Homogeneous Nucleation Model Research Articles

On Nucleation Pathways and Particle Size Distribution Evolutions in Stratospheric Aircraft Exhaust Plumes with H2SO4 Enhancement.

Stratospheric aerosol injection (SAI) is proposed as a means of reducing global warming and climate change impacts. Similar to aerosol enhancements produced by volcanic eruptions, introducing particles into the stratosphere would reflect sunlight and reduce the level of warming. However, uncertainties remain about the roles of nucleation mechanisms, ionized molecules, impurities (unevaporated residuals of injected precursors), and ambient conditions in the generation of SAI particles optimally sized to reflect sunlight. Here, we use a kinetic ion-mediated and homogeneous nucleation model to study the formation of H2SO4 particles in aircraft exhaust plumes with direct injection of H2SO4 vapor. We find that under the conditions that produce particles of desired sizes (diameter ∼200-300 nm), nucleation occurs in the nascent (t < 0.01 s), hot (T = 360-445 K), and dry (RH = 0.01-0.1%) plume and is predominantly unary. Nucleation on chemiions occurs first, followed by neutral new particle formation, which converts most of the injected H2SO4 vapor to particles. Coagulation in the aging and diluting plumes governs the subsequent evolution to a narrow (σg = 1.3) particle size distribution. Scavenging by exhaust soot is negligible, but scavenging by acid impurities or incomplete H2SO4 evaporation in the hot exhaust plume and enhanced background aerosols can matter. This research highlights the need to obtain laboratory and/or real-world experiment data to verify the model prediction.

Acoustic vaporization of perfluorohexane droplets is induced by heterogeneous nucleation at 1.1 MHz

We investigated the ADV of perfluorohexane (PFH) nano and micro-droplets at a frequency of 1.1 MHz, at conditions where there is no superharmonic focusing. Our experiments were performed on suspensions of droplets in glycerol to avoid sedimentation. The ADV pressure threshold was defined as the pressure for which there is half a chance to observe a vaporization event. Our experiments showed that the threshold depends on the number of insonified droplets and the data were fitted by a statistical model, that is independant on the mechanism leading to ADV. The fit allows the derivation of the threshold in the case of a single insonified droplet. We further observed that the value of the ADV pressure threshold of a single PFH droplet decreases as its radius increases. In addition, at a constant droplet radius, the threshold did not vary when the PFH volume inside the droplet decreases, thanks to the encapsulation of an increasing number of water droplets. These results are incompatible with a model of homogeneous nucleation (where a nucleus can appear anywhere into the PFH volume). However, we developed a heterogeneous nucleation model, where the nucleus appears at the inner droplet surface, that successfully predicts our experimental ADV results.

Physicochemical mechanisms of aggregation and fibril formation of α-synuclein and apolipoprotein A-I.

Deposition and accumulation of amyloid fibrils is a hallmark of a group of diseases called amyloidosis and neurodegenerative disorders. Although polypeptides potentially have a fibril-forming propensity, native proteins have evolved into proper functional conformations to avoid aggregation and fibril formation. Understanding the mechanism for regulation of fibril formation of native proteins provides clues for the rational design of molecules for inhibiting fibril formation. Although fibril formation is a complex multistep reaction, experimentally obtained fibril formation curves can be fitted with the Finke-Watzky (F-W) two-step model for homogeneous nucleation followed by autocatalytic fibril growth. The resultant F-W rate constants for nucleation and fibril formation provide information on the chemical kinetics of fibril formation. Using the F-W two-step model analysis, we investigated the physicochemical mechanisms of fibril formation of a Parkinson's disease protein α-synuclein (αS) and a systemic amyloidosis protein apolipoprotein A-I (apoA-I). The results indicate that the C-terminal region of αS enthalpically and entropically suppresses nucleation through the intramolecular interaction with the N-terminal region and the intermolecular interaction with existing fibrils. In contrast, the nucleation of the N-terminal fragment of apoA-I is entropically driven likely due to dehydration of large hydrophobic segments in the molecule. Based on our recent findings, we discuss the similarity and difference of the fibril formation mechanisms of αS and the N-terminal fragment of apoA-I from the physicochemical viewpoints.

Modeling the Precipitation of Aluminum Nitride Inclusions during Solidification of High‐Aluminum Steels

High‐aluminum advanced high‐strength steels have received increasing interest due to their excellent combination of strength and ductility. The control of nonmetallic inclusions in steel is among the most important issue for the production of high‐aluminum steel. This study proposes a model for the evolution of size distributions of AlN inclusions during solidification of steel based on the Kampmann–Wagner numerical model and microsegregation calculation. Both homogeneous (pure AlN) and heterogeneous precipitations (AlN+oxide or MnS) are described using homogeneous nucleation and free growth models of Greer et al. respectively. The model is applied to calculate the size distributions of AlN in high‐Al (up to 5%) Fe–Cr–Al steels and high‐ and medium‐manganese steels and validated by the experimental data in the literature. The model correctly describes the influence of cooling rates on the precipitation of AlN in Fe–Cr–Al steels and high‐manganese steels, and the sizes of AlN are reduced and the number densities of AlN inclusions are increased by increasing the cooling rate. The effects of nitrogen and aluminum concentration in medium‐manganese steel on inclusion precipitation are investigated by the model calculation. The increases in nitrogen and aluminum concentration facilitate the homogeneous precipitation of AlN inclusions.

Co-condensation and interaction mechanism of acidic gases in supersonic separator: A method for simultaneous removal of carbon dioxide and hydrogen sulfide from natural gas

Supersonic separator offers a new research field for the simultaneous purification of acidic gases (such as carbon dioxide (CO2) and hydrogen sulfide (H2S)). However, the condensation characteristics and interaction mechanism of various acidic components in the methane (CH4) are not clear, resulting in low liquefaction efficiency. In this paper, mathematical models of homogeneous nucleation of the CH4-CO2/CH4-H2S binary mixture and heterogeneous condensation of the CH4-CO2-H2S ternary mixture were established. Numerical calculations and a detailed description of the condensation process were carried out. The results demonstrate that the liquefaction efficiency of CO2 can reach a high of 67.47 % by the homogeneous nucleation in the CH4-CO2, whereas the liquefaction efficiency of H2S is only 16.91 % in the CH4-H2S when the condensable inflow mole fraction is 10 %. The heterogeneous condensation of H2S will be promoted by the condensation nuclei of CO2 in the CH4-CO2-H2S. Although the nucleation rate of H2S is significantly reduced from 4.88 × 1021 to 0.369 m−3·s−1 compared with the CH4-H2S, the liquefaction efficiency of H2S is greatly increased from 16.91 % to 39.5 %. In actual gas processing, the condensation nuclei of CO2 will promote the heterogeneous condensation of the component H2S and increase the condensation efficiency of the H2S droplets.

Multiple Glass Transitions in Bismuth and Tin beyond Melting Temperatures

Liquid-liquid transitions were discovered above the melting temperature (Tm) in Bi and Sn up to 2 Tm, viewed as glass transitions at Tg = Tn+ &gt; Tm of composites nucleated at Tx &lt; Tm and fully melted at Tn+. A glassy fraction (f) disappeared at 784 K in Sn. (Tn+) increases with singular values of (f) depending on Tx with (f) attaining 100% at Tg = Tn+ = 2 Tm. The nonclassical model of homogeneous nucleation is used to predict Tx, Tn+ and the specific heat. The singular values of (f) leading to (Tn+) correspond to percolation thresholds of configurons in glassy phases. A phase diagram of glassy fractions occurring in molten elements is proposed. The same value of (Tx) can lead to multiple (Tg). Values of (Tg = Tn+) can be higher than (2 Tm) for Tx/Tm &lt; 0.7069. A specific heat equal to zero is predicted after cooling from T ≤ 2 Tm and would correspond to a glassy phase. Weak glassy fractions are nucleated near (Tn+) after full melting at (Tm) without transition at (Tx). Resistivity decreases were observed after thermal cycling between solid and liquid states with weak and successive values of (f) due to Tx/Tm &lt; 0.7069.

Crystallization of Aluminum droplet at low undercooling: homogeneous nucleation approach

Crystallization in an undercooled Aluminum (Al) droplet occurs via the formation of crystalline nuclei by homogeneous or heterogeneous nucleation and successive growth of nuclei. Clusters of a new phase appear in the system due to fluctuations and after reaching a critical size grow up to microscopic size. Crystallization event at low undercooling 6.4°C of 9.91 mg in compact Al sample was detected using isothermal differential scanning calorimetry (DSC) after several tenths of minutes. In this case, standard analysis based on Johnson-Mehl-Avrami-Kolmogorov (JMAK) model is not appropriate as Avrami parameter n obtained by fitting of DSC data is too low (n ≤ 1 and thus the dimensionality of the system d = n – 1 ≤ 0). Al growth rate is extremely high and that is why we presume that the time delay of crystallization, detected by DSC, is slightly higher than nucleation time delay. A homogeneous nucleation model is applied to determine the basic characteristics of nucleation: the size distribution of nuclei, nucleation rate, total number of nuclei and crystallization fraction at the nucleation process. The number of atoms in a liquid Aluminum droplet decreases with time as the formation of a new crystalline phase occurs. As a consequence, a decrease in stationary nucleation occurs. It is shown that decrease in the number of atoms in a liquid Al droplet is predominantly caused by formation of subcritical clusters.

Concentration dependence of the crystal nucleation kinetics in undercooled Cu-Ge melts.

The crystallization temperature of deeply undercooled Cu-Ge alloy melts is repeatedly measured. A statistical analysis is applied on the undercooling distributions obtained from nine different compositions, ranging from the pure semimetal (Ge) to the pure metal (Cu). By considering each undercooling distribution as an inhomogeneous Poisson process, the nucleation rates for every composition are calculated. The Thompson-Spaepen model for homogeneous nucleation in binary alloys is applied, enabling the estimation of nucleation parameters, such as kinetic pre-factors and interfacial energies, as a function of composition. Furthermore, the Turnbull coefficient α, a dimensionless solid-liquid interfacial energy constant, is also calculated as a function of alloy constitution, suggesting a dependence on the liquid composition. The composition-dependent changes of α are of considerable importance, since the α is originally defined for pure systems as a quantity dependent on crystal structure, and is nevertheless used for describing nucleation kinetics of binary and glass forming multi-component alloy systems.

A modified Euler-Lagrange-Euler approach for modelling homogeneous and heterogeneous condensing droplets and films in supersonic flows

The phase change in supersonic flows is of great interest in many industrial applications including steam turbines, nozzles, ejectors and aircraft. However, the phase change phenomenon is still not fully understood due to the completed flow behavior including nucleation, condensation, film generation and shock waves in supersonic flows. In the present study, we proposed a modified Euler-Lagrange-Euler model to explore the internal flow mechanism within supersonic separators. The mutual heat and mass transfer of the gaseous phase, droplets, and liquid film were simulated in supersonic flows. The homogeneous nucleation and growth model was innovatively added to ensure the model's comprehensiveness. The feasibility of the proposed model was validated by experiments. Then, the interaction of heterogeneous and homogeneous condensation in supersonic condensation flow was excavated for the first time. The results show the heterogeneous droplet diameter's decrease or concentration's increase had a significant inhibitory effect on homogeneous condensation. Subsequently, the supersonic swirl field's generation, the dynamic evolution of the homogeneous/heterogeneous droplet condensation and deposition, the liquid film development, and the heat-mass transfer between them in the supersonic separator were analyzed using the proposed model. Furthermore, the separation capacity of the supersonic separator was evaluated considering the co-action of homogeneous and heterogeneous condensation. Results show that increasing inlet droplet concentration from 0.0001 kg/s to 0.0025 kg/s can increase vapor separation efficiency and dew point depression from 61.39 % to 84.74 % and 19.03 K to 28.28 K, respectively.

Homogeneous nucleation and crystallization model of aluminum droplet based on isothermal DSC analysis

Homogeneous nucleation and crystallization model of aluminum droplet based on isothermal DSC analysis

On the Comprehensive Precipitation of Hydroxyapatites Unraveled by a Combined Kinetic-Thermodynamic Approach.

The present study combines experimental and theoretical approaches to investigate the competitive precipitation of calcium phosphates (CaPs) in aqueous solution in order to understand and control both the structural and textural properties of the synthesized hydroxyapatites (HAps). Some of the precipitation reactions were followed by in situ Raman spectroscopy or achieved under kinetically controlled conditions. The CaP precursors of HAps were identified as a function of the precipitation pH of the medium and the order of introduction of the precursor ions in the synthesis reactor. Their formation was rationalized by calculations based on a homogeneous nucleation model. Depending on the synthesis conditions, precipitation reaction pathways of HAps are proposed by bringing together the kinetic model developed in the present study and our previous thermodynamic model. HAps are complex materials due to the ease with which large amounts of crystallographic defects, such as carbonates and hydrogen phosphates, can be incorporated in their structure. As these defects play a key role in material sciences (bone substitute, heterogeneous acid-base catalysis, etc.), the present work also includes the analysis of the formation of these crystallographic defects in the apatitic framework, allowing a better control of their incorporation through careful selection of operating parameters.

Ice nucleation imaged with X-ray spectro-microscopy.

Ice nucleation is one of the most uncertain microphysical processes, as it occurs in various ways and on many types of particles. To overcome this challenge, we present a heterogeneous ice nucleation study on deposition ice nucleation and immersion freezing in a novel cryogenic X-ray experiment with the capability to spectroscopically probe individual ice nucleating and non-ice nucleating particles. Mineral dust type particles composed of either ferrihydrite or feldspar were used and mixed with organic matter of either citric acid or xanthan gum. We observed in situ ice nucleation using scanning transmission X-ray microscopy (STXM) and identified unique organic carbon functionalities and iron oxidation state using near-edge X-ray absorption fine structure (NEXAFS) spectroscopy in the new in situ environmental ice cell, termed the ice nucleation X-ray cell (INXCell). Deposition ice nucleation of ferrihydrite occurred at a relative humidity with respect to ice, RHi, between ∼120–138% and temperatures, T ∼ 232 K. However, we also observed water uptake on ferrihydrite at the same T when deposition ice nucleation did not occur. Although, immersion freezing of ferrihydrite both in pure water droplets and in aqueous citric acid occurred at or slightly below conditions for homogeneous freezing, i.e. the effect of ferrihydrite particles acting as a heterogeneous ice nucleus for immersion freezing was small. Microcline K-rich feldspar mixed with xanthan gum was also used in INXCell experiments. Deposition ice nucleation occurred at conditions when xanthan gum was expected to be highly viscous (glassy). At less viscous conditions, immersion freezing was observed. We extended a model for heterogeneous and homogeneous ice nucleation, named the stochastic freezing model (SFM). It was used to quantify heterogeneous ice nucleation rate coefficients, mimic the competition between homogeneous ice nucleation; water uptake; deposition ice nucleation and immersion freezing, and predict the T and RHi at which ice was observed. The importance of ferrihydrite to act as a heterogeneous ice nucleating particle in the atmosphere using the SFM is discussed.

Deformation behaviour of Cu and Cu–Al in the dislocation starved regime: A molecular dynamics study

In general, with the addition of solutes, the yield strength of alloys is expected to increase; this phenomenon is known as solid solution strengthening. However, this model of strengthening implicitly assumes that dislocations are available and it is their motion that causes plastic deformation. On the other hand, in dislocation starved regimes, it is the nucleation of dislocations that controls the deformation behaviour. In this regime, the solute atoms can act as sites of heterogeneous nucleation for dislocations and “anomalous” softening with alloying additions are not uncommon. In this study, using Molecular Dynamics (MD) simulations, we show anomalous softening in Cu–Al alloys deformed at 300 K. We show that there are two components to this softening; in addition to the heterogeneous nucleation at solute sites, the reduction in stacking fault energy with alloying addition promotes the (homogeneous) nucleation of partial dislocation loops. In order to be consistent, we interpret the MD simulation results of deformation behaviour using parameters and energies derived from the same potentials used in the simulations. Specifically, we carry out the thermodynamic integration to evaluate the free energies in crystals with and without the stacking faults and hence calculate the SFE as a function of Al content at 300 K. Using the SFE values thus obtained, and using a continuum model of homogeneous nucleation of partial dislocation loops, we rationalise the deformation behaviour seen in pure copper. On the other hand, in Cu–Al alloys, the drop in yield strength can only be explained using a combination of the continuum model (which assumes homogeneous nucleation), and the reduction in heterogeneous nucleation barrier (which is a function of the ratio of the unstable and stable stacking fault energies). Thus, our results indicate that deformation experiments of pure copper and copper–aluminium alloys in the dislocation starved regime could be interesting and might show qualitatively and quantitatively different behaviour.

Prediction of Second Melting Temperatures Already Observed in Pure Elements by Molecular Dynamics Simulations.

A second melting temperature occurs at a temperature Tn+ higher than Tm in glass-forming melts after heating them from their glassy state. The melting entropy is reduced or increased depending on the thermal history and on the presence of antibonds or bonds up to Tn+. Recent MD simulations show full melting at Tn+ = 1.119Tm for Zr, 1.126Tm for Ag, 1.219Tm for Fe and 1.354Tm for Cu. The non-classical homogeneous nucleation model applied to liquid elements is based on the increase of the Lindemann coefficient with the heating rate. The glass transition at Tg and the nucleation temperatures TnG of glacial phases are successfully predicted below and above Tm. The glass transition temperature Tg increases with the heating rate up to Tn+. Melting and crystallization of glacial phases occur with entropy and enthalpy reductions. A universal law relating Tn+ and TnG around Tm shows that TnG cannot be higher than 1.293Tm for Tn+= 1.47Tm. The enthalpies and entropies of glacial phases have singular values, corresponding to the increase of percolation thresholds with Tg and TnG above the Scher and Zallen invariant at various heating and cooling rates. The G-phases are metastable up to Tn+ because the antibonds are broken by homogeneous nucleation of bonds.

Mathematical modeling of dispersed media flows in the presence of nucleation, coagulation and phase transitions

A model of motion of a gas-dispersed medium in the presence of processes of nucleation, coagulation and phase transitions has been constructed. A homogeneous nucleation model is used to describe the nucleation process. It is believed that the process of cluster coagulation occurs due to their Brownian motion. The analysis of the solution of the coagulation equation in the particular case of monodisperse clusters in the presence of a source and sink of particles is carried out. To determine the rate of phase transitions the Hertz-KnudsenLangmuir formula is used. The calculations were carried out on the basis of a quasi-one-dimensional model within the equilibrium approximation (when the velocities and temperatures of the phases coincide). As a result of the study the main properties of the flow of a two-phase mixture in a channel in the presence of nucleation, coagulation, and phase transformations have been established. It is shown that the vapor temperature increases along the channel and reaches the saturation temperature at some distance from the channel entrance. Calculations have shown that the coagulation process has a rather strong effect on the distribution of cluster sizes along the channel.

Validation of non-classical homogeneous nucleation model for G-glass and L-glass formations in liquid elements with recent molecular dynamics simulations

A first-order transition from liquid to homogenous glass denoted L-glass is predicted since 2016, in liquid elements having a Lindemann constant equal to 0.103, with a non-classical homogeneous nucleation model, accompanied by a latent heat of 10.5 % of the melting heat. The transition under pressure of 4He is the first example of this phenomenon. Recent molecular dynamic simulations of Qi An et al identify, in addition, a first-order freezing transition from liquid (L) to metastable heterogenous solid-like phase, denoted as the G-glass, when a supercooled liquid evolves isothermally below its melting temperature Tm at deep undercooling. These observations are related to the general phenomenon of first-order transitions of glacial phases obtained by annealing above Tg at various heating or cooling rates or by isotherm annealing. The non-classical model of homogenous nucleation describes the first-order transitions of L-glass and G-glass to liquid in perfect agreement with these simulations.

Progress in rod bundle CHF in the past 40 years

Critical Heat Flux (CHF) prediction remains one of the most important tasks in thermal hydraulics of Light Water Reactors (LWR’s). During recent years, tremendous progress has been made in understanding and predicting rod bundle CHF. However, due to the unique features associated with rod bundle subchannel systems, including complex and compact anisotropic geometry, non-uniform axial/radial heating, open channel interactions, periodic (positional) mixing vane grids (MVG’s) mixing (Yang et al., 2014), and a broad range of operation conditions (Yang and Han et al., 2019), a precise prediction of CHF in rod bundles, entirely based on analytical methods without the support of any extensive experimental database, is still beyond the present modelling and computational capabilities. For Pressurized Water Reactors (PWR’s), CHF occurs at a relatively low coolant quality and is primarily driven by the Departure from Nucleate Boiling (DNB) type event, which can be triggered by liquid sublayer dryout, bubble crowding, homogeneous nucleation, or other mechanisms causing local starvation of liquid under subcooled flow boiling or low quality saturated boiling conditions, and the dryout event, which describes CHF under a high void situation when liquid film on the fuel surface dries out, usually happens in a high quality saturated annular flow. Boiling Water Reactors (BWR’s) operate at a relatively lower pressure and can reach much higher coolant qualities that correspond to annular two-phase flow conditions. This dominant CHF mechanism, dryout, is based on the gradual thinning and drying out of the liquid film.This paper provides an overview of the progress made in the experimental and analytical investigations of CHF in both PWR and BWR rod bundles during the past 40 years. A complete comprehensive concept map is developed to outline most of the key mechanistic CHF models covering the entire range of flow regimes. The limitation and the potential approaches for the application of mechanistic models to rod bundle CHF prediction are reviewed. This includes the recently proposed, rod bundle specific NHNM (Non-uniform heater Homogeneous Nucleation Model [Yang, 2017]). Various industrial empirical correlations are reviewed together with their corresponding subchannel codes and required rod bundle CHF experiments. The need for clear guidelines and standards for benchmarking new rod bundle CHF test facilities is discussed.Various approaches on investigating, understanding, modeling, and predicting the occurrence of rod bundle CHF are reviewed from mechanistic models, semi-empirical and empirical approaches to advanced CFD simulation. The achievements and limitations in those methods are discussed with suggestions for future advancement.

Analytical Study on Homogeneous Nucleation and Bubble Evolution Inside Monocomponent Fuel Droplet

Homogeneous nucleation and bubble evolution inside a fuel droplet trigger the occurrence of flash boiling, which shows a high potential to improve the droplet evaporation. To understand the bubble dynamic characteristics, an analytical study on homogeneous nucleation and bubble evolution has been performed, based on the flash boiling model proposed in our work. First, the nucleation rate graph of seven fuels within a wide range of operating temperatures is obtained according to the homogeneous nucleation model. Then the variation of homogeneous nucleation characteristics with fuel temperature and ambient pressure is discussed. Finally, the bubble evolution and boiling explosion of a single droplet are studied for different fuels at 490 K, 530 K, and 560 K, respectively. The results show that the nucleation characteristics are mainly affected by the fuel physical properties, especially the boiling point and surface tension. Moreover, the transitional and heat transfer controlled stages during bubble evolution are significantly affected by the nucleation rate, which causes temperature change and affects the boiling explosion time.

Numerical Study of Homogenous Nucleation of Boron Oxide Vapor in Laval Nozzles

A model of nonstationary homogeneous nucleation of boron oxide vapor in chemically reacting gas mixtures is developed. The model is used to perform a numerical study of homogeneous nucleation of boron oxide vapor in Laval nozzles with different geometric configurations. Typical sizes of boron oxide condensation nuclei and their concentrations are determined. The potential barrier of nucleation, nucleation rate, and nucleation delay time are estimated. Important qualitative features of homogeneous nucleation evolution along the nozzle are identified. Based on the data obtained, recommendations for the application and further development of the model are developed.

Distribution of condensation droplets in the last stage of steam turbine under small flow rate condition

The parameter variation, condensation and distribution of wet steam are very complicated when the steam turbine works under small flow rate condition. In this paper, the two-phase fluid model, the homogeneous nucleation model and the droplet growth model are combined to study the parameter variation in the last stage flow field, the condensation and distribution rule of wet steam and the interaction among them under small flow rate condition. The results show that the condensation location of wet steam, the number and size of droplets are influenced greatly by the location of vortex and the parameters of flow field. The droplet is mainly distributed on the side of pressure surface and the downstream of trailing edge of rotor blade. And the distribution of droplet corresponds to the distribution of the vortex. At 5%THA condition, the flow angle fluctuates violently, and the velocity triangle presents a distribution of “X“ shape. Besides, the vortex at corresponding locations is obvious, which corresponds to the distribution of droplets. The larger the droplet number, the larger the droplet size is.