Direct Simulations of Homogeneous Bubble Nucleation: Agreement with CNT and no Local Hot Spots

We present results from direct, large-scale molecular dynamics (MD) simulations of homogeneous bubble (liquid-to-vapor) nucleation. The simulations contain half a billion Lennard-Jones (LJ) 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 (NVE) 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 events will occur are not above the average temperature, and no correlation of temperature fluctuations with subsequent bubble formation is seen.Comment: 15 pages, 13 figures. Submitted to PRE. Simulation movies available at http://www.ics.uzh.ch/~diemand/movies

Probing new intra-atomic force with isotope shifts

In the development of atomic clocks, some atomic transition frequencies are measured with remarkable precision. These measured spectra may include effects of a new force mediated by a weakly interacting boson. Such effects might be distilled out from possible violation of a linear relation in isotope shifts between two transitions, as known as King's linearity, with relatively suppressed theoretical uncertainties. We discuss the experimental sensitivity to a new force in the test of the linearity as well as the linearity violation owing to higher order effects within the Standard Model. The sensitivity to new physics is limited by such effects. We have found that for Yb$^+$, the higher order effect is in the reach of future experiments. The sensitivity to a heavy mediator is also discussed. It is analytically clarified that the sensitivity becomes weaker than that in the literature. Our numerical results of the sensitivity are compared with other weak force search experiments.Comment: 16 pages, 3 figures; published versio

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 new 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 $\simeq 0.3 \sigma$ independently of the temperature for argon bubble nucleation, where $\sigma$ is the unit length of the Lenard-Jones potential. With this Tolman correction and our new prefactor one gets accurate bubble nucleation rate predictions in the parameter range probed by current experiments and molecular dynamics simulations.Comment: 10pages, 6figures, Accepted for publication in Physical Review

Free energy of cluster formation and a new scaling relation for the nucleation rate

Recent very large molecular dynamics simulations of homogeneous nucleation with $(1-8) \cdot 10^9$ Lennard-Jones atoms [Diemand et al. J. Chem. Phys. {\bf 139}, 074309 (2013)] allow us to accurately determine the formation free energy of clusters over a wide range of cluster sizes. This is now possible because such large simulations allow for very precise measurements of the cluster size distribution in the steady state nucleation regime. The peaks of the free energy curves give critical cluster sizes, which agree well with independent estimates based on the nucleation theorem. Using these results, we derive an analytical formula and a new scaling relation for nucleation rates: $\ln J' / \eta$ is scaled by $\ln S / \eta$, where the supersaturation ratio is $S$, $\eta$ is the dimensionless surface energy, and $J'$ is a dimensionless nucleation rate. This relation can be derived using the free energy of cluster formation at equilibrium which corresponds to the surface energy required to form the vapor-liquid interface. At low temperatures (below the triple point), we find that the surface energy divided by that of the classical nucleation theory does not depend on temperature, which leads to the scaling relation and implies a constant, positive Tolman length equal to half of the mean inter-particle separation in the liquid phase.Comment: 7 figure

Pure iron grains are rare in the universe

The abundant forms in which the major elements in the universe exist have been determined from numerous astronomical observations and meteoritic analyses. Iron (Fe) is an exception, in that only depletion of gaseous Fe has been detected in the interstellar medium, suggesting that Fe is condensed into a solid, possibly the astronomically invisible metal. To determine the primary form of Fe, we replicated the formation of Fe grains in gaseous ejecta of evolved stars by means of microgravity experiments. We found that the sticking probability for formation of Fe grains is extremely small; only several atoms will stick per hundred thousand collisions, so that homogeneous nucleation of metallic Fe grains is highly ineffective, even in the Fe-rich ejecta of Type Ia supernovae. This implies that most Fe is locked up as grains of Fe compounds or as impurities accreted onto other grains in the interstellar medium

Bubble Evolution and Properties in Homogeneous Nucleation Simulations

We analyze the properties of naturally formed nano-bubbles 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 non-spherical, yet they quickly become spherical as they grow.Comment: 14 pages, 14 figures. Accepted for publication in Physical Review E, now matches published versio