Abstract
Vapor bubbles are formed in liquids by two mechanisms: evaporation (temperature above the boiling threshold) and cavitation (pressure below the vapor pressure). The liquid resists in these metastable (overheating and tensile, respectively) states for a long time since bubble nucleation is an activated process that needs to surmount the free energy barrier separating the liquid and the vapor states. The bubble nucleation rate is difficult to assess and, typically, only for extremely small systems treated at atomistic level of detail. In this work a powerful approach, based on a continuum diffuse interface modeling of the two-phase fluid embedded with thermal fluctuations (Fluctuating Hydrodynamics) is exploited to study the nucleation process in homogeneous conditions, evaluating the bubble nucleation rates and following the long term dynamics of the metastable system, up to the bubble coalescence and expansion stages. In comparison with more classical approaches, this methodology allows on the one hand to deal with much larger systems observed for a much longer times than possible with even the most advanced atomistic models. On the other it extends contin- uum formulations to thermally activated processes, impossible to deal with in a purely determinist setting.
Highlights
Thermal fluctuations play a dominant role in the dynamics of fluid systems below the micrometer scale
Classical nucleation theory (CNT) [10] provides the basic understanding of the phenomenon, which is nowadays addressed through more sophisticated models like density functional theory (DFT) [11,12] or by means of molecular dynamics (MD) simulations [13]
The thermodynamic range of applicability of this approach is subjected to some restrictions: (1) at the very first stage of nucleation the vapor nuclei, smaller than the critical size, need to be numerically resolved; analogously, (2) the thin liquid-vapor interface needs to be captured for the correct evaluation of the capillary stresses; and (3) fluctuating hydrodynamics predicts that the fluctuation intensity grows with the inverse cell volume, V, leading to intense fluctuations, contrary to the assumption of weak noise needed to derive the model
Summary
Thermal fluctuations play a dominant role in the dynamics of fluid systems below the micrometer scale. The thermodynamic range of applicability of this approach is subjected to some restrictions: (1) at the very first stage of nucleation the vapor nuclei, smaller than the critical size, need to be numerically resolved; analogously, (2) the thin liquid-vapor interface needs to be captured for the correct evaluation of the capillary stresses; and (3) fluctuating hydrodynamics predicts that the fluctuation intensity grows with the inverse cell volume, V , leading to intense fluctuations, contrary to the assumption of weak noise needed to derive the model ( δf 2 / f 1) Notwithstanding these restrictions, where it can be applied, this mesoscale approach offers a good level of accuracy (as will be shown when discussing the results) at a very cheap computational cost compared to other techniques. IV is devoted to our conclusions and to the open problems in the field
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