Chapter 10 - Bubble nucleation

Kinetics of bubble nucleation in a rhyolitic melt: an experimental study of the effect of ascent rate

The transfer of volatiles from the Earth's interior to the atmosphere occurs through degassing of magma, the dynamics of which assert a significant control on volcanic eruptions. The first and most critical step in degassing is the nucleation of gas bubbles, which requires that a sufficient number of volatile molecules cluster together to overcome the free energy associated with the formation of a new interface between nucleus and surrounding melt. This free energy is a function of surface tension, typically assumed to equate to the macroscopically measurable value. Surface tension estimates inferred from bubble nucleation experiments in silicate melts are, however, lower than direct macroscopic measurements, making it difficult to accurately predict magma ascent and decompression rates from measured bubble number densities in pyroclasts. We provide a potential resolution to this problem through an integrated study of bubble nucleation experiments and modeling thereof, based on nonclassical nucleation theory. We find that surface tension between critical bubble nuclei and the surrounding melt depends on the degree of supersaturation and is lower than the macroscopically measured value. This is consistent with the view that far from equilibrium the interface between a nucleus and surrounding metastable bulk phase is diffuse instead of sharp. As a consequence, the increase in nucleation rate with supersaturation is significantly larger at high supersaturations than predicted by classical nucleation theory.

Influence of Bubbles on the Energy Conversion Efficiency of Electrochemical Reactors

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.

Experimental demonstration of continuous bubble nucleation in rhyolite

We present experimental data on the thermodynamics and kinetics of bubble nucleation and growth in weakly H2O‐oversaturated rhyolitic melts. The high‐temperature (900–1100°C) experiments involve heating of rhyolitic obsidian from Hrafntinnuhryggur, Krafla, Iceland to above their glass transition temperature (Tg ∼ 690°C) at 0.1 MPa for times of 0.25–24 h. During experiments, the rhyolite cores increase in volume as H2O vapor‐filled bubbles nucleate and expand. The extent of vesiculation, as tracked by porosity, is mapped in temperature‐time (T‐t) space. At constant temperature and for a characteristic dwell time, the rhyolite cores achieve a maximum volume where the T‐t conditions reach thermochemical equilibrium. For each T‐t snapshot of vesiculation, we use 3‐D analysis of X‐ray computed tomographic (XCT) images of the quenched cores to obtain the bubble number density (BND) and bubble‐size distribution (BSD). BNDs for the experimental cores are insensitive to T and t, indicating a single nucleation event. All BSDs converge to a common distribution, independent of T, melt viscosity (η), or initial degree of saturation, suggesting a common growth process. We use these data to calibrate an empirical model for predicting the rates and amounts of vesiculation in rhyolitic melts as a function of η and thermochemical affinity (A): two computable parameters that are dependent on T, pressure and H2O content. The model reproduces the experimental data set and data from the literature to within experimental error, and has application to natural volcanic systems where bubble formation and growth are not diffusion limited (e.g., lavas, domes, ignimbrites, conduit infill).

Predictions of the superheat limit of a liquid can be made using the equation of state or classical nucleation theory or bubble formation model based on molecular interactions. The spinodal lines predicted by the Redlich-Kwong equation of state accurately predict the superheat limit for hydrocarbons such as pentane, hexane, and heptane. The classical bubble nucleation theory assuming a nucleation rate of 1012 bubles/m3⋅s and the molecular interaction-based bubble nucleation model with a nucleation rate of 1028 nuclei/cm3⋅s effectively predict the superheat limit of hydrocarbons, alcohols and halocarbons very well. However, bubble nucleation models based on molecular interactions predict vaporization of the liquid at the superheat limit as indicated by the nucleation rates estimated by Lienhard. The superheat limit of liquids, as measured by various experimental techniques and methods, is close to the spinodal limit of liquids. The superheat limit of liquids measured by various experimental techniques and methods is close to the spinodal of liquid. This study reviews various experimental methods for measuring the superheat limit of liquids, including the droplet explosion technique and pulse heating methods, recent experimental findings on the superheat limit of liquids on microscale surfaces, and the role of nucleation rate in bubble nucleation. Various experiments have shown that the superheat limit occurs close to the spinodal point of a liquid at a given pressure as predicted by Lienhard.

Nucleation, the initial process in vapor condensation, crystal nucleation, melting, and boiling, is the localized emergence of a distinct thermodynamic phase at the nanoscale that macroscopically grows in size with the attachment of growth units. These phase changes are the result of atomistic events driven by thermal fluctuations. The occurrence of atomistic level events with the length scales on the order of 10–10 m and time scales of 10–13 S equivalent to the vibrational frequency of atoms makes the nucleation a very complicated phenomenon to study. Even though abundant literature is available about fundamental aspects of nucleation, the knowledge on these phenomena is far from complete. The classical pathway to nucleation which was once considered to have general applicability to all nucleating systems is gradually giving way to a nonclassical pathway which is now considered as a dominating mechanism in solution crystallization and other systems. In this review, an attempt is made to compare underlying physical principles involved in various nucleating systems and their theoretical treatment based on classical nucleation theory, and other important theories such as a density functional approach and diffuse interface theory. The limitations of classical theory, the gradual evolution of a nonclassical two-step pathway to nucleation, and the questions that have to be addressed in the future are discussed systematically.

Three different derivations of the classical binary nucleation theory are considered in detail. It is shown that the derivation originally presented by Wilemski [J. Chem. Phys. 80, 1370 (1984)] is consistent with more extensive derivations [Oxtoby and Kashchiev, J. Chem. Phys. 100, 7665 (1994)]; Debenedetti, Metastable Liquids: Concepts and Principles (Princeton University Press, Princeton, 1996) if and only if the assumption is made that the surface of tension of the binary nucleus coincides with the dividing surface specified by the surface condition ∑nsivli=0, where the nsi denote surface excess numbers of molecules of species i, and the v’s are partial molecular volumes. From this condition, it follows that (1) the surface tension is curvature independent and (2) that the nucleus volume is V=∑nlivli=∑givli, where the nli are the numbers of molecules in the uniform liquid phase of the droplet model encompassed by the surface of tension, and the gi are the total molecular occupation numbers contained by the nucleus. We show, furthermore, that the above surface condition leads to explicit formulas for the surface excess numbers nsi in the nucleus. Computations for the ethanol–water system show that the surface number for water molecules (ns,H2O) causes the negative occupation numbers (gH2O) obtained earlier using the classical nucleation theory. The unphysical behavior produced by the classical theory for surface active systems is thus a direct consequence of the assumption of curvature independence of surface tension. Based on the explicit formulas for nsi, we calculate the full free-energy surfaces for binary nucleation in the revised classical theory and compare these with the free-energy surfaces in the Doyle (unrevised classical) theory. Significant differences in nucleus size and composition are found between these models and they are related to surface excess density. It is shown that only for the revised classical theory is the nucleus composition consistent with the Gibbs dividing surface model.

Ultrasonic foam processing of polyurethane for reaction injection moulding (RIM) was studied experimentally to investigate feasibility of ultrasonic bubble nucleation in polyurethane. Bubble nucleation was also studied theoretically to predict the rate of nucleation. Classical nucleation theory and cluster theory have been employed for explanation of the nucleation phenomena. A polyol resin was saturated with nitrogen at various pressures and the pressure was released slowly in order to generate supersaturated resin. Other components of the selected polyurethane system were added to the supersaturated resin and ultrasonic disruption was applied to the system producing enhanced nucleation. The ultrasonic excitation created a good foam structure even at a low saturation pressure around 0.15 MPa (1.5 atm). The effect of the ultrasonic activation on the bubble nucleation was considered and included in the nucleation theories. The cluster nucleation theory along with consideration of the ultrasonic effect predicted a higher rate of nucleation than the classical nucleation theory for the same condition.

Experimental and numerical analysis of bubble nucleation in foaming polymer

Classical nucleation theory relies on the capillarity approximation: the assumption that the free energy of a small cluster of a new phase can be described by a bulk free energy difference (from thermodynamics) plus a surface term (with effects of curvature neglected). We have used density functional theory to develop a nonclassical theory, one which allows the order parameters to vary through the cluster in order to give the lowest possible barrier to nucleation. This approach has been applied to crystallization of liquids from the melt and to condensation of liquids from the vapor, and shows significant deviations from classical nucleation theory. A simple, exactly soluble model will be introduced and used to explore the limits of validity of classical nucleation theory.

In the continuous production of microcellular thermoplastic foam, a polymer−physical foaming agent (PFA) solution is subjected to a rapid pressure drop through an extrusion foaming die. Simulations were run for the flow of a polymer−PFA solution through an extrusion foaming die with an abrupt axisymmetric contraction. The pressure drops across the die obtained through the simulations showed good qualitative agreement with experimental pressure drop measurements on the foaming extrusion die obtained in our laboratory. Field values of pressure, temperature, and velocity were obtained at each point in the foaming die. Once the values of pressure and temperature were obtained along each point in the foaming die, classical nucleation theory for bubble nucleation was invoked to predict the local bubble nucleation rate downstream of the saturation surface. The hydrodynamic constraints to the nucleation rate were calculated by using a modified form of the classical nucleation theory that accounted for the diffusional and viscosity constraints to the rate of homogeneous nucleation. The capillarity approximation was found not to be valid for bubble nucleation of CO2 in polymers; a correction accounting for the curvature dependence of surface tension was applied to get nonzero nucleation rates for the system to reconcile theoretically predicted rates with experimental observations.

A longstanding question in the study of nucleation of liquids from the vapor phase is the validity of the classical nucleation theory (CNT) of Becker, Doring, and Zeldovich[l]. Experiments have been designed [2,3]to probe the range of validity of the classical theory, and have concluded that that theory is remarkably successful, although careful measurements are capable of showing small deviations. The introduction by Lothe and Pound [4] of large correction factors to classical nucleation rates has excited a great deal of controversy, but has led to much poorer agreement of theory with experiment. More recent theories [5] are closer to the classical prediction, but still do not agree with experiment as well as CNT. There are two ways to go beyond the CNT and the capillarity approximation that it implies. The first is to attempt direct statistical mechanical evaluation of the partition functions of small clusters of molecules, a procedure that is difficult for clusters as large as those important in nucleation processes. The second is the approach we follow [6]: the use of density functional theory in statistical mechanics to calculate the free energies of non-uniform fluids. Our approach includes, in a mean field sense, nonclassical effects such as curvature-dependent surface tensions and finite interfacial widths, and goes over naturally to the classical theory in the limit of large droplets.

Study of shear nucleation theory in continuous microcellular foam extrusion