Theoretical and Experimental Studies of Acoustic Reflection of Bubbly Liquid in Multilayer Media

Round 1

Reviewer 1 Report

In this paper, the authors investigate theoretically and experimentally the acoustic reflection properties of a bubbly liquid layer sandwiched by a pair of thin plates immersed in water, for the case of normal incidence. Such a layered fluid medium is considered as a simplified model to mimic human tissues containing bubbles. A two-phase effective-fluid model is utilized for the homogenization of the bubbly liquid in the long-wavelength limit. The effective parameters derived this way are then applied to solving the classical scattering problem of a two-port, layered system, followed by a series of experimental measurements.

 

This work is interesting and overall well-presented. The results are relevant and technically sound. I am especially impressed by the clever design of the experimental setup. The manuscript is therefore suitable for publication in Applied Sciences. I have some minor comments for the authors to consider:

 

1. Equations (15) and (16) could be organized better. Currently, they look somewhat vague and confusing. I would suggest the authors to provide the expression of the characteristic impedance of the bubbly liquid and simplify the form of Eqs. (15) and (16) into a function of only impedance and layer thickness, just as the model depicted by Fig. 2. It would be even better and more straightforward if the authors use a transfer-matrix formulation (though not necessary) since it can serve as a general framework for any layered medium.

 

2. It seems that the acrylic plates are modeled as fluid-like media without considering the shear wave velocity. I would suggest the authors to discuss the validity of this treatment. In addition, is it possible to include the influence of the plates into the theoretical model (e.g., using the transfer-matrix method I mentioned in my previous comment)?

 

3. In Fig. 9, multiple echo-like wave packets can be observed for low voltage values yet tend to disappear as the voltage increases. Could the authors provide an explanation?

 

4. Can the results in Fig. 12 (flattened responses at high voltages) be predicted by the theoretical model?

 

Other formatting or grammar issues:

1. Line 88, “The results both calculating and measuring…”

2. Throughout the manuscript, the frequency interval delta_f should be in italic.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper presents a study on the detection of bubbles in a liquid through an innovative ultrasonic technique. The authors find via theoretical and experimental results, for which data agree quiet well, that it is possible to determine the bubble density in a liquid within a multi-layer material via the measurement of the reflection coefficient, obtained by pulse-echo, by means of the frequency difference between the consecutive valleys of that coefficient when represented vs. frequency. 

The study is interesting and useful for an important community working in ultrasound and mechanical engineering. The paper is structured correctly and it deserves, in my opinion, a publication in Applied Sciences. However, the authors should take into account the following comments before this manuscript can be published. 

1) English language should be edited (moderately). 

2) Some references on the topics of the paper should be added to the Introduction (see a potential list at the end of my comments). 

3) Line 47: the authors should include references in this paragraph. 

4) Line 53: references from Zabolotskaya et al from the Seventies should be included and commented in this paragraph. 

5) Line 69: "The acoustic properties..." should start the following paragraph. 

6) Line 71: 3) Line 47: the authors should include references in this paragraph. 

7) Line 73: "In 1998" should be removed. 

8) Section 2: the authors should include references in this section.

9) Line 102: this paragraph should be explained with more details.

10) Line 107: [6] should be [8].

11) Line 108: the authors should add "in an equivalent pure fluid".

12) Line 117: "too small" should be explained.

13) Line 117: "approximation" should be removed.

14) Intermediate steps to obtain Eqs. (7) and (8) should be given.

15) Line 123: "Then, from Eq. (7), the equivalent..." should be added.

16) Line 125: notation is not clear enough (ro_10?); the entire notation should be homogenized.

17) Line 131. why equationS?

18) All the symbols used must be defined (M_1?, M_2? (Eq. (10); Eq. (13); Fig. 2).

19)  Line 135: Eq. (8)? 

20) Line 147: a reference is needed after "follows". 

21) Line 152: "For example" should be removed. 

22) Line 153 & Eq. (15) & Eq. (16): the reflection coefficient should have a symbol. 

23) Line 154: "(see Fig. 2)" should be added. 

24) Line 158: "as a function of gas content" should be added. 

25) Line 163: is "tiny" the appropriate word? 

26) Line 171: this derivation should be given here. 

27) Line 179: "for a given gas-content value" or similar should be added. 

28) Fig. 1: "vs. gas content" should be added. 

29) Line 192: this sentence should be rephrased. 

30) Line 194: this sentence should be rephrased. 

31) Line 195: "very obvious" should be replaced. 

32) Line 205: what is the value 3400 m/s? 

33) Fig. 6: why is not c=1570, which was used before (Fig. 5, Line 206), used here?; this should be explained. 

34) Lines 238-240: the authors should explain why or include a reference. 

35) Fig. 7, right, is difficult to see correctly. 

36) Line 276: the author should tell us how the reflection coefficient is calculated for Fig. 9. 

37) Line 292: why half-height? 

38) Line 324: "a bubbly liquid". 

 

Potential list of references to be added (these are some only examples): E.A. Zabolotskaya et al. (1973, 1967, 1992); M. Cavaro et al (2019, 2011); C. Vanhille et al. (2009, 2010, 2017). 

Author Response

Please see the attachment.

Author Response File: Author Response.docx