Binary Nucleation. II. Time Lags

The role of the time lag needed to attain steady state nucleation in binary vapors is discussed. Under appropriate conditions it is possible to obtain both a large predicted rate of binary nucleation and a large time lag. In this circumstance, homogeneous nucleation of the more concentrated component may be the predominant process. It is of obvious importance to the experimentalist to differentiate between these possibilities. Approximate formulas for the time lags are developed, and representative calculations for the ethanol-water system are reported

Binary Nucleation Kinetics. IV. Directional Properties and Cluster Concentrations at the Saddle Point

Using a new approach, Stauffer\u27s expression for the rate of steady state binary nucleation and Trinkaus\u27s expression for the steady state cluster concentrations f are derived directly from the diffusion equation that governs the evolution of f in composition space. The behavior of φ (≡f/N, where N is the equilibrium cluster concentration) is explored since this function provides a characterization of the nucleating binary system that, to lowest order, is independent of the actual composition of the mother phase. The angle ω that describes the direction of ▽ φ at the saddle point differs, in general, from the angle φ found by Stauffer for the direction of the nucleation current at the saddle point. These two angles are related by the formula: tan φ=r tan ω, where r is the ratio of impingement frequencies defined by Stauffer. In general, at the saddle point, ▽ φ also fails to lie in the direction of steepest descent on the free energy surface

Neutron Scattering from Aerosols: Intraparticle Structure Factor, Guinier Analysis of Particle Speed, and Crossed Beam Kinematics

A theoretical formalism for neutron scattering from systems of particles is applied to liquid nanodroplet aerosols. A term arising from intraparticle, intermolecular correlations is identified. The kinematical theory of two body scattering is recast into a form convenient for interpreting the results of experiments with crossed beams of neutrons and aerosol particles. Based on a theoretical analysis of the scattered intensity in the Guinier region, a method for determining the particle velocity directly from the experimental data is outlined. The method is not restricted by assumptions about particle shape, composition, uniformity, or size distribution

Some Issues of Thermodynamic Consistency in Binary Nucleation Theory

The generalized Kelvin equations used to determine the critical nucleus composition in some binary nucleation theories are shown to be thermodynamically inconsistent. Also, the surface tension calculated by the method of Flageollet-Daniel, Gamier, and Mirabel [J. Chem. Phys. 78, 2600 (1983)] is shown to be thermodynamically consistent with respect to the dynamic surface tension, contrary to the recent assertion of Spiegel, Zahoransky, and Wittig

Volumes of Critical Bubbles from the Nucleation Theorem

A corollary of the nucleation theorem due to Kashchiev [Nucleation: Basic Theory with Applications (Butterworth-Heinemann, Oxford, 2000)] allows the volume V* of a critical bubble to be determined from nucleation rate measurements. The original derivation was limited to one-component, ideal gas bubbles with a vapor density much smaller than that of the ambient liquid. Here, an exact result is found for multicomponent, nonideal gas bubbles. Provided a weak density inequality holds, this result reduces to Kashchiev\u27s simple form which thus has a much broader range of applicability than originally expected. Limited applications to droplets are also mentioned, and the utility of the pT,x form of the nucleation theorem as a sum rule is note

Binary Nucleation. I. Theory Applied to Water-Ethanol Vapors

A quantitative study of nucleation in vapor mixtures of ethanol and water near 273°C is presented. First, Reiss\u27 theory of binary nucleation is reexamined. The theory is modified slightly in order to yield the proper limit for homogeneous nucleation in a one-component system. Moreover, a corrected expression for the equilibrium concentration of mixed clusters is derived. Calculations of the critical vapor activities needed to produce a visible condensate are presented and compared with the results of Flood\u27s cloud chamber experiments. The agreement is only fair, but qualitative accord is found

Nonequilibrium Thermodynamics of Fuel Cells: Heat Release Mechanisms and Voltage

Nonequilibrium thermodynamics is used to analyze the spatial distribution of heat release mechanisms occurring in fuel cells operating under load in nonisothermal steady states. Novel contributions to heat release in the bulk electrolyte are found which are analogous to Peltier and Thomson effects in metallic conductors. Expresions for the heat release at individual electrodes are presented. An equation for the voltage of these cells is also derived. © 1980 American Institute of Physics

Intrinsic Viscosity of Stiff Dumbbells from Time Correlation Functions

The intrinsic viscosity of a suspension of stiff dumbbells is evaluated by a time correlation function method. The required moments of the internal coordinates are calculated directly from the diffusion equation, without explicit evaluation of the Green\u27s function. For the rigid dumbbell, the correct high frequency limit is obtained, disposing of recent doubts over this possibility. The interplay of dumbbell stiffness and shearing frequency is also illustrated

The Kelvin Equation And Self-Consistent Nucleation Theory

Issues of self-consistency are reviewed for several unary equilibrium size distributions based on the capillarity approximation. Some apparent difficulties of interpretation are resolved. In terms of the kinetic approach to nucleation theory, the influence of self-consistency on the nucleation rate is shown to arise entirely from differences in the dimer evaporation rates for nearly all versions of classical theory. The nucleation rate behavior of the Kelvin model is explored. In this model, the Kelvin equation is used to prescribe all cluster evaporation rates. Nucleation rates predicted by the Kelvin model are quantitatively similar to those of the self-consistent classical (SCC) theory, but not to other simple versions of the classical theory. This behavior arises entirely from the relatively close coincidence of the SCC and Kelvin dimer evaporation rates. This means that, for the distribution-based versions of classical theory, the SCC model is the closest analogue of the Kelvin model. Because the Kelvin equation is fundamentally inadequate for very small clusters, the close relationship between the Kelvin and SCC formulations indicates that both are equally lacking in fundamental justification. The Kelvin model may, however, have some pragmatic utility, and a simple analytical rate expression is also derived for it to simplify the calculation of nucleation rates for this model