Spontaneous cavitation in a Lennard-Jones liquid at negative pressures

A capillary-induced negative pressure is able to initiate heterogeneous cavitation

A capillarity-induced negative pressure is of general importance for understanding the phase behaviors of liquids in small pores and cracks. A unique example is the embolism in the xylem of plants and the cavitation at the limiting negative pressure generated by evaporation of water from nanocapillaries in the cell walls of leaves. In this work, by combining the effect of a capillary and cavitation together, we demonstrate with molecular dynamics (MD) simulations that capillarity is able to induce spontaneous cavitation in the presence of hydrophobic heterogeneities. Our simulation results reveal separately how the capillary generates a negative pressure and how the generated negative pressure affects the onset of cavitation. We then interpret the cavitation mechanism and determine the occurrence of cavitation as a function of the hydrophobicity of the nucleating substrates where the cavitation initiates and as a function of the hydrophilicity of the capillary tube from which the negative pressure generates. Our results reveal that the capillary-induced cavitation can be described well with a heterogeneous nucleation mechanism, within the framework of classical nucleation theory.

Surface tension of cavitation bubbles

We have studied homogeneous cavitation in liquid nitrogen and normal liquid helium. We monitor the fluid content in a large number of independent mesopores with an ink-bottle shape, either when the fluid in the pores is quenched to a constant pressure or submitted to a pressure decreasing at a controlled rate. For both fluids, we show that, close enough to their critical point, the cavitation pressure threshold is in good agreement with the Classical Nucleation Theory (CNT). In contrast, at lower temperatures, deviations are observed, consistent with a reduction of the surface tension for bubbles smaller than two nanometers in radius. For nitrogen, we could accurately measure the nucleation rate as a function of the liquid pressure down to the triple point, where the critical bubble radius is about one nanometer. We find that CNT still holds, provided that the curvature dependence of the surface tension is taken into account. Furthermore, we evaluate the first- and second-order corrections in curvature, which are in reasonable agreement with recent calculations for a Lennard-Jones fluid.

Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state

We explore the dynamics of a compressible fluid bubble surrounded by an incompressible fluid of infinite extent in three dimensions, constructing bubble solutions with finite time blowup under this framework when the equation of state relating pressure and volume is soft (e.g. with volume singularities that are locally weaker than that in the Boyle–Mariotte law), resulting in a finite time blowup of the surrounding incompressible fluid as well. We focus on two families of solutions, corresponding to a soft polytropic process (with the bubble decreasing in size until eventual collapse, resulting in velocity and pressure blowup) and a cavitation equation of state (with the bubble expanding until it reaches a critical cavitation volume, at which pressure blows up to negative infinity, indicating a vacuum). Interestingly, the kinetic energy of these solutions remains bounded up to the finite blowup time, making these solutions more physically plausible than those developing infinite energy. For all cases considered, we construct exact solutions for specific parameter sets, as well as analytical and numerical solutions that show the robustness of the qualitative blowup behaviours for more generic parameter sets. Our approach suggests novel—and perhaps physical—routes to the finite time blowup of fluid equations.

Surface Topography Effects on Pool Boiling via Non-equilibrium Molecular Dynamics Simulations

In this work, we investigate nucleate pool boiling via non-equilibrium molecular dynamics simulations. The effect of nano-structured surface topography on nucleation and transition to a film-like boiling regime is studied at the molecular scale, by varying the cavity aspect ratio, wall superheat, and wettability through a systematic parametric analysis conducted on a Lennard-Jones (LJ) system. The interplay of the aforementioned factors is rationalized by means of a classical nucleation theory-based model. The solid surface is heated uniformly from the bottom in order to induce the nanobubble nucleation. Insight into the cavity behavior in heat transfer problems is achieved by looking at temperature and heat flux profiles inside the cavity itself, as well as at the time of nucleation, for different operating conditions. The role of the cavity size in controlling the vapor embryo formation is highlighted, and its dependence on the other investigated parameters is summarized in a phase diagram. Our results show that heterogeneity at the nanoscale plays a key role in determining pool boiling heat transfer performance, suggesting a promising approach to optimize nanostructured surfaces for energy and thermal management applications.

Cavitation Mean Expectation Time in a Stretched Lennard-Jones Fluid under Confinement

We investigate the nucleation of cavitation bubbles in a confined Lennard-Jones fluid subjected to negative pressures in a cubic enclosure. We perform molecular dynamics (MD) simulations with tunable interatomic potentials that enable us to control the wettability of solid walls by the liquid, that is, its contact angle. For a given temperature and pressure, as the solid is taken more hydrophobic, we put in evidence, an increase in nucleation probability. A Voronoi tessellation method is used to accurately detect the bubble appearance and its nucleation rate as a function of the contact angle. We adapt classical nucleation theory (CNT) proposed for the heterogeneous case on a flat surface to our situation where bubbles may appear on flat walls, edges, or corners of the confined box. We finally calculate a theoretical mean expectation time in these three cases. The ratio of these calculated values over the homogeneous case is computed and compared successfully against MD simulations. Beyond the infinite liquid case, this work explores the heterogeneous nucleation of cavitation bubbles, not only in the flat surface case but for more complex confining geometries.

Communication: On the diffusion tensor in macroscopic theory of cavitation

The classical description of nucleation of cavities in a stretched fluid relies on a one-dimensional Fokker-Planck equation (FPE) in the space of their sizes r, with the diffusion coefficient D(r) constructed for all r from macroscopic hydrodynamics and thermodynamics, as shown by Zeldovich. When additional variables (e.g., vapor pressure) are required to describe the state of a bubble, a similar approach to construct a diffusion tensor D^ generally works only in the direct vicinity of the thermodynamic saddle point corresponding to the critical nucleus. It is shown, nevertheless, that "proper" kinetic variables to describe a cavity can be selected, allowing to introduce D^ in the entire domain of parameters. In this way, for the first time, complete FPE's are constructed for viscous volatile and inertial fluids. In the former case, the FPE with symmetric D^ is solved numerically. Alternatively, in the case of an inertial fluid, an equivalent Langevin equation is considered; results are compared with analytics. The suggested approach is quite general and can be applied beyond the cavitation problem.

Hydrodynamic cavitation in Stokes flow of anisotropic fluids

Cavitation, the nucleation of vapour in liquids, is ubiquitous in fluid dynamics, and is often implicated in a myriad of industrial and biomedical applications. Although extensively studied in isotropic liquids, corresponding investigations in anisotropic liquids are largely lacking. Here, by combining liquid crystal microfluidic experiments, nonequilibrium molecular dynamics simulations and theoretical arguments, we report flow-induced cavitation in an anisotropic fluid. The cavitation domain nucleates due to sudden pressure drop upon flow past a cylindrical obstacle within a microchannel. For an anisotropic fluid, the inception and growth of the cavitation domain ensued in the Stokes regime, while no cavitation was observed in isotropic liquids flowing under similar hydrodynamic parameters. Using simulations we identify a critical value of the Reynolds number for cavitation inception that scales inversely with the order parameter of the fluid. Strikingly, the critical Reynolds number for anisotropic fluids can be 50% lower than that of isotropic fluids.

Cavitation is the formation of vapour bubbles within a liquid and is undesirable in many industrial applications. Here Stieger et al. show how the anisotropic fluids influence this process in a nematic liquid crystal and find that orientational ordering of molecules can tune the onset of cavitation.

Time-dependent cavitation in a viscous fluid

Kinetics of nucleation and growth of empty bubbles in a nonvolatile incompressible fluid under negative pressure is considered within the generalized Zeldovich framework. The transient matched asymptotic solution obtained earlier for predominantly viscous nucleation is used to evaluate the distribution of growing cavities over sizes. Inertial effects described by the Rayleigh-Plesset equation are further included. The distributions are used to estimate the volume occupied by cavities, which leads to increase of pressure and eventual self-quenching of nucleation. Numerical solutions are obtained and compared with analytics. Due to rapid expansion of cavities the conventional separation of the nucleation and the growth time scales can be less distinct, which increases the role of transient effects. In particular, in the case of dominant viscosity a typical power-law tail of the quasistationary distribution is replaced by a time-dependent exponential tail. For fluids of the glycerin type such distributions can extend into the micrometer region, while in low-viscosity liquids (water, mercury) exponential distributions are short lived and are restricted to nanometer scales due to inertial effects.

Comment on "Simple improvements to classical bubble nucleation models"

A critical analysis of several statements concerning experimental studies, molecular dynamics simulations, and the theoretical interpretation of bubble nucleation processes is performed. In particular, it is shown that the Tolman equation does not supply us, in general, with a satisfactory theoretically founded description of the curvature dependence of the surface tension and the dependence of the steady-state nucleation rate of bubbles and droplets on supersaturation in the framework of classical nucleation theory.

Reply to "Comment on 'Simple improvements to classical bubble nucleation models' "

We reply to the Comment by Schmelzer and Baidakov [Phys. Rev. E 94, 026801 (2016)].10.1103/PhysRevE.94.026801 They suggest that a more modern approach than the classic description by Tolman is necessary to model the surface tension of curved interfaces. Therefore we now consider the higher-order Helfrich correction, rather than the simpler first-order Tolman correction. Using a recent parametrization of the Helfrich correction provided by Wilhelmsen et al. [J. Chem. Phys. 142, 064706 (2015)]JCPSA60021-960610.1063/1.4907588, we test this description against measurements from our simulations, and find an agreement stronger than what the pure Tolman description offers. Our analyses suggest a necessary correction of order higher than the second for small bubbles with radius ≲1 nm. In addition, we respond to other minor criticism about our results.

Spontaneous cavitation in a Lennard-Jones liquid: Molecular dynamics simulation and the van der Waals-Cahn-Hilliard gradient theory

The process of bubble nucleation in a Lennard-Jones (LJ) liquid is studied by molecular dynamics (MD) simulation. The bubble nucleation rate J is determined by the mean life-time method at temperatures above that of the triple point in the region of negative pressures. The results of simulation are compared with classical nucleation theory (CNT) and modified classical nucleation theory (MCNT), in which the work of formation of a critical bubble is determined in the framework of the van der Waals-Cahn-Hilliard gradient theory (GT). It has been found that the values of J obtained in MD simulation systematically exceed the data of CNT, and this excess in the nucleation rate reaches 8-10 orders of magnitude close to the triple point temperature. The results of MCNT are in satisfactory agreement with the data of MD simulation. To describe the properties of vapor-phase nuclei in the framework of GT, an equation of state has been built up which describes stable, metastable and labile regions of LJ fluids. The surface tension of critical bubbles γ has been found from CNT and data of MD simulation as a function of the radius of curvature of the surface of tension R*. The dependence γ(R*) has also been calculated from GT. The Tolman length has been determined, which is negative and in modulus equal to ≈(0.1 - 0.2) σ. The paper discusses the applicability of the Tolman formula to the description of the properties of critical nuclei in nucleation.

Curvature Dependence of the Liquid-Vapor Surface Tension beyond the Tolman Approximation

Surface tension is a macroscopic manifestation of the cohesion of matter, and its value σ_{∞} is readily measured for a flat liquid-vapor interface. For interfaces with a small radius of curvature R, the surface tension might differ from σ_{∞}. The Tolman equation, σ(R)=σ_{∞}/(1+2δ/R), with δ a constant length, is commonly used to describe nanoscale phenomena such as nucleation. Here we report experiments on nucleation of bubbles in ethanol and n-heptane, and their analysis in combination with their counterparts for the nucleation of droplets in supersaturated vapors, and with water data. We show that neither a constant surface tension nor the Tolman equation can consistently describe the data. We also investigate a model including 1/R and 1/R^{2} terms in σ(R). We describe a general procedure to obtain the coefficients of these terms from detailed nucleation experiments. This work explains the conflicting values obtained for the Tolman length in previous analyses, and suggests directions for future work.

Simple improvements to classical bubble nucleation models

We revisit classical nucleation theory (CNT) for the homogeneous bubble nucleation rate and improve the classical formula using a correct prefactor in the nucleation rate. Most of the previous theoretical studies have used the constant prefactor determined by the bubble growth due to the evaporation process from the bubble surface. However, the growth of bubbles is also regulated by the thermal conduction, the viscosity, and the inertia of liquid motion. These effects can decrease the prefactor significantly, especially when the liquid pressure is much smaller than the equilibrium one. The deviation in the nucleation rate between the improved formula and the CNT can be as large as several orders of magnitude. Our improved, accurate prefactor and recent advances in molecular dynamics simulations and laboratory experiments for argon bubble nucleation enable us to precisely constrain the free energy barrier for bubble nucleation. Assuming the correction to the CNT free energy is of the functional form suggested by Tolman, the precise evaluations of the free energy barriers suggest the Tolman length is ≃0.3σ independently of the temperature for argon bubble nucleation, where σ is the unit length of the Lennard-Jones potential. With this Tolman correction and our prefactor one gets accurate bubble nucleation rate predictions in the parameter range probed by current experiments and molecular dynamics simulations.

Evaluation of finite-size effects in cavitation and droplet formation

Nucleation of bubbles and droplets is of fundamental interest in science and technology and has been widely investigated through experiments, theory, and simulations. Giving the rare event nature of these phenomena, nucleation simulations are computationally costly and require the use of a limited number of particles. Moreover, they are often performed in the canonical ensemble, i.e., by fixing the total volume and number of particles, to avoid the additional complexities of implementing a barostat. However, cavitation and droplet formation take place differently depending on the ensemble. Here, we analyze the importance of finite-size effects in cavitation and droplet formation. We present simple formulas which predict the finite-size corrections to the critical size, the nucleation barrier, and the nucleation rates in the canonical ensemble very accurately. These results can be used to select an appropriate system-size for simulations and to get a more precise evaluation of nucleation in complex substances, by using a small number of molecules and correcting for finite-size effects.

Bubble evolution and properties in homogeneous nucleation simulations

We analyze the properties of naturally formed nanobubbles in Lennard-Jones molecular dynamics simulations of liquid-to-vapor nucleation in the boiling and the cavitation regimes. The large computational volumes provide a realistic environment at unchanging average temperature and liquid pressure, which allows us to accurately measure properties of bubbles from their inception as stable, critically sized bubbles, to their continued growth into the constant speed regime. Bubble gas densities are up to 50% lower than the equilibrium vapor densities at the liquid temperature, yet quite close to the gas equilibrium density at the lower gas temperatures measured in the simulations: The latent heat of transformation results in bubble gas temperatures up to 25% below those of the surrounding bulk liquid. In the case of rapid bubble growth-typical for the cavitation regime-compression of the liquid outside the bubble leads to local temperature increases of up to 5%, likely significant enough to alter the surface tension as well as the local viscosity. The liquid-vapor bubble interface is thinner than expected from planar coexistence simulations by up to 50%. Bubbles near the critical size are extremely nonspherical, yet they quickly become spherical as they grow. The Rayleigh-Plesset description of bubble-growth gives good agreement in the cavitation regime.

Direct simulations of homogeneous bubble nucleation: Agreement with classical nucleation theory and no local hot spots

We present results from direct, large-scale molecular dynamics simulations of homogeneous bubble (liquid-to-vapor) nucleation. The simulations contain half a billion Lennard-Jones atoms and cover up to 56 million time steps. The unprecedented size of the simulated volumes allows us to resolve the nucleation and growth of many bubbles per run in simple direct micro-canonical simulations while the ambient pressure and temperature remain almost perfectly constant. We find bubble nucleation rates which are lower than in most of the previous, smaller simulations. It is widely believed that classical nucleation theory (CNT) generally underestimates bubble nucleation rates by very large factors. However, our measured rates are within two orders of magnitude of CNT predictions; only at very low temperatures does CNT underestimate the nucleation rate significantly. Introducing a small, positive Tolman length leads to very good agreement at all temperatures, as found in our recent vapor-to-liquid nucleation simulations. The critical bubbles sizes derived with the nucleation theorem agree well with the CNT predictions at all temperatures. Local hot spots reported in the literature are not seen: Regions where a bubble nucleation event will occur are not above the average temperature, and no correlation of temperature fluctuations with subsequent bubble formation is seen.