Thermal fluctuations in metastable fluids

In this work, the thermal fluctuations of fluid in metastable conditions have been theoretically investigated. The fluid is described with a diffuse interface approach based on the Van der Waals squared-gradient theory (SGT), where the free energy is augmented by a density square gradient term to take into account capillary effects. By averaging physical observables on coarse-graining cells, it is found that capillarity strongly modifies the fluctuation statistics when increasing fluid metastability. A remarkable difference with respect to simple fluid description is also detected when approaching nanoscopic scales. Peculiarly, near spinodal loci, the classical theory envisages a divergent behavior of density fluctuations intensity, while the SGT provides a finite variance of the density field. The scaling behavior of density fluctuations near spinodal lines is analytically derived and discussed. Finally, the correlation length of the capillary system is identified for different metastabilities. Also in the latter case, the critical exponents are theoretically calculated. The theoretical results are corroborated by Landau–Lifshitz–Navier–Stokes fluctuating hydrodynamics simulations

Fluctuating hydrodynamics model for homogeneous and heterogeneous vapor bubble nucleation

At the molecular scale, even in conditions of thermodynamic equilibrium, the fluids do not exhibit a deterministic behavior. Going down below the micrometer scale, the effects of thermal fluctuations play a dominant role in the dynamics of the system, calling for a suitable description of thermal fluctuations. These models not only play an important role in physics of fluids, but a deep understanding of these phenomena is necessary for the progress of some of the latest nanotechnology. For instance the modeling of thermal fluctuations is crucial in the design of flow micro-devices, in the study of biological systems, such as lipid membranes, in the theory of Brownian engines and in the development of artificial molecular motor prototypes. Another problem with a huge technological impact is the phenomenon of nucleation – the precursor of the phase transition in metastable systems – in this context related to bubble formation in liquid-vapor phase transition. Vapor bubbles form in liquids by two main mechanisms: boiling, by increasing the tempe- rature over the boiling threshold, and cavitation, by reducing the pressure below the vapor pressure threshold. The liquid can be held in these metastable states (overheating and tensile conditions, respectively) for a long time without forming bubbles. Bubble nucleation is indeed an activated process, requiring a significant amount of energy to overcome the free energy barrier and bring the liquid from the metastable conditions to the thermodynami- cally stable state where vapor is observed. Depending on the thermodynamic conditions, the nucleation time may be exceedingly long, the so-called "rare- event" issue. Nowadays molecular dynamics is the unique tool to investigate such thermally activated processes. However, its computational cost limits its application to small systems (less than few tenth of nanometers) and to very short times, preventing the study of hydrodynamic interactions. The latter effects are crucial to understand the cavitation phenomenon in its entirety, starting from the vapor embryos nucleation up to the macroscopic motion. In this thesis a continuum diffuse interface model of the two-phase fluid has been embedded with thermal fluctuations in the context of the so-called Fluctuating Hydrodynamics (FH) and has been exploited to address cavitation. This model provides a set of partial stochastic differential equations, whose deterministic part is represented by the capillary Navier-Stokes equations and reproducing the Einstein-Boltzmann probability distribution for the macroscopic fields. This mesoscale approach enables the description of the liquid-vapor transition in extended systems and the evaluation of bub- ble nucleation rates in different metastable conditions by means of numerical simulations. Such model is expected to have a huge impact on the understanding of the nucleation dynamics since, by reducing the computational cost by orders of magnitude, it allows the unique possibility of investigating systems of realistic dimensions on macroscopic time scales. In addition, after the nucleating phase, the deterministic equations have been used to address the collapse of a cavitation nanobubble near a solid boundary, showing an unprecedented description of interfacial flows that naturally takes into account topology modification and phase changes (both vapor/liquid and vapor/supercritical fluid transformations)

Thermally activated vapor bubble nucleation: the Landau-Lifshitz/Van der Waals approach

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

Dynamics of a vapor nanobubble collapsing near a solid boundary

In the present paper a diffuse interface approach is used to address the collapse of a sub-micron vapor bubble near solid boundaries. This formulation enables an unprecedented description of interfacial flows that naturally takes into account topology modification and phase changes (both vapor/liquid and vapor/supercritical fluid transformations). Results from numerical simulations are exploited to discuss the complex sequence of events associated with the bubble collapse near a wall, encompassing shock-wave emissions in the liquid and reflections from the wall, their successive interaction with the expanding bubble, the ensuing asymmetry of the bubble and the eventual jetting phase

Diffuse interface modeling of laser-induced nano/micro cavitation bubbles

In the present work, a diffuse interface model has been used to numerically investigate the laser-induced cavitation of nano/microbubbles. The mesoscale approach is able to describe the cavitation process in its entirety, starting from the vapor bubble formation due to the focused laser energy deposition, up to its macroscopic motion.In particular, the simulations show a complete and detailed description of the bubble formation and the subsequent breakdown wave emission with a precise estimation of the energy partition between the shockwave radiating in the liquid and the internal energy of the bubble. The scaling of the ratio between the energy stored in the bubble at its maximum radius and the one deposited by the laser is found in agreement with experimental observation on macroscopic bubble

Cavitation over solid surfaces: microbubble collapse, shock waves, and elastic response

We discuss the interaction of the strongly nonlinear fluid motion induced by the collapse of a vapor microbubble over a planar surface and the elastic dynamics of the underlying solid. The fluid is described using an extension of the Navier-Stokes equations endowed with distributed capillary stresses in the context of a diffuse interface approach. The collapse of the bubble is triggered by overpressure in the liquid and leads to an intense jet that pierces the bubble, changing the bubble topology from spheroidal to toroidal, and impinges the solid wall inducing an intense and strongly localized load. Moreover, at bubble collapse, a compression wave is launched into the liquid surrounding the bubble. By propagating along the solid surface, the compression wave combined with the liquid jet excites the dynamics of the elastic solid, producing a complex system of waves, including, longitudinal, transversal, and Rayleigh waves, propagating in the solid. It is conjectured that the intense deformation of the solid induced by the strongly localized liquid jet may lead to the plastic deformation of the solid producing the surface pitting observed in many applications subject to cavitation induced material damage

Water cavitation from ambient to high temperatures

Abstract Predicting cavitation has proved a formidable task, particularly for water. Despite the experimental difficulty of controlling the sample purity, there is nowadays substantial consensus on the remarkable tensile strength of water, on the order of −120 MPa at ambient conditions. Recent progress significantly advanced our predictive capability which, however, still considerably depends on elaborate fitting procedures based on the input of external data. Here a self-contained model is discussed which is shown able to accurately reproduce cavitation data for water over the most extended range of temperatures for which accurate experiments are available. The computations are based on a diffuse interface model which, as only inputs, requires a reliable equation of state for the bulk free energy and the interfacial tension. A rare event technique, namely the string method, is used to evaluate the free-energy barrier as the base for determining the nucleation rate and the cavitation pressure. The data allow discussing the role of the Tolman length in determining the nucleation barrier, confirming that, when the size of the cavitation nuclei exceed the thickness of the interfacial layer, the Tolman correction effectively improves the predictions of the plain Classical Nucleation Theory

Fluctuating hydrodynamics as a tool to investigate nucleation of cavitation bubbles

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

Multi-scale modelling of boiling heat transfer:Exploring the applicability of an enhanced volume of fluid method in sub-micron scales

The advancement of technology has led to a significant increase in thermal loads, thus presenting new challenges in heat dissipation. Traditional single-phase cooling systems are often inadequate to meet these demands. As a result, phase-change technologies utilizing boiling and condensation, which can achieve high heat transfer coefficients, have garnered considerable attention. To delve into the complex physics of boiling heat transfer, researchers are increasingly turning to numerical simulation methods such as the Volume of Fluid (VOF) and the Diffuse Interface (DI) approaches. The VOF method, widely employed for macro-scale simulations ranging from micrometers to millimeters, effectively tracks bubble growth and detachment. Conversely, the DI method represents the interface as a continuous phase field and is primarily used for mesoscale simulations spanning from nanometers to micrometers. While the DI method excels in resolving mesoscale interfacial phenomena, it is computationally expensive for larger domains. Considering the strengths and weaknesses of both the VOF and DI methods, there is a growing interest in developing a multi-scale modeling approach that amalgamates their benefits. To pursue this objective, initial efforts are being made to evaluate the scaling capability of VOF towards lower spatial and temporal limits. Hence, an enhanced and customized VOF methodology has been developed within the OpenFOAM toolbox. This methodology is employed to investigate various bubble growth scenarios, progressively exploring its applicability at lower temporal and spatial scales to identify the lower limits of its application. By taking this first step towards combining the strengths of both the VOF and DI methods through a multi-scale modeling approach, the presented paper paves the way for enhancing the accuracy and efficiency of modelling approaches for boiling heat transfer while tackling a challenge associated with varying spatial and temporal scales. This endeavor not only pushes the boundaries of computational fluid dynamics but also holds promise for addressing real-world thermal management issues in diverse technological applications