Range Of Nucleation Rates Research Articles

Spontaneous boiling-up of gas-saturated liquids: Attainable superheating of ethane–helium and ethane–hydrogen solutions

The fluctuation growth of a vapor-gas bubble is described as a diffusion process in the space of three variables: the bubble volume V and the partial pressures P1 and P2 of the mixture components in the bubble. The dynamics of the nucleus growth takes into account the viscosity, the solvent volatility and the diffusion supply of the substance dissolved. An equation has been obtained for nucleation rate J expressed as a function of temperature, pressure, and solution concentration. Nucleation in superheated ethane–helium and ethane–hydrogen solutions was studied by the lifetime measurement method. Temperature and pressure dependencies of the nucleation rate have been established at pressures p = 1.6 and 2.0 MPa in solutions containing up to 0.05 mol% of helium and up to 0.31 mol% of hydrogen. The range of nucleation rates studied was J = (2.3·106 – 1.4·108) m−3s−1. The experimental results were compared to classical nucleation theory (CNT). Similarly to pure ethane, there is systematic “underheating” of the solutions as compared to the temperatures predicted by the CNT. The discrepancy found between theory and experiment is explained by the size-dependence of the surface tension of critical bubbles. It is noted that although, unlike hydrogen, helium in ethane acts as a surface-inactive component, this does not lead to an excess of the attainable superheating temperature of the ethane–helium solution over the superheating temperature of the ethane–hydrogen solution.

Kinetics of spontaneous boiling-up of a methane–nitrogen solutions

The mean life time method has been used to investigate the kinetics of nucleation in a superheated methane–nitrogen solution. Measurements have been made in the range of nucleation rates J = (1.2·104–1.6·108) m−3s−1. Temperature dependences of the nucleation rate have been obtained for seven compositions of the solution at pressures p = 1.0 and 1.6 MPa. The results of the experiments have been compared with classical nucleation theory (CNT). In contrast to pure methane and hydrogen, where superheating temperatures achieved by experiment are lower than their theoretical values, in methane–nitrogen solutions the opposite behavior is found. Close to the equimolecular composition limiting superheatings of solutions exceed theoretical values by (1.2–1.6) K. Possible reasons for the disagreement between CNT and experiment (size dependence of the surface tension of critical bubbles, bypassing the saddle point of the activation barrier, etc) are analyzed.

Kinetics of Nucleation in Superheated Liquid Oxygen-Nitrogen Solutions. 1. Experiment and Classical Homogeneous Nucleation Theory.

The method of lifetime measurement has been used to investigate the kinetics of spontaneous boiling-up of superheated liquid oxygen-nitrogen solutions. Experiments have been conducted at pressures of 0.5 and 1.0 MPa in the range of nucleation rates 104-108 m-3 s-1 in the whole concentration range. The temperature and concentration dependences of the nucleation rate have been determined. The sections corresponding to homogeneous nucleation have been singled out on experimental isobars. At fixed nucleation rates and pressures, the concentration dependence of the attainable-superheat temperature is close to a linear one. A comparison of experimental data with classical nucleation theory (CNT) has revealed systematic discrepancies, which are of qualitatively different character for pure liquids and solutions. In a pure liquid, the surface tension of critical bubbles is less, and in a solution, it is greater than at a flat interface.

Attainable superheating of liquid n-butane

Temperatures of the attainable superheating of liquid n-butane have been determined at pressures from 0.4 to 2.0 MPa in the range of nucleation rates J = 104–108 s−1 m−3. The data obtained have been compared with classical nucleation theory (CNT). At J > 106 s−1 m−3, satisfactory agreement between theory and experiment has been noted in both the value of the limiting superheating and the slope of the temperature dependence of the nucleation rate. It is shown that temperatures of the attainable superheatings of hydrocarbons of the methane series satisfy the one-parameter similarity. The possibility of manifestation of heterogeneous nucleation in experiment is discussed.

Laboratory study of H2SO4/H2O nucleation using a new technique – a laminar co-flow tube

Nucleation of aerosol particles from gaseous precursors is an important stage in the formation of atmospheric secondary aerosols or in industrial applications, particularly coal burning boilers. We introduce a novel laboratory device for studying binary or ternary nucleation – a laminar co-flow tube (LCFT) – and provide first data for the H2SO4/H2O system, showing that LCFT is able to cover a wide range of nucleation rates. The experimental set-up and the underlying transport processes are explained. Advantages of LCFT over methods employing turbulent mixing are suppression of wall losses and an accurate mathematical model. The determined nucleation rates are by about two orders of magnitude lower than typical literature values. Results of various nucleation experiments often show systematic differences unexplained by the present level of knowledge. Introduction of the LCFT technique based on a well-defined laminar diffusion process may help to identify the method-related biases.

Homogeneous SPC/E water nucleation in large molecular dynamics simulations.

We perform direct large molecular dynamics simulations of homogeneous SPC/E water nucleation, using up to ∼ 4 ⋅ 10(6) molecules. Our large system sizes allow us to measure extremely low and accurate nucleation rates, down to ∼ 10(19) cm(-3) s(-1), helping close the gap between experimentally measured rates ∼ 10(17) cm(-3) s(-1). We are also able to precisely measure size distributions, sticking efficiencies, cluster temperatures, and cluster internal densities. We introduce a new functional form to implement the Yasuoka-Matsumoto nucleation rate measurement technique (threshold method). Comparison to nucleation models shows that classical nucleation theory over-estimates nucleation rates by a few orders of magnitude. The semi-phenomenological nucleation model does better, under-predicting rates by at worst a factor of 24. Unlike what has been observed in Lennard-Jones simulations, post-critical clusters have temperatures consistent with the run average temperature. Also, we observe that post-critical clusters have densities very slightly higher, ∼ 5%, than bulk liquid. We re-calibrate a Hale-type J vs. S scaling relation using both experimental and simulation data, finding remarkable consistency in over 30 orders of magnitude in the nucleation rate range and 180 K in the temperature range.

Nucleation in ethane–nitrogen solutions. I. Homogeneous nucleation

The method of lifetime measurement is used to investigate the kinetics of spontaneous boiling-up of ethane–nitrogen solutions. Superheating temperatures Tn of solutions have been determined in experiments at pressure p=1.0, 1.6MPa and nitrogen concentration in ethane x=0.5, 1.5mol% in the nucleation rate range J=1×104–2×108s−1m−3. At J>3×106s−1m−3 one can observe a satisfactory agreement between experimental data and homogeneous nucleation theory with respect to the temperature dependence of the nucleation rate and a systematic disagreement in the superheating temperature. At x=0.5mol% attainable superheating temperatures achieved by experiment coincide within the experimental error with theoretical values, and at x=1.5mol% exceed them by approximately 1.7K. It is shown that one possible reason of such “excess superheating” of a solution beyond the theoretical value of Tn may be the absence of adsorption equilibrium at the critical bubble–ambient solution interface.

Analysis of feedbacks between nucleation rate, survival probability and cloud condensation nuclei formation

Abstract. Aerosol nucleation is an important source of particle number in the atmosphere. However, in order to become cloud condensation nuclei (CCN), freshly nucleated particles must undergo significant condensational growth while avoiding coagulational scavenging. In an effort to quantify the contribution of nucleation to CCN, this work uses the GEOS-Chem-TOMAS global aerosol model to calculate changes in CCN concentrations against a broad range of nucleation rates and mechanisms. We then quantify the factors that control CCN formation from nucleation, including daily nucleation rates, growth rates, coagulation sinks, condensation sinks, survival probabilities, and CCN formation rates, in order to examine feedbacks that may limit growth of nucleated particles to CCN. Nucleation rate parameterizations tested in GEOS-Chem-TOMAS include ternary nucleation (with multiple tuning factors), activation nucleation (with two pre-factors), binary nucleation, and ion-mediated nucleation. We find that nucleation makes a significant contribution to boundary layer CCN(0.2%), but this contribution is only modestly sensitive to the choice of nucleation scheme, ranging from 49 to 78% increase in concentrations over a control simulation with no nucleation. Moreover, a two order-of-magnitude increase in the globally averaged nucleation rate (via changes to tuning factors) results in small changes (less than 10%) to global CCN(0.2%) concentrations. To explain this, we present a simple theory showing that survival probability has an exponentially decreasing dependence on the square of the condensation sink. This functional form stems from a negative correlation between condensation sink and growth rate and a positive correlation between condensation sink and coagulational scavenging. Conceptually, with a fixed condensable vapor budget (sulfuric acid and organics), any increase in CCN concentrations due to higher nucleation rates necessarily entails an increased aerosol surface area in the accumulation mode, resulting in a higher condensation sink, which lowers vapor concentrations and growth rates. As a result, slowly growing nuclei are exposed to a higher frequency of coagulational scavenging for a longer period of time, thus reducing their survival probabilities and closing a negative feedback loop that dampens the impact of nucleation on CCN. We confirm quantitatively that the decreases in survival probability predicted by GEOS-Chem-TOMAS due to higher nucleation rates are in accordance with this simple theory of survival probability.

Homogeneous nucleation rate measurements in supersaturated water vapor

The rate of homogeneous nucleation in supersaturated vapors of water was studied experimentally using a thermal diffusion cloud chamber. Helium was used as a carrier gas. Our study covers a range of nucleation rates from 3x10(-1) to 3x10(2) cm(-3) s(-1) at four isotherms: 290, 300, 310, and 320 K. The molecular content of critical clusters was estimated from the slopes of experimental data. The measured isothermal dependencies of nucleation rate of water on saturation ratio were compared with the prediction of the classical theory of homogeneous nucleation, the empirical prediction of Wolk et al. [J. Chem. Phys. 117, 10 (2002)], the scaled model of Hale [Phys. Rev. A 33, 4156 (1986)], and the former nucleation onset data.

Attainable Superheat of Argon−Helium, Argon−Neon Solutions

The method of lifetime measurement has been used to investigate the kinetics of spontaneous boiling-up of superheated argon-helium and argon-neon solutions. Experiments were made at a pressure of p = 1.5 MPa and concentrations up to 0.33 mol% in the range of nucleation rates from 10 (4) to 10 (8) s (-1) m (-3). The homogeneous nucleation regime has been distinguished. With good agreement between experimental data and homogeneous nucleation theory in temperature and concentration dependences of the nucleation rate, a systematic underestimation by 0.25-0.34 K has been revealed in superheat temperatures over the saturated line attained by experiment as compared with theoretical values calculated in a macroscopic approximation. The revealed disagreement between theory and experiment is connected with the dependence of the properties of new-phase nuclei on their size.

Homogeneous nucleation rates of higher n-alcohols measured in a laminar flow diffusion chamber.

Nucleation rate isotherms of n-butanol, n-pentanol, n-hexanol, n-heptanol, and n-octanol were measured in a laminar flow diffusion chamber using helium as carrier gas. The measurements were made at 250-310 K, corresponding to reduced temperatures of 0.43-0.50, and at atmospheric pressure. Experimental nucleation rate range was from 10(3) to 10(7) cm(-3) s(-1). The expression and accuracy of thermodynamic parameters, in particular equilibrium vapor pressure, were found to have a significant effect on calculated nucleation rates. The results were compared to the classical nucleation theory (CNT), the self-consistency corrected classical theory (SCC) and the Hale's scaled model of the CNT. The average ratio between the experimental and theoretical nucleation rates for all alcohols used was 1.5x10(3) when the CNT was used, and 0.2x10(-1) when the SCC was used and 0.7x10(-1) when the Hale's scaled theory was used. The average values represent all the alcohols used at the same reduced temperatures. The average ratio was about the same throughout the temperature range, although J(exp)/J(the) calculated with the Hale's scaled theory increased slightly with increasing temperature. The saturation ratio dependency was predicted closest to experiment with the classical nucleation theory. The nucleation rates were compared to those found in the literature. The measurements were in reasonable agreement with each other. The molecular content of critical alcohol clusters was between 35 and 80 molecules. At a fixed reduced temperature, the number of molecules in a critical cluster decreased as a function of alcohol carbon chain length. The number of molecules in critical clusters was compared to those predicted by the Kelvin equation. The theory predicted the critical cluster sizes well.

Kinetics of Two-Phase Electrocrystallization Processes : II. Generalized Form of the Transients

In the previous paper of this series the forms of the potentiostatic current-time transients (CTTs) due to the instantaneous nucleation and competitive growth of two crystallographic phases of a deposit were identified. In this paper the patterns of behavior of the CTTs over the whole range of nucleation rates, from the lower to the upper limit, that is, from the so-called progressive to the instantaneous limit of nucleation rates, are examined. It is found that the forms of the CTTs remain essentially the same for all rates of nucleation, apart from the expected kinetic shifts and the dependency of current on the deposition time in the early stages. An equation for the slope of the grain boundaries between the two phases is derived. It is shown that grain boundaries between the two phases are a function only of their relative rates of growth and are independent of their nucleation rates. © 2004 The Electrochemical Society. All rights reserved.

Empirical function for homogeneous water nucleation rates

Very recently, Wölk and Strey [J. Phys. Chem. B 105, 11683 (2001)] presented empirical temperature correction functions for calculating homogeneous nucleation rates J of H2O and D2O (1<J/cm−3 s−1<1020) from classical nucleation theory over an extended range of temperature T (200<T/K<310) and supersaturations S (5<S<200). Here, we critically test the correction functions to the Becker–Döring nucleation rate equation JBD against an extensive set of experimental data, and find that the equations distinctly improve the agreement between theory and experiment for very little extra work. The success of the corrected nucleation rate functions is surprising, given that they were developed based on experimental nucleation rates measured in a nucleation pulse chamber over a limited nucleation rate range 105<J/cm−3 s−1<1010, supersaturation range 6<S<22, and temperature range 220<T/K<260.

Nucleation and Three-Dimensional Growth: Deviation from Diffusion Control

Direct numerical simulation of nucleation and three-dimensional growth is used to examine the impact on chronoamperometry measurements of growth that is not diffusion controlled at all times. Results are given for a range of nucleation rates. It is shown that deviation from diffusion-controlled growth can significantly modify not only the quantitative interpretation of the transients but can impact the qualitative signatures that are used to distinguish between instantaneous and progressive nucleation. The influence of ohmic-potential losses on chronoamperometry response is also demonstrated. © 2002 The Electrochemical Society. All rights reserved.

A Laminar Flow Diffusion Chamber for Homogeneous Nucleation Studies

A new version of laminar flow diffusion chamber was developed for unary homogeneous nucleation from vapor to liquid studies. The developed laminar flow diffusion chamber can quantitatively measure nucleation rates as a function of saturation ratio and temperature. A numerical model was developed for calculations of temperature and saturation ratio profiles inside the laminar flow diffusion chamber. Several experiments were made to ensure the proper and reliable operation of the device and the numerical model. Nucleation rates of n-hexanol were measured using helium as a carrier gas from 265.0 to 295.0 K. The measured nucleation rate range was from 103 to 107 cm-3 s-1. Temperature and saturation ratio dependencies were compared to the classical nucleation theory. The saturation ratio dependency was well predicted by the theory. Results were compared to the measurements made by others. They were in reasonable agreement at the lower end of the temperature range of this study. The carrier gas effect was also ...

Homogeneous nucleation of n-pentanol in a laminar flow diffusion chamber

Nucleation rate isotherms of n-pentanol were measured in laminar flow diffusion chamber. n-pentanol was chosen for nucleating vapor and helium for carrier gas as a part of a world wide joint experiment on homogeneous nucleation. Experimental temperature range was from 260 to 290 K. Experimental nucleation rate range was from 103 to 107 cm−3 s−1. The results were compared to the classical nucleation theory and experimental data found in literature. Experimental results were three orders of magnitude higher than predicted by the theory. The difference was constant over the whole experimental range. The saturation ratio dependency of nucleation rate was well predicted by the theory. The number of molecules in the critical clusters was quite consistent with the theory. The results were in reasonable agreement with data found in literature.

Cahn–Hilliard-type density functional calculations for homogeneous ice nucleation in undercooled water

The free energy of ice nuclei and the nucleation rate in undercooled water are calculated in the framework of a single-order parameter Cahn–Hilliard theory. The coefficients of the quartic free energy-order parameter relationship and of the square-gradient term are chosen in order to reproduce the measured Gibbs free energy difference, the ice–water interfacial free energy, and the interface thickness predicted by molecular dynamics simulations. Without adjustable parameters, the model reproduces fairly the experimental nucleation rates down to −40°C. A simple one-parameter model is adopted to describe the specific heat anomaly of liquid water at lower temperatures. The range of nucleation rates allowed by thermodynamically consistent choices of this parameter encloses extreme experimental values (∼1030m−3s−1) Bartell and Huang obtained at deep undercoolings (∼− 73°C). The temperature and size-dependencies of the interfacial properties (free energy, Tolman-length, etc.) are discussed.

A pulse-expansion wave tube for nucleation studies at high pressures

The design and performance of a new pulse-expansion wave tube for nucleation studies at high pressures are described. The pulse-expansion wave tube is a special shock tube in which a nucleation pulse is formed at the endwall of the high pressure section. The nucleation pulse is due to reflections of the initial shock wave at a local widening situated in the low pressure section at a short distance from the diaphragm. The nucleation pulse has a duration of the order of 200 μs, while nucleation pressures that can be achieved range from 1 to 50 bar total pressure. Droplet size and droplet number density can accurately be determined by a 90°-Mie light scattering method and a light extinction method. The range of nucleation rates that can be measured is 108 cm-3 s-1<J<1011 cm-3 s-1. We will illustrate the functioning and possibilities of the new pulse-expansion wave tube by nucleation rate measurements in the gas-vapour mixture nitrogen/water in the temperature range 200–260 K, and in the mixture methane/n-nonane as a function of supersaturation S at various total pressures up to 40 bar and temperatures around 240 K.

Generalization of transient equations due to the growth of hemispheroids

Abstract A generalized form of current-time transient, operative over the whole range of nucleation rates and applicable to both preferred and non-preferred site nucleation processes, is derived for the model of growth of hemispheroids. This generalized form is shown to reduce at high and low rates of nucleation to the forms derived for instantaneous and progressive nucleation of hemispheroids respectively. The flow of current is shown to reach a maximum before approaching a steady value. It is found that 89.5%–90.8% of the surface of the electrode is covered, depending on the rate of nucleation, by the time the current reaches a maximum value. Generalized forms of transients for the flow of charge and for the average thickness of the deposit are also derived. The transient behaviour of these quantities over all nucleation rates is characterized.

Analysis of experimental nucleation data for silver and SiO using scaled nucleation theory

The experimental vapor phase nucleation data of Nuth et al., for silver [J. A. Nuth, K. A. Donnelly, B. Donn, and L. U. Lilleleht, J. Chem. Phys. 77, 2639 (1982)] and SiO [J. A. Nuth and B. Donn, J. Chem. Phys. 85, 1116 (1986)] are reanalyzed using a scaled model for homogeneous nucleation [B. N. Hale, Phys. Rev. A 33, 4156 (1986)]. The approximation is made that the vapor pressure at the nucleation site is not diminished significantly from that at the source (crucible). It is found that the data for ln S have a temperature dependence consistent with the scaled theory ln S≊ΓΩ3/2 [Tc/T−1]3/2, and predict critical temperatures 3800±200 K for silver and 3700±200 K for SiO. One can also extract an effective excess surface entropy per atom Ω=2.1±0.1 and an effective surface tension σ≊1500−0.45T ergs/cm2 for the small silver clusters (assuming a range of nucleation rates from 105 to 1011 cm−3 s−1). The corresponding values for SiO are Ω≊1.7±0.1 and σ≊820−0.22T ergs/cm2 (assuming a range of nucleation rates from 109 to 1012 cm−3 s−1).