OPEN ACCESS
Vapor bubbles can be formed in liquids by increasing the temperature over the boiling threshold (evaporation) or by reducing the pressure below its vapor pressure threshold (cavitation). The liquid can be held in these tensile conditions (metastable states) for a long time without any bubble formation. The bubble nucleation is indeed an activated process, in fact a given amount of energy is needed to bring the liquid from that local stable condition into a more stable one, where a vapor bubble is formed. Crucial question in this field is how to correctly estimate the bubble nucleation rate, i.e. the amount of vapor bubbles formed in a given time and in a given volume of liquid, in different thermodynamic conditions. Several theoretical models have been proposed, ranging from classical nucleation theory, to density functional theory. These theories can give good estimate of the energy barriers but lack of a precise estimate of the nucleation rate, especially in complex systems. Molecular dynamics simulations can give more precise results, but the computational cost of this technique makes it unfeasible to be applied on systems larger than few tenth of nanometers. In this work the approach of fluctuating hydrodynamics has been embedded into a continuum diffuse interface modeling of the two-phase fluid. The resulting model provides a complete description of both the thermodynamic and fluid dynamic fields enabling the description of vapor-liquid phase change through stochastic fluctuations. The continuum model has been exploited to investigate the bubble nucleation rate in different metastable conditions. Such an approach has a huge impact since it reduces the computational cost and allows to investigate longer time scales and larger spatial scales with respect to more conventional techniques.
bubble, diffuse interface, fluctuating hydrodynamics, nucleation, thermal fluctuations
[1] Landau, L. & Lifshitz, E., Statistical physics: Course of theoretical physics (Vol. 5). Pergamon Press, Oxford, 1980.
[2] Fox, R.F. & Uhlenbeck, G.E., Contributions to non-equilibrium thermodynamics. I. Theory of hydrodynamical fluctuations. Physics of Fluids (1958–1988), 13(8), pp. 1893–1902, 1970. https://doi.org/10.1063/1.1693183
[3] Donev, A., Vanden-Eijnden, E., Garcia, A. & Bell, J., On the accuracy of finite-volume schemes for fluctuating hydrodynamics. Communications in Applied Mathematics and Computational Science, 5(2), pp. 149–197, 2010. https://doi.org/10.2140/camcos.2010.5.149
[4] Balboa, F., Bell, J.B., Delgado-Buscalioni, R., Donev, A., Fai, T.G., Griffith, B.E. & Peskin, C.S., Staggered schemes for fluctuating hydrodynamics. Multiscale Modeling & Simulation, 10(4), pp. 1369–1408, 2012. https://doi.org/10.1137/120864520
[5] Naji, A., Atzberger, P.J. & Brown, F.L., Hybrid elastic and discrete-particle approach to biomembrane dynamics with application to the mobility of curved integral membrane proteins. Physical Review Letters, 102(13), p. 138102, 2009. https://doi.org/10.1103/physrevlett.102.138102
[6] Chow, C.C. & Buice, M.A., Path integral methods for stochastic differential equations. The Journal of Mathematical Neuroscience (JMN), 5(1), p. 8, 2015. https://doi.org/10.1186/s13408-015-0018-5
[7] Jones, S., Evans, G. & Galvin, K., Bubble nucleation from gas cavities? a review. Advances in Colloid and Interface Science, 80(1), pp. 27–50, 1999. https://doi.org/10.1016/s0001-8686(98)00074-8
[8] Kashchiev, D. & Van Rosmalen, G., Review: Nucleation in solutions revisited. Crystal Research and Technology, 38(7–8), pp. 555–574, 2003. https://doi.org/10.1002/crat.200310070
[9] Brennen, C.E., Cavitation and bubble dynamics. Cambridge University Press, New York, NY, 2013.
[10] Diemand, J., Angélil, R., Tanaka, K.K. & Tanaka, H., Direct simulations of homogeneous bubble nucleation: Agreement with classical nucleation theory and no local hot spots. Physical Review E, 90(5), p. 052407, 2014. https://doi.org/10.1103/physreve.90.052407
[11] Azouzi, M.E.M., Ramboz, C., Lenain, J.F. & Caupin, F., A coherent picture of water at extreme negative pressure. Nature Physics, 9(1), pp. 38–41, 2013. https://doi.org/10.1038/nphys2475
[12] Blander, M. & Katz, J.L., Bubble nucleation in liquids. AIChE Journal, 21(5), pp. 833–848, 1975.
https://doi.org/10.1002/aic.690210502
[13] Oxtoby, D.W. & Evans, R., Nonclassical nucleation theory for the gas–liquid transition. The Journal of Chemical Physics, 89(12), pp. 7521–7530, 1988. https://doi.org/10.1063/1.455285
[14] Weinan, E., Ren, W. & Vanden-Eijnden, E., String method for the study of rare events. Physical Review B, 66(5), p. 052301, 2002. https://doi.org/10.1103/physrevb.66.052301
[15] Giacomello, A., Meloni, S., Chinappi, M. & Casciola, C.M., Cassie–Baxter and Wenzel states on a nanostructured surface: phase diagram, metastabilities, and transition mechanism by atomistic free energy calculations. Langmuir, 28(29), pp. 10764–10772, 2012. https://doi.org/10.1021/la3018453
[16] Lutsko, J.F., Density functional theory of inhomogeneous liquids. IV. squared-gradient approximation and classical nucleation theory. The Journal of Chemical Physics, 134(16), p. 164501, 2011. https://doi.org/10.1063/1.3582901
[17] Magaletti, F., Marino, L. & Casciola, C., Shock wave formation in the collapse of a vapor nanobubble. Physical Review Letters, 114(6), p. 064501, 2015. https://doi.org/10.1103/physrevlett.114.064501
[18] De Zarate, J.M.O. & Sengers, J.V., Hydrodynamic fluctuations in fluids and fluid mixtures. Elsevier, San Diego, CA, 2006.
[19] Chaudhri, A., Bell, J.B., Garcia, A.L. & Donev, A., Modeling multiphase flow using fluctuating hydrodynamics. Physical Review E, 90(3), p. 033014, 2014. https://doi.org/10.1103/physreve.90.033014
[20] Stratonovich, R.L., Nonlinear nonequilibrium thermodynamics I: linear and nonlinear fluctuation-dissipation theorems (Vol. 57). Springer Science & Business Media, 2012.
[21] Berne, B.J. & Pecora, R., Dynamic light scattering: with applications to chemistry, biology, and physics. Courier Corporation, 1976.
[22] Magaletti, F., Gallo, M., Marino, L. & Casciola, C.M., Shock-induced collapse of a vapor nanobubble near solid boundaries. International Journal of Multiphase Flow, 84, pp. 34–45, 2016. https://doi.org/10.1016/j.ijmultiphaseflow.2016.02.012
[23] Atzberger, P.J., Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction–diffusion systems. Journal of Computational Physics, 229(9), pp. 3474–3501, 2010. https://doi.org/10.1016/j.jcp.2010.01.012
[24] Johnson, J.K., Zollweg, J.A. & Gubbins, K.E., The Lennard-Jones equation of state revisited. Molecular Physics, 78(3), pp. 591–618, 1993. https://doi.org/10.1080/00268979300100411