Temperature Dependence of the Evaporation Coefficient of Water in Air and Nitrogen under Atmospheric Pressure: Study in Water Droplets

Shining New Light on the Kinetics of Water Uptake by Organic Aerosol Particles

The uptake of water vapor by various organic aerosols is important in a number of applications ranging from medical delivery of pharmaceutical aerosols to cloud formation in the atmosphere. The coefficient that describes the probability that the impinging gas-phase molecule sticks to the surface of interest is called the mass accommodation coefficient, α_M. Despite the importance of this coefficient for the description of water uptake kinetics, accurate values are still lacking for many systems. In this Feature Article, we present various experimental techniques that have been evoked in the literature to study the interfacial transport of water and discuss the corresponding strengths and limitations. This includes our recently developed technique called photothermal single-particle spectroscopy (PSPS). The PSPS technique allows for a retrieval of α_M values from three independent, yet simultaneous measurements operating close to equilibrium, providing a robust assessment of interfacial mass transport. We review the currently available data for α_M for water on various organics and discuss the few studies that address the temperature and relative humidity dependence of α_M for water on organics. The knowledge of the latter, for example, is crucial to assess the water uptake kinetics of organic aerosols in the Earth's atmosphere. Finally, we argue that PSPS might also be a viable method to better restrict the α_M value for water on liquid water.

A purely kinetic description of the evaporation of water droplets

The process of water evaporation, although deeply studied, does not enjoy a kinetic description that captures known physics and can be integrated with other detailed processes such as drying of catalytic membranes embedded in vapor-fed devices and chemical reactions in aerosol whose volumes are changing dynamically. In this work, we present a simple, three-step kinetic model for water evaporation that is based on theory and validated by using well-established thermodynamic models of droplet size as a function of time, temperature, and relative humidity as well as data from time-resolved measurements of evaporating droplet size. The kinetic mechanism for evaporation is a combination of two limiting processes occurring in the highly dynamic liquid-vapor interfacial region: direct first order desorption of a single water molecule and desorption resulting from a local fluctuation, described using third order kinetics. The model reproduces data over a range of relative humidities and temperatures only if the interface that separates bulk water from gas phase water has a finite width, consistent with previous experimental and theoretical studies. The influence of droplet cooling during rapid evaporation on the kinetics is discussed; discrepancies between the various models point to the need for additional experimental data to identify their origin.

Assessing relative humidity dependent photoacoustics to retrieve mass accommodation coefficients of single optically trapped aerosol particles

Photoacoustic spectroscopy is a standout technique widely used for absorption measurements of atmospheric aerosols. Here we investigate the relative humidity dependence of photoacoustics and its implication for evaporation kinetics.

The evaporation kinetics of pure water droplets at varying drying rates and the use of evaporation rates to infer the gas phase relative humidity

Numerous analytical models have been applied to describe the evaporation/condensation kinetics of volatile components from aerosol particles for use in many applications. However, the applicability of these models for treating cases that lead to substantial and rapid changes in particle temperature due to, for example, evaporative cooling remain to be compared with measurements. We consider three typical treatments, comparing predictions of the evaporation rates of pure water droplets over a wide range in gas phase relative humidity (RH) and exploring the sensitivity of the predictions to uncertainties in the thermophysical gas and condensed-phase parameters. We also compare predictions from the three treatments to measurements of the evaporation rates of pure water droplets with varying RH using an electrodynamic balance (EDB), concluding that only two of the model treatments are sufficiently able to account for the level of evaporative cooling (typically as high as 12 K). Finally, we show that the RH can be inferred accurately from the evaporation rate of pure water droplets over the full range in accessible RH and comparison with the model predictions (within absolute uncertainties of 2.5% RH over the range 20% to 95% RH), considering the level of agreement with independent measurements made through determining the equilibrated size of aqueous sodium chloride and sodium nitrate droplets.

Molecular Mechanism of Water Evaporation

Evaporation is the process by which water changes from a liquid to a gas or vapor, and is a key step in Earth's water cycle. At the molecular level, evaporation requires breaking at least one very strong intermolecular bond between two water molecules at the interface. Despite the importance of this process the molecular mechanism by which an evaporating water molecule gains sufficient energy to escape from the surface has remained elusive. Here, we show, using molecular dynamics simulations at the water-air interface with polarizable classical force field models, that the high kinetic energy of the evaporated water molecule is enabled by a well-timed making and breaking of hydrogen bonds involving at least three water molecules at the interface, the recoil of which allows one of the molecules to escape. The evaporation of water is thus enabled by concerted, ultrafast hydrogen-bond dynamics of interfacial water, and follows one specific molecular pathway.

A molecular dynamics test of the Hertz-Knudsen equation for evaporating liquids

The precise determination of evaporation flux from liquid surfaces gives control over evaporation-driven self-assembly in soft matter systems. The Hertz-Knudsen (HK) equation is commonly used to predict evaporation flux. This equation states that the flux is proportional to the difference between the pressure in the system and the equilibrium pressure for liquid/vapor coexistence. We applied molecular dynamics (MD) simulations of one component Lennard-Jones (LJ) fluid to test the HK equation for a wide range of thermodynamic parameters covering more than one order of magnitude in the values of flux. The flux determined in the simulations was 3.6 times larger than that computed from the HK equation. However, the flux was constant over time while the pressures in the HK equation exhibited strong fluctuations during simulations. This observation suggests that the HK equation may not appropriately grasp the physical mechanism of evaporation. We discuss this issue in the context of momentum flux during evaporation and mechanical equilibrium in this process. Most probably the process of evaporation is driven by a tiny difference between the liquid pressure and the gas pressure. This difference is equal to the momentum flux i.e. momentum carried by the molecules leaving the surface of the liquid during evaporation. The average velocity in the evaporation flux is very small (two to three orders of magnitude smaller than the typical velocity of LJ atoms). Therefore the distribution of velocities of LJ atoms does not deviate from the Maxwell-Boltzmann distribution, even in the interfacial region.

Nonequilibrium kinetic boundary condition at the vapor-liquid interface of argon

A boundary condition for the Boltzmann equation (kinetic boundary condition, KBC) at the vapor-liquid interface of argon is constructed with the help of molecular dynamics (MD) simulations. The KBC is examined at a constant liquid temperature of 85 K in a wide range of nonequilibrium states of vapor. The present investigation is an extension of a previous one by Ishiyama, Yano, and Fujikawa [Phys. Rev. Lett. 95, 084504 (2005)] and provides a more complete form of the KBC. The present KBC includes a thermal accommodation coefficient in addition to evaporation and condensation coefficients, and these coefficients are determined in MD simulations uniquely. The thermal accommodation coefficient shows an anisotropic behavior at the interface for molecular velocities normal versus tangential to the interface. It is also found that the evaporation and condensation coefficients are almost constant in a fairly wide range of nonequilibrium states. The thermal accommodation coefficient of the normal velocity component is almost unity, while that of the tangential component shows a decreasing function of the density of vapor incident on the interface, indicating that the tangential velocity distribution of molecules leaving the interface into the vapor phase may deviate from the tangential parts of the Maxwell velocity distribution at the liquid temperature. A mechanism for the deviation of the KBC from the isotropic Maxwell KBC at the liquid temperature is discussed in terms of anisotropic energy relaxation at the interface. The liquid-temperature dependence of the present KBC is also discussed.

Evaporation of freely suspended single droplets: experimental, theoretical and computational simulations

Evaporation is ubiquitous in nature. This process influences the climate, the formation of clouds, transpiration in plants, the survival of arctic organisms, the efficiency of car engines, the structure of dried materials and many other phenomena. Recent experiments discovered two novel mechanisms accompanying evaporation: temperature discontinuity at the liquid-vapour interface during evaporation and equilibration of pressures in the whole system during evaporation. None of these effects has been predicted previously by existing theories despite the fact that after 130 years of investigation the theory of evaporation was believed to be mature. These two effects call for reanalysis of existing experimental data and such is the goal of this review. In this article we analyse the experimental and the computational simulation data on the droplet evaporation of several different systems: water into its own vapour, water into the air, diethylene glycol into nitrogen and argon into its own vapour. We show that the temperature discontinuity at the liquid-vapour interface discovered by Fang and Ward (1999 Phys. Rev. E 59 417-28) is a rule rather than an exception. We show in computer simulations for a single-component system (argon) that this discontinuity is due to the constraint of momentum/pressure equilibrium during evaporation. For high vapour pressure the temperature is continuous across the liquid-vapour interface, while for small vapour pressures the temperature is discontinuous. The temperature jump at the interface is inversely proportional to the vapour density close to the interface. We have also found that all analysed data are described by the following equation: da/dt = P(1)/(a + P(2)), where a is the radius of the evaporating droplet, t is time and P(1) and P(2) are two parameters. P(1) = -λΔT/(q(eff)ρ(L)), where λ is the thermal conductivity coefficient in the vapour at the interface, ΔT is the temperature difference between the liquid droplet and the vapour far from the interface, q(eff) is the enthalpy of evaporation per unit mass and ρ(L) is the liquid density. The P(2) parameter is the kinetic correction proportional to the evaporation coefficient. P(2) = 0 only in the absence of temperature discontinuity at the interface. We discuss various models and problems in the determination of the evaporation coefficient and discuss evaporation scenarios in the case of single- and multi-component systems.

Bulk, surface, and gas-phase limited water transport in aerosol

The influence of solute species on mass transfer to and from aqueous aerosol droplets is investigated using an electrodynamic balance coupled with light scattering techniques. In particular, we explore the limitations imposed on water evaporation by slow bulk phase diffusion and by the formation of surface organic films. Measurements of evaporation from ionic salt solutions, specifically sodium chloride and ammonium sulfate, are compared with predictions from an analytical model framework, highlighting the uncertainties associated with quantifying gas diffusional transport. The influence of low solubility organic acids on mass transfer is reported and compared to both model predictions and previous work. The limiting value of the evaporation coefficient that can be resolved by this approach, when uncertainties in key thermophysical quantities are accounted for, is estimated. The limitation of slow bulk phase diffusion on the evaporation rate is investigated for gel and glass states formed during the evaporation of magnesium sulfate and sucrose droplets, respectively. Finally, the effect of surfactants on evaporation has been probed, with soluble surfactants (such as sodium dodecyl sulfate) leading to little or no retardation of evaporation through slowing of surface layer kinetics.

Comparison of approaches for measuring the mass accommodation coefficient for the condensation of water and sensitivities to uncertainties in thermophysical properties

We compare and contrast measurements of the mass accommodation coefficient of water on a water surface made using ensemble and single particle techniques under conditions of supersaturation and subsaturation, respectively. In particular, we consider measurements made using an expansion chamber, a continuous flow streamwise thermal gradient cloud condensation nuclei chamber, the Leipzig Aerosol Cloud Interaction Simulator, aerosol optical tweezers, and electrodynamic balances. Although this assessment is not intended to be comprehensive, these five techniques are complementary in their approach and give values that span the range from near 0.1 to 1.0 for the mass accommodation coefficient. We use the same semianalytical treatment to assess the sensitivities of the measurements made by the various techniques to thermophysical quantities (diffusion constants, thermal conductivities, saturation pressure of water, latent heat, and solution density) and experimental parameters (saturation value and temperature). This represents the first effort to assess and compare measurements made by different techniques to attempt to reduce the uncertainty in the value of the mass accommodation coefficient. Broadly, we show that the measurements are consistent within the uncertainties inherent to the thermophysical and experimental parameters and that the value of the mass accommodation coefficient should be considered to be larger than 0.5. Accurate control and measurement of the saturation ratio is shown to be critical for a successful investigation of the surface transport kinetics during condensation/evaporation. This invariably requires accurate knowledge of the partial pressure of water, the system temperature, the droplet curvature and the saturation pressure of water. Further, the importance of including and quantifying the transport of heat in interpreting droplet measurements is highlighted; the particular issues associated with interpreting measurements of condensation/evaporation rates with varying pressure are discussed, measurements that are important for resolving the relative importance of gas diffusional transport and surface kinetics.

Measurements of mass and heat transfer at a liquid water surface during condensation or evaporation of a subnanometer thickness layer of water

A novel approach for exploring the molecular dynamics during condensation or evaporation at a liquid water surface is reported at pressures between 2 and 100 kPa. By introducing or removing a heating laser illuminating an optically tweezed aqueous aerosol droplet, the temperature of the droplet can be controlled with sub-mK accuracy and the change in size to reequilibrate with the surroundings monitored with subnanometer accuracy. The time constant for equilibration is shown to provide important insight into the coupling of heat and mass transfer during condensation or evaporation.

Coefficients of evaporation and gas phase diffusion of low-volatility organic solvents in nitrogen from interferometric study of evaporating droplets

Evaporation of motionless, levitating droplets of pure, low-volatility liquids was studied with interferometric methods. Experiments were conducted on charged droplets in the electrodynamic trap in nitrogen at atmospheric pressure at 298 K. Mono-, di-, tri-, and tetra(ethylene glycols) and 1,3-dimethyl-2-imidazolidinone were studied. The influence of minute impurities (<0.1%) upon the process of droplet evaporation was observed and discussed. The gas phase diffusion and evaporation coefficients were found from droplet radii evolution under the assumption of known vapor pressure. Diffusion coefficients were compared with independent measurements and calculations (in air). Good agreement was found for mono- and di(ethylene glycols), and for 1,3-dimethyl-2-imidazolidinone, which confirmed the used vapor pressure values. The value of equilibrium vapor pressure for tri(ethylene glycol) was proposed to be 0.044 +/- 0.008 Pa. The evaporation coefficient was found to increase from 0.035 to 0.16 versus the molecular mass of the compound.

On the evaporation of ammonium sulfate solution

Aqueous evaporation and condensation kinetics are poorly understood, and uncertainties in their rates affect predictions of cloud behavior and therefore climate. We measured the cooling rate of 3 M ammonium sulfate droplets undergoing free evaporation via Raman thermometry. Analysis of the measurements yields a value of 0.58 +/- 0.05 for the evaporation coefficient, identical to that previously determined for pure water. These results imply that subsaturated aqueous ammonium sulfate, which is the most abundant inorganic component of atmospheric aerosol, does not affect the vapor-liquid exchange mechanism for cloud droplets, despite reducing the saturation vapor pressure of water significantly.