The evaporation/condensation transition of liquid droplets

The condensation of a supersaturated vapor enclosed in a finite system is considered. A phenomenological analysis reveals that the vapor is found to be stable at densities well above coexistence. The system size at which the supersaturated vapor condenses into a droplet is found to be governed by a typical length scale which depends on the coexistence densities, temperature and surface tension. When fluctuations are neglected, the chemical potential is seen to show a discontinuity at an effective spinodal point, where the inhomogeneous state becomes more stable than the homogeneous state. If fluctuations are taken into account, the transition is rounded, but the slope of the chemical potential versus density isotherm develops a discontinuity in the thermodynamic limit. In order to test the theoretical predictions, we perform a simulation study of droplet condensation for a Lennard-Jones fluid and obtain loops in the chemical potential versus density and pressure. By computing probability distributions for the cluster size, chemical potential, and internal energy, we confirm that the effective spinodal point may be identified with the occurrence of a first order phase transition, resulting in the condensation of a droplet. An accurate equation of state is employed in order to estimate the droplet size and the coexisting vapor density and good quantitative agreement with the simulation data is obtained. The results highlight the need of an accurate equation of state data for the Laplace equation to have predictive power.     

Isotope fractionation of water during evaporation without condensation

The microscopic events engendering liquid water evaporation have received much attention over the last century, but remain incompletely understood. We present measurements of isotope fractionation occurring during free molecular evaporation from liquid microjets and show that the isotope ratios of evaporating molecules exhibit dramatic differences from equilibrium vapor values, strong variations with the solution deuterium mole fraction, and a clear temperature dependence. These results indicate the existence of an energetic barrier to evaporation and that the evaporation coefficient of water is less than unity. These new insights into water evaporation promise to advance our understanding of the processes that control the formation and lifetime of clouds in the atmosphere.     

Competing evaporation and condensation processes during the boiling of methane

The atomistic mechanism of the boiling of methane is explored from molecular dynamics simulations. The liquid --> vapor transition is initiated by local density fluctuations resulting in a nanometer-sized domain that exhibits both liquid and vapor characteristics. Though the rates of evaporation and condensation events increase dramatically in this area, the overall balance exhibits only a marginal net rate of evaporation. Growth of the precritical domain leads to the nucleation of a vapor phase in which isolated methane molecules are confined by a liquid-vapor interface. After crossing the transition state, the system experiences progressive destabilization of the liquid phase and the evaporation processes clearly outnumber the condensation events.     

Statistical theory of evaporation and condensation processes in liquid droplets

The process of evaporation of liquid droplets is described by the nonequilibrium statistical operator method. A microscopic expression for the evaporation coefficient is derived; it considers the influence of several factors (presence of ions, external fields, ultraviolet irradiation, etc.) on the evaporation process. Algorithms for determining the steady-state evaporation rate under various conditions are found. Original Russian Text ? V.V. Ryazanov, 2006, published in Kolloidnyi Zhurnal, 2006, Vol. 68, No. 2, pp. 243–254.     

Correlation between the rates of benzylidene condensation of R-tetrazol-1-ylphenylamines and their dissociation constants

Benzylidene condensation of R-tetrazol-1-ylphenylamines with 4-fluorobenzaldehyde was studied. The correlation between the logarithm of the rate constant of the condensation of 4-fluorobenzaldehyde with R-tetrazol-1-ylphenylamines and their pK _BH+ values was found. The reaction constant ρ in the Hammett equation was determined.     

Electrical processes upon the evaporation and condensation of water and ice

A mathematical model of electrical processes that take place upon the evaporation of water and sublimation of ice, as well as the condensation growth of water and ice phases from vapor, is proposed. The transfer of the main charge carriers, such as (i) protons and hydroxide ions (in ice, water, and vapor and (ii) orientational defects (in ice and water) is taken into account. Upon the evaporation of water and the sublimation of ice, the first carriers are accumulated before the phase front and cause positive charges in the surface of the water and ice, while the second carriers are depleted (their concentration becomes lower than the thermodynamic value) and impart a negative charge to water and ice. The contribution of protons and hydroxide ions dominates at a low rate of evaporation. In the condensation of vapor and relevant growth of water and ice phases, the polarity of surface charge is opposite to that observed upon evaporation. The values of interfacial current and signs of phase charges upon sublimation, evaporation, and condensation that are predicted in the model comply with experimental data.     

Laser evaporation and condensation of Er in hydrogen and inert atmosphere

Er, condensing under Ar at room temperature after exposure to laser pulses, forms with particle sizes of approximately 1.25 × 10^?8 to 5.0 × 10^?8 m. When this process is carried out under hydrogen atmosphere the dihydride is formed.     

Nature of capillary condensation and evaporation processes in ordered porous materials

We report on a detailed experimental study of capillary condensation-evaporation processes of N(2) in ordered mesoporous SBA-15 silica. We have carried out measurements of boundary hysteresis loops, reversal curves, and subloops in order to test whether this material behaves as an assembly of independent cylindrical pores open at both ends. With these data, we come to the conclusion that, whereas the boundary hysteresis loop has the classical shape of type H1 associated with condensation-evaporation in cylindrical pores open at both ends, the capillary evaporation does not take place at equilibrium as it is generally assumed. Moreover, the pores do not desorb independently of one another.     

Kinetic simulation of the oxidative condensation of methane

The kinetics of the oxidative condensation of methane (OCM) over a mixed-oxide lithium-manganese-tungsten-silicate catalyst has been simulated, and systems of stoichiometric chemical equations possible under the OCM conditions have thereby been discriminated. A phenomenological kinetic model has been developed to fit the observed rates of formation and disappearance of the compounds involved in OCM.     

Multi-Monte Carlo method for coagulation and condensation/evaporation in dispersed systems

A new multi-Monte Carlo (MMC) method is promoted to consider general dynamic equation (GDE) for particle coagulation and condensation/evaporation. MMC method introduces the concept of a "weighted fictitious particle" and is based on time-driven Monte Carlo technique, constant number of fictitious particles technique, and constant volume technique. MMC method for independent coagulation, for independent condensation/evaporation, and for simultaneous coagulation and condensation/evaporation are validated by some special cases in which analytical solutions exist, in which numerical results agree with corresponding analytical solutions well. Furthermore, the computation cost of MMC method is low enough to be applied in engineering computation and general scientific quantitative analysis.     

Kinetic energy release during evaporation from large sodium clusters

We have measured the distribution of momenta of atoms evaporating from large sodium clusters produced in a supersonic expansion source. The distributions are well described by phase space theory when polarization effects are included in the atomic capture cross section. Alternatively, the data can be fitted by a simple powerlaw preexponential. The cluster temperature extracted from both models differ, but still agree reasonable well with evaporative ensemble predictions. The data rule out a non-trivial transition state.     

Molecular dynamics study on evaporation and condensation of n-dodecane at liquid-vapor phase equilibria

Molecular dynamics simulations are performed to study the evaporation and condensation of n-dodecane (C(12)H(26)) at temperatures in the range 400-600 K. A modified optimized potential for liquid simulation model is applied to take into account the Lennard-Jones, bond bending and torsion potentials with the bond length constrained. The equilibrium liquid-vapor n-dodecane interface thickness is predicted to be ~1.2-2.0 nm. It is shown that the molecular chains lie preferentially parallel to the interface in the liquid-vapor transition region. The predicted evaporation/condensation coefficient decreased from 0.9 to 0.3 when temperature increased from 400 to 600 K. These values can be used for the formulation of boundary conditions in the kinetic modeling of droplet heating and evaporation processes; they are noticeably different from those predicted by the transition state theory. We also present the typical molecular behaviors in the evaporation and condensation processes. The molecular exchange in condensation, typical for simple molecules, has never been observed for n-dodecane molecular chains.     

Layering, condensation, and evaporation of short chains in narrow slit pores

The phase behavior of short-chain fluids in slit pores is investigated by using a nonlocal-density-functional theory that takes into account the effects of segment size, chain connectivity, and van der Waals attractions explicitly. The layering and capillary condensation/evaporation transitions are examined at different chain length, temperature, pore width, and surface energy. It is found that longer chains are more likely to show hysteresis loops and multilayer adsorptions along with the capillary condensation and evaporation. Decreasing temperature favors the inclusion of layering transitions into the condensation/evaporation hysteresis loops. For large pores, the surface energy has relatively small effect on the pressures of the capillary condensation and evaporation but affects significantly on the layering pressures. It is also observed that all phase transitions within the pore take place at pressures lower than the corresponding bulk saturation pressure. The critical temperature of condensation/evaporation is always smaller than that of the bulk fluid. All coexistence curves for confined phase transitions are contained within the corresponding bulk vapor-liquid coexistence curve. As in the bulk phase, the longer the chain length, the higher are the critical temperatures of phase transitions in the pore.     

Nucleation rates for the condensation of monovalent metals

We show that consideration of both cluster growth and magic numbers are necessary to accurately calculate nucleation rates for the condensation of alkali and coinage metal vapors. The effects are not additive. Rates calculated using the modified theory differ up to several orders of magnitude from typical classical calculations. Calculated rates compare favorably with experimental nucleation onset and rate data for lithium, sodium, cesium, and silver. Verifiable predictions are made for the other alkali and coinage metals.     

Verification of Onsager's reciprocal relations for evaporation and condensation using non-equilibrium molecular dynamics

Non-equilibrium molecular dynamic (NEMD) simulations have been used to study heat and mass transfer across a vapor-liquid interface for a one-component system using a Lennard-Jones spline potential. It was confirmed that the relation between the surface tension and the surface temperature in the non-equilibrium system was the same as in equilibrium (local equilibrium). Interfacial transfer coefficients were evaluated for the surface, which expressed the heat and mass fluxes in temperature and chemical potential differences across the interfacial region (film). In this analysis it was assumed that the Onsager reciprocal relations were valid. In this paper we extend the number of simulations such that we can calculate all four interface film transfer coefficients along the whole liquid-vapor coexistence curve. We do this analysis both for the case where we use the measurable heat flux on the vapor side and for the case where we use the measurable heat flux on the liquid side. The most important result we found is that the coupling coefficients within the accuracy of the calculation are equal. This is the first verification of the validity of the Onsager relations for transport through a surface using molecular dynamics. The interfacial film transfer coefficients are found to be a function of the surface temperature alone. New expressions are given for the kinetic theory values of these coefficients which only depend on the surface temperature. The NEMD values were found to be in good agreement with these expressions.     

A critical assessment of capillary condensation and evaporation equations: a computer simulation study

Nonaqueous reverse micelles of brij surfactants are prepared in benzene and ethylammonium nitrate (EAN). The effect of polar head group bulk on reverse micellar size was studied with brij-52, brij-56 and brij-58 whereas the effect of polarity of hydrocarbon chain was investigated taking brij-52 and brij-93 with varying W(s) (W(s)=[EAN]/[surfactant]). Dynamic light scattering (DLS) has been employed to reveal the size and shape of the reverse micelles. Micropolarities of these reverse micelles were investigated by visible spectroscopy using methylene blue (MB) and methyl orange (MO) as molecular optical probes. It has been revealed from the experimental results that with increase in polar head group size reverse micellar size increases. Moreover, it is also observed that with increasing polarity of the hydrocarbon chain the average size of the reverse micelles decreases. It can be concluded that polar head group size and polarity of hydrocarbon chain play important roles in determining reverse micellar size of the brij surfactants apart from the W(s) ratio, nature of the solvent medium, and concentration of the surfactants.     

From chains to rings, and back again: structural rearrangements during evaporation and condensation

The mechanistic details of the sequence of structural changes that occur in weakly bound molecular complexes upon change in phase have yet to be presented in detail. Consider the structural rearrangements that occur at the interface between the liquid and its vapor for species such as hydrofluoric acid or the low molecular weight aliphatic acids. There are both experimental and theoretical evidence that liquid HF consists of extended zig-zag chains [1], whereas the vapor consists predominantly of non-planar cyclic structures [2]. Similarly, the cyclic structures of gaseous aliphatic acid dimers was established decades ago but in the solid and liquid phases, the molecular configurations are zig-zag chains [3].     

Kinetic spectrophotometric determination of thiobenzamides and their partition coefficients in water/1-octanol by using an iodine/azide indicator reaction

The kinetic method is based on catalysis, by thiobenzamide and/or its derivatives, of the oxidation of azide by iodine at 25°C in 0.1 M acetate buffer (pH 4.7) containing iodate, iodide and azide. Thiobenzamide and its 4-methoxy-, 4-methyl-, 4-chloro- and 4-nitro derivatives (0.5–3 μM) are determined by measuring the decrease in the absorbance of iodine at 350 nm at a fixed time (2 min). The detection limits are 0.05–0.1 μM and the relative standard deviations are <2%. The proposed method is used to determine the partition coefficients of thiobenzamide and its derivatives in water/1-octanol; the equilibrated aqueous phase was analysed.     

Experimental investigation of contact angle, curvature, and contact line motion in dropwise condensation and evaporation

Image-analyzing interferometry is used to measure the apparent contact angle and the curvature of a drop and a meniscus during condensation and evaporation processes in a constrained vapor bubble (CVB) cell. The apparent contact angle is found to be a function of the interfacial mass flux. The interfacial velocity for the drop during condensation and evaporation is a function of the apparent contact angle and the rate of change of radius of curvature. The dependence of velocity on the apparent contact angle is consistent with Tanner's scaling equation. The results support the hypothesis that evaporation/condensation is an important factor in contact line motion. The main purpose of this article is to present the experimental technique and the data. The equilibrium contact angle for the drop is found experimentally to be higher than that for the corner meniscus. The contact angle is a function of the stress field in the fluid. The equilibrium contact angle is related to the thickness of the thin adsorbed film in the microscopic region and depends on the characteristics of the microscopic region. The excess interfacial free energy and temperature jump were used to calculate the equilibrium thickness of the thin adsorbed film in the microscopic region.