An Analysis of Bubble Migration in Horizontal Thermo-Capillarity Using the VOF Modeling

Round 1

Reviewer 1 Report

The presented paper is devoted to the 2D numerical simulations of bubble dynamics. Strictly speaking, the bubble migration, driven by thermo-capillary force under the temperature gradients, perpendicular to the gravity force direction, is simulated. For the modelling of the bubble interface between the vapor and fluid phases, the volume-of-fluid (VOF) method is used. During the computations, some interesting results on the beuuble behaviour are obtained.

From the reviewer's point of view, the results, presented in the paper are worthy for publication and the MINOR revision is required.

Comments:

1. Please write in details, why the VOF method is used among many other method. What about its advantages? From my point of view, the lattice Boltzmann method is better adopted to the multiphse simulations.
2. Eqs. (2)-(3). Please note correctly, why the same velocity vector U is used for both phases.
3. In eq. (3) - \nabla p must be used.
4. In (5) u is vector (use bold font). The same for F in (7).
5. L. 114. Incompressible flow is considered??? So why you use the eq. (2), if both \rho are the constants, instead of the incompressibility condition?

Author Response

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Reviewer 2 Report

This manuscript investigates the motion of bubbles when a gradient of temperature is applied to the liquid. A volume of fluid method is used to simulate the bubbles and the surface tension is allowed to change with the temperature. The results have been compared with theoretical and experimental studies, which demonstrate qualitative agreement. Overall, the results are very interesting, and the paper is well written. I list below my comments.

In Sec. 4.2.3 it is written: “Fig. 6 shows both our simulation results and previous experiment work [15]”, but ref 15 uses numerical simulations. Is it the right reference?

From the figures with droplet position in time (e.g., fig.8), the velocity is not constant. How to define the Weber number in these cases as it depends on the velocity?

In Fig.2, the bubble does not touch the plates. Does this motion with the temperature gradient still happen when wetting is considered as in Ref. [doi.org/10.1002/fld.4988]? What if the gradient is applied on the plates and not in the liquid? These questions can be referred to as follow up studies.

Author Response

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Reviewer 3 Report

Review comments for applsci-1691198

An analysis of bubble migration in horizontal thermo-capillarity using the VOF modeling

By Ranjith Kumar, Yu-Chen Lin, Chia-Wei Lin, Ming-Chieh Lin, Hua-Yi Hsu

This manuscript numerically studied the bubble migration driven by the thermo-capillary force under the temperature gradients perpendicular to gravity direction. The effects of the temperature gradient and bubble radius sizes on the movement of the bubbles are investigated, and some force discussions are given. More in-deep analyses of the effects of the temperature gradient and bubble radius sizes are needed. Following are the further comments.

1. 1, what’s the distance of the bubble from the bottom wall?
2. Line 125, “The non-dimensional settings are ??=3.85, ??=1, ??=1.023, ??=3.849, 125 and ??=8×10−2 to 4”, pls give the definitions of the above dimensionless number.
3. The simulation model includes the gravity while the validation case adopts zero gravity (Line 158). Thus, the reliability of the simulation model needs to be improved. Did the authors compare the migration velocity obtained from the simulation and Eq. (10)?
4. 2, what is the size of the computational domain? Pls add scale bars in Figs. 2 and 5.
5. Pls adjust the direction of Fig. 5sg to align with that in the physical model presented in Fig. 1.
6. Did the surface tension or natural convection dominate the bubble migration?
7. Why do the rising bubbles oscillate? Pls add the velocity, pressure and temperature fields to give some explanation.
8. Line 209, “As bubble size increases, velocity rises, ……”, why?
9. Line 250, “….the bubble with a larger size can reach the left wall faster…”, why?
10. Line 245, “In Fig.8 (a), when the bubble radius R is 0.045 m”. R should be 0.0045m?
11. 10 – 12, what is the meaning of Y? The authors are recommended to re-write the sentences describing these figures to make the reader easier to understand the effect of temperature gradient on the Weber and Capillary numbers.
12. The authors should link the results by force analysis to those by the simulations.

Author Response

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Round 2

Reviewer 3 Report

The paper is well revised and could be accepted for publication.