analyze the condition of the CB  in the next taken picture (usually in the middle of the breakage). I agree  that this approach does not allow accurate breakage kinetics analysis but  still gives an useful information about the CB viscous properties. We think to add  some more clarification in the paper.