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Effect of entropy on the nucleation of cavitation bubbles in water under tension

### Abstract

Water can exist in a metastable liquid state under tension for long times before the system relaxes into the vapor via cavitation, i.e., bubble
nucleation. Microscopic information on the cavitation process can be extracted from experimental data by the use of the nucleation theorem, which relates measured cavitation rates to the size of the critical bubble. To apply the nucleation theorem to experiments performed along an isochoric path, for instance, in cavitation experiments in mineral inclusions, knowledge of the bubble
entropy is required. Using computer simulations, we compute the entropy of bubbles in water as a function of their volume over a wide range of tensions from free energy calculations. We find that the bubble
entropy is an important contribution to the free energy that significantly lowers the barrier to bubble
nucleation, thereby facilitating cavitation. Furthermore, the bubble
entropy per surface area depends on the curvature of the liquid–vapor interface, decreasing approximately linearly with its mean curvature over the studied range of bubble volumes. At room temperature, the entropy of a flat liquid–vapor interface at ambient pressure is very similar to that of critical bubbles over a wide range of tensions, which justifies the use of the former as an approximation when interpreting data from experiments. Based on our simulation results, we obtain an estimate for the volume of the critical bubble from experimentally measured cavitation rates.

Published by AIP Publishing.

Received 13 June 2016
Accepted 22 September 2016
Published online 07 October 2016

Acknowledgments:
This work was supported by the Austrian Science Fund (FWF) under Grant No. P24681-N20 and SFB Vicom F41. The authors thank J. L. F. Abascal, F. Caupin, P. Geiger, M. A. Gonzalez, and C. Valeriani for insightful comments. The computational results presented have been achieved using the Vienna Scientific Cluster (VSC).

Article outline:

I. INTRODUCTION
II. METHODS
A. Simulation details
B. Order parameter
C. Entropy of the flat liquid–vapor interface
III. RESULTS AND DISCUSSION
IV. CONCLUSIONS

/content/aip/journal/jcp/145/21/10.1063/1.4964327

5.

L. Mercury and K. Shmulovich, in Transport and Reactivity of Solutions in Confined Hydrosystems, NATO Science for Peace and Security Series C: Environmental Security, edited by L. Mercury, N. Tas, and M. Zilberbrand (Springer Netherlands, 2014), pp. 159–171.

6.

G. Pallares, M. El Mekki Azouzi, M. A. González, J. L. Aragones, J. L. F. Abascal, C. Valeriani, and F. Caupin, Proc. Natl. Acad. Sci. U. S. A. 111, 7936 (2014).

http://dx.doi.org/10.1073/pnas.1323366111
24.

G. Menzl,

M. A. Gonzalez,

P. Geiger,

F. Caupin,

J. L. F. Abascal,

C. Valeriani, and

C. Dellago, e-print

arXiv:1606.03392 (2016).

25.

M. A. Gonzalez, G. Menzl, J. L. Aragones, P. Geiger, F. Caupin, J. L. F. Abascal, C. Dellago, and C. Valeriani, J. Chem. Phys. 141, 18C511 (2014).

http://dx.doi.org/10.1063/1.4896216
26.

Note that we altered the nomenclature to facilitate readability: v and ξ in this work correspond to and v in Ref. 25, respectively.

33.

Alternatively, one could in principle fit the surface free energy for very small bubbles with a suitable function and extrapolate this fit to zero to obtain the normalization of the free energy. However, although the order parameter employed here is calibrated such that it yields a physically meaningful estimate for the volume of a bubble, the smallest cavity it can detect depends on the chosen parameters employed in the grid-based detection of bubbles in the system (namely, the spatial resolution of the grid and the chosen distance within which a grid-point is considered to be occupied by nearby water molecules). As such, if one were to simply fit the free energy for low v and extrapolate this fit to zero, the obtained estimate for the free energy of cavitation would depend on the arbitrary parameters employed in the detection of bubbles in the system. Since the obtained normalization affects the height g(v^{*}) of the free energy barrier, which is connected to the probability of encountering a bubble of critical size (and thus to the cavitation rate), this dependence on the detection of minute cavities is clearly unphysical. Consequently, in order to mitigate the impact of arbitrary parameters on the estimate for the free energy of cavitation, we extrapolate the fit given in Eq. (9), which reproduces the free energy very accurately over a wide range of bubble volumes, to zero to obtain the normalization of the free energy.

34.

S. J. Bucci, F. G. Scholz, P. I. Campanello, L. Montti, M. Jimenez-Castillo, F. A. Rockwell, L. L. Manna, P. Guerra, P. L. Bernal, O. Troncoso, J. Enricci, M. N. Holbrook, and G. Goldstein, Tree Physiol. 32, 880 (2012).

http://dx.doi.org/10.1093/treephys/tps054
38.

L. Rowland, A. C. L. da Costa, D. R. Galbraith, R. S. Oliveira, O. J. Binks, A. A. R. Oliveira, A. M. Pullen, C. E. Doughty, D. B. Metcalfe, S. S. Vasconcelos, L. V. Ferreira, Y. Malhi, J. Grace, M. Mencuccini, and P. Meir, Nature 528, 119 (2015).

http://dx.doi.org/10.1038/nature15539
48.

D. H. Trevena, Cavitation and Tension in Liquids (Adam Hilger, Bristol, 1987).

49.

C. E. Brennen, Cavitation and Bubble Dynamics (Oxford University Press, New York, 1995).

50.

J.-P. Franc and M. Jean-Marie, Fundamentals of Cavitation (Kluwer Academic Publishers, Dordrecht, 2004).

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2016-10-07

2016-10-21

### Abstract

Water can exist in a metastable liquid state under tension for long times before the system relaxes into the vapor via cavitation, i.e., bubble
nucleation. Microscopic information on the cavitation process can be extracted from experimental data by the use of the nucleation theorem, which relates measured cavitation rates to the size of the critical bubble. To apply the nucleation theorem to experiments performed along an isochoric path, for instance, in cavitation experiments in mineral inclusions, knowledge of the bubble
entropy is required. Using computer simulations, we compute the entropy of bubbles in water as a function of their volume over a wide range of tensions from free energy calculations. We find that the bubble
entropy is an important contribution to the free energy that significantly lowers the barrier to bubble
nucleation, thereby facilitating cavitation. Furthermore, the bubble
entropy per surface area depends on the curvature of the liquid–vapor interface, decreasing approximately linearly with its mean curvature over the studied range of bubble volumes. At room temperature, the entropy of a flat liquid–vapor interface at ambient pressure is very similar to that of critical bubbles over a wide range of tensions, which justifies the use of the former as an approximation when interpreting data from experiments. Based on our simulation results, we obtain an estimate for the volume of the critical bubble from experimentally measured cavitation rates.

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