Bulk, Surface, and Gas-Phase Limited Water Transport in Aerosol

Oct 24, 2012 - *E-mail: [email protected]. ... In particular, we explore the limitations imposed on water evaporation by slow bulk phase diffusio...
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Bulk, Surface, and Gas-Phase Limited Water Transport in Aerosol James F. Davies, Allen E. Haddrell, Rachael E. H. Miles, Craig R. Bull, and Jonathan P. Reid* School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, U.K. ABSTRACT: 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.

1. INTRODUCTION The rate of mass transfer to and from aerosol droplets plays a key role across all aspects of aerosol science. In the atmosphere, growth rates of droplets influence cloud formation and lifetime,1,2 directly impacting our ability to understand and predict the indirect effect of aerosol on climate. In medicine, aerosols used in drug delivery undergo rapid changes in conditions during generation and inhalation, with droplets undergoing significant changes in size.3 Industrial processes, such as spray drying4 and fuel combustion,5 are dominated by evaporation processes and a full understanding of both mass and heat transfer is important to ensure maximum efficiency. The mass transport of water to and from aerosol droplets is influenced by the gas phase composition and surface water activity, the bulk solution viscosity and the kinetics of transport through the surface region.6 More specifically, the presence of a dissolved species in an aqueous droplet will change the water activity at the droplet surface and, thus, the vapor pressure of water immediately above the surface.7 The difference between this vapor pressure of water and the gas phase partial pressure defines the concentration gradient along which the diffusive mass flux occurs, controlling the rate of gas-phase diffusion and the mass flux driving evaporation or condensation. Additionally, the flux of mass to or from a droplet requires the removal of latent heat from, or supply to, the droplet surface through conduction and convection of heat within the surrounding gas phase. If the gas phase is unable to transport the necessary heat flux, the droplet surface temperature changes: evaporation frequently leads to a droplet temperature that is suppressed below that of the surrounding gas phase, and condensation leads to a droplet temperature that is elevated. Associated with © 2012 American Chemical Society

the change in temperature will be a change in the saturation vapor pressure of water at the surface. This decreases the mass flux and lowers the thermal flux imbalance, with the heat flux to and from the droplet in balance. The coupling of heat and mass transfer is therefore of great importance in understanding evaporation and condensation processes. For water droplet sizes that are large compared with the mean free path of molecules in the surrounding gas phase, typically particles larger than ∼0.5 μm at 100 kPa (Knudsen number, Kn ≈ 0.1), the rate of evaporation or condensation is largely governed by the rate of diffusion or thermal conduction in the gas phase. This is referred to as the continuum regime. However, two limiting cases can be conceived for which transport in the gas phase is not the rate-determining process, even for such large particles. First, evaporation or condensation may be limited by the slow diffusion of water within the bulk of a particle, establishing significant concentration gradients that limit the resulting flux of water to or from the particle.8 Second, it has been suggested that the presence of surface active organic films may impede the kinetics of water transport through the surface layer, lowering what is referred to as the evaporation coefficient or mass accommodation coefficient.9 (The mass and evaporation coefficients are assumed equal by the laws of microscopic reversibility and for the purposes of this paper are used interchangeably). In this paper, we present complementary examples of water evaporation from aerosol droplets in which the evaporation rate is controlled by gas diffusion or slow Received: August 31, 2012 Revised: October 24, 2012 Published: October 24, 2012 10987

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Table 1. List of the Species Used in This Study along with Selected Properties, Including Density and Solubility

interface even for particles up to 100s μm in radius.18−21 Shulman et al. reported significant changes in evaporation rate for a number of solute systems (ammonium sulfate, oxalic acid, adipic acid, cis-pinonic acid and sodium dodecyl sulfate), suggesting surface active species were restricting exchange at the surface as the solute concentration increased. In particular, the authors reported that SDS at an initial concentration of 0.00993 M in a water droplet caused a decrease in the evaporation rate of the particle by a factor of 10. We shall consider these systems further here. A recently developed implementation of the electrodynamic balance (EDB) is utilized in this study as a means of confining droplets with well-defined initial conditions. By defining the initial particle composition and size, we are able to calculate the droplet composition at any point during the evaporative process purely from its size alone. In the following sections, we present mass transport data from a series of eight aqueous solute systems. First, to demonstrate the validity of certain assumptions used in our work, we have studied evaporation from simple salt solutions, sodium chloride, and ammonium sulfate, comparing our data to theoretical simulations. Following from these salt solutions, we have looked at a number of organic acids in order to observe how species of decreasing solubility affect evaporation when highly supersaturated states are reached. We present data for water evaporation from sucrose droplets into variable RH conditions and report measurements of uptake and loss of water in levitated droplets of MgSO4, resolving the time dependence of size changes due to changes in RH. Finally, the effect of

bulk diffusion, and assess the impact and sensitivity of surface kinetic limitations. In a number of solute systems it has been reported that the formation of amorphous and glassy states in the bulk of an aerosol particle can result in significant changes in the transport of water, oxidants, or volatile components between the gas and condensed phases, correlated with an increase in the viscosity of the particle bulk or a reduction in diffusion constants.10−12 Sucrose, for example, has been shown to form a highly viscous solution droplet or even a glassy state on drying resulting in impeded growth and evaporation due to slow diffusion of water in the bulk phase.10,13 The formation of a glass has been reported for inorganic aerosol species too, such as droplets containing iodate species at low relative humidity (RH), again slowing the rate of water transport.14 Glasses are not the only amorphous state that may form; two-phase gels may also develop, such as in magnesium sulfate.11 Formation of an inorganic network of contact ion pairs results in impeded water diffusion as molecules must travel along limited channels and pores in the gel structure.15 A Raman microscope was used by Li et al.11 to probe the time scales of water transport in the gel phase by studying the rate of exchange of D2O by H2O. In this publication, we further investigate the slow transport of water in sucrose and magnesium sulfate droplets at low RHs. Although surface kinetics15−17 are not expected to influence mass transport to a significant degree for the droplet sizes, aqueous systems, and conditions considered in this study, it has been suggested that surface active species may have a significant effect on the rate of mass transport across the gas/liquid 10988

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water activity treatment for sodium chloride and ammonium sulfate31,32 and a UNIFAC parametrization for organic species, implemented using the Aerosol Diameter Dependent Equilibrium Model (ADDEM).33,34 Values for the diffusion coefficients and thermal conductivities of water vapor and nitrogen gas and their associated uncertainties were taken from the recommendations of Miles et al.35 and are only summarized here. The parametrizations of Lemmon et al.36 and Sengers et al.37 were used to determine the thermal conductivity of nitrogen and water vapor, respectively, both with an associated uncertainty of ±2%. The diffusion coefficient of water in nitrogen was calculated according to a parametrization based on the work of Massman38 and combined with the diffusion coefficient of water in water35 using Blanc’s Law. The binary diffusion coefficient suffers an uncertainty of ±6%.35 The temperature, gas flow velocity, and gas phase humidity were set according to each experiment and are discussed in more detail in the relevant sections.

surfactant species is investigated, utilizing SDS to elucidate the effect of soluble ionic surfactants on evaporation.

2. EXPERIMENTAL DESCRIPTION The experimental setup used in this study is based on the cylindrical EDB of Heinisch23 and has been described by us previously.24 Briefly, the application of AC and DC voltages to the inner cylindrical electrodes of the trap creates an electric potential in which a droplet with net charge is confined at the center. Droplets were introduced into the chamber with a MicroFab MJ-APB-01 microdispenser, and a small charge was imparted upon them by the presence of an induction electrode. The droplet charge was found to be 20−50 fC based on measurements using an electrometer and Faraday cup.25 Once a droplet was held, it was illuminated by laser light of wavelength 532 nm, and the elastic scattering pattern was imaged on a CCD at 100 Hz. The scattering pattern was used with both Mie theory and a geometrical optics approximation26 to obtain the radius of the droplet with an accuracy of ±200 nm. Measurements using full Mie theory simulations demonstrate a precision of around 5 nm, while those using the geometrical optics approximation have a precision of around 150 nm, due in part to optical resonances that are not accounted for in the calculations. Data were collected and processed as described in our previous work, with data from rapid evaporation measurements (10 droplets in all cases.24 The key benefit of using the cylindrical EDB comes from the ability to generate droplets of known concentration and confine them within ∼100 ms of creation, allowing initial conditions to be well-defined. Repeat measurements are facile due to the automated droplet-on-demand procedures employed, allowing large data sets to be collected and averaged. The use of the lower cylindrical electrode as a gas inlet allows the conditions to which a confined droplet is exposed to be controlled, maintained, and changed at a rapid rate by application of a low velocity (∼6 cm s−1) nitrogen jet. The exponential halftime for a change in droplet size due to a change in RH was measured using a confined lithium chloride solution droplet and found to be 20−30 s, providing a measure of the time scale required for the gas phase conditions to be changed. A list of all species studied can be found in Table 1 along with selected bulk properties. A gas flow consisting of nitrogen gas from a cylinder (BOC) was humidified, combined with dry nitrogen to obtain the desired humidity, and introduced into the EDB chamber. The mass flux equations of Kulmala et al.27 were used to simulate the experimental data based on mass transfer being controlled by gas phase diffusion, with transition corrections estimated according to the Fuchs-Suttugin treatment. The model accounts for the depression in droplet temperature due to removal of latent heat, as described by Miles et al.,17 to a limit of around 3 K.27 For larger changes in temperature, the calculated mass flux begins to deviate from more accurate numerical simulations, resulting in an underestimate of the rate during evaporation. The mass accommodation coefficient,6,28−30 the subject of much debate in the literature, is set at 1 for all simulations discussed here unless explicitly stated otherwise, and its impact on our measurements is discussed. Under atmospheric pressure, and for the droplet sizes investigated here, the sensitivity of the evaporation rate (μm2 s−1) to an order of magnitude reduction in the mass accommodation coefficient, from 1.0 to 0.1, is just 2%. The water activity at the droplet surface was found using the Clegg

3. RESULTS AND DISCUSSION We describe measurements of the evaporation kinetics of aqueous droplets with various inorganic and organic solutes, beginning with the simple salts sodium chloride and ammonium sulfate. 3.1. Evaporation of Droplets of Aqueous Solutions of Simple Salts. Knowledge of the initial solute concentration of a droplet when first captured by the EDB is based on two assumptions. Generally droplets become confined by the fields within 100 ms of creation, and the first assumption is that a short extrapolation in the (radius)2 profile back to t = 0 s gives us an accurate estimate of the initial size, as discussed by Davies et al.24 The second assumption is that the concentration of solute in the droplet at this estimated size for t = 0 s is equal to the solution concentration in the dispenser. We have discussed this previously and found it was necessary to apply a sequence of pulses to the dispenser in order to flush solution from the tip, which had become concentrated due to evaporation from the orifice, prior to trapping a droplet for kinetic analysis.24 From these assumptions a dry mass can be calculated and, from this, a mass (or molar) concentration and a refractive index at any size can be deduced. We have previously shown this method to be valid,24 corroborating further here. Under humid conditions, solution droplets will reach an equilibrium size with the gas phase water vapor. In order to apply our assumptions of initial conditions, droplets of ammonium sulfate (Fisher Scientific) and sodium chloride were injected into conditions of high RH (∼80%), and their approach to equilibrium was measured, shown in Figure 1a,b respectively. The equilibrium size attained by the droplet depends upon the gas phase conditions to which it was exposed and can be used to estimate the RH. First, by taking the initial droplet size and solution concentration estimated from the approach described in the previous paragraph, the mass of solute was found and an equivalent spherical dry particle radius estimated using a solid phase density of 1.77 g cm−3 for (NH4)2SO4 and 2.165 g cm−3 for NaCl. Then, the radial growth factor upon reaching equilibrium was estimated from the wet and dry particle sizes. Using the water activity treatment of Clegg for (NH4)2SO4,32 which has been shown to agree within ±0.2% to experimental data,39 and NaCl,31 the equilibrium water activity was deduced, equivalent to the gas phase RH. The value of RH inferred by this method has an absolute uncertainty of ±1% derived from the uncertainty in 10989

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ascribed by the authors to be due to a kinetic limitation imposed by high solute concentration at the surface. Our observations are not consistent with these conclusions, and our work instead supports the previous work by Drisdell et al.40 who noted no significant impact on water evaporation rate due to the presence of ammonium sulfate at a concentration of ∼3 M, equivalent to a water activity of ∼0.87. Drisdell et al. have also presented work investigating surface active ions and have seen only a small depression in the rate of water evaporation in droplets containing perchlorate ions, equivalent to a 25% decrease in the evaporation coefficient compared to pure water.18 Thus, we suggest that a mass transfer limitation imposed on water transport in ammonium sulfate aerosol at a water activity of 0.8 is unlikely given the many studies that have examined the equilibrium state of this system. Instead, the data presented by Shulman et al.19 could be interpreted as being consistent with the droplet reaching an initial equilibrium with the surrounding vapor followed by a slow drift in chamber conditions (i.e., RH) and equilibrated size. A systematic underestimation of the concentration of solute in an evaporating droplet at early time leads to an underestimation of the size that would be achieved at equilibrium; we have already highlighted in our own measurements that this is something that can lead to problems in interpreting the data if not fully accounted for.24 Thus, the droplets in the Shulman data are likely to have reached equilibrium at a size greater than expected, and a subsequent drift downward in RH resulted in the observed slow change over >10 s. Correcting such a systematic underestimation, and ensuring greater RH stability, would bring consistency between the work of Shulman et al.19 and the measurements we present here. Contrary to the case of high RH, under dry conditions droplets containing sodium chloride will efflorescence and crystallize. Efflorescence of sodium chloride droplets under dry conditions was noted at the point where the elastic scattering pattern lost the uniform fringe separation typical of a spherical droplet. By taking the size at this point, a concentration was calculated at which crystallization was observed (Figure 2). Efflorescence is not a thermodynamically controlled process,

Figure 1. (a) Evaporation of 20 g/L (0.15 M) aqueous droplets of (NH4)2SO4 in ∼80% RH. A growth factor was obtained by taking the final size and estimate of the dry size of the droplet and, using the Clegg treatment, the water activity was deduced. The white dash line shows the model simulation using this water activity. The dark gray envelope represents the uncertainty associated with the experimental parameters, and the light gray envelope indicates the uncertainty associated with the thermophysical parameters in the simulation. (b) Evaporation of 20.4 g/L (0.35 M) aqueous droplets of NaCl in ∼80% RH. The white dash line shows the simulation, with the thermophysical uncertainties represented in light gray and the experimental uncertainties in dark gray. The water activity here was determined from the Clegg treatment (see text).

the equilibrium size of the droplet. RH values estimated by this method agree within their uncertainties, with the measurements made by commercial RH probes, which can suffer uncertainties of > ± 2% under conditions of high humidity. The gas phase RH inferred from this process was used in the model treatment, and excellent agreement between simulation and experimental data was found. The other uncertainties associated with the simulations are represented in Figure 1 by the gray shaded envelopes. Shulman et al.19 discussed the possibility that surface enhancement of ammonium sulfate may impede water transport, thus causing a significant slowing in the evaporation rate prior to the droplet attaining an equilibrium state with the gas phase water concentration. The authors performed measurements in an EDB at an RH of around 80%, with a time-resolution 99.5%) behaved in a different manner, with efflorescence occurring at ∼80% RH. When evaporating into an atmosphere of RH ∼90%, an aqueous equilibrium state was obtained. The model simulation again gives good agreement; however, the uncertainty envelope is larger due to the smaller final size attained. Both the crystallization and smaller size at equilibrium are consequences of the considerably lower hygroscopicity of adipic acid when compared with oxalic acid. There are no previously reported values for the efflorescence RH of adipic acid; however, it has been noted that the deliquescence RH for adipic acid is >95%, compared to 93% for oxalic acid, demonstrating its lower water solubility.43 cis-Pinonic acid (Sigma Aldrich 98%) droplets were not observed to reach an aqueous equilibrium under any humidity conditions used. Instead, efflorescence was observed, with the concentration approaching 50 times the bulk solubility limit. For each of these compounds, Shulman et al.19 reported a considerable decrease in the evaporation rate after 8−12 s, proposing that the solute concentration at the surface had achieved such a level as to impede water transport. Our data show no indication of this, despite using almost identical

Figure 3. (a) Evaporation of 20 g/L (0.14 M) oxalic acid droplets into ∼80% RH. The white dash line shows the model simulation, and the uncertainty in RH is indicated by the gray envelope. (b) Evaporation of 8 g/L (0.055 M) adipic acid droplets into ∼80% (gray) and ∼90% (black). Model treatment is shown only for the higher humidity as equilibration was observed. (c) Evaporation of 2 g/L (0.011 M) cispinonic acid droplets into ∼80% RH. No equilibrated state was obtained even at ∼90% RH (not shown here).

conditions and initial concentrations. Instead, our observations agree with mass transport simulations in which gas phase diffusion is the limiting process and surface kinetics have little impact. One possible reason for the difference between the work presented here and that of Shulman et al. comes from the droplet creation procedure. We use a glass capillary microdispenser, inducing charge on droplets as they form from the capillary. We have previously reported the effect that 10991

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evaporation of water, during the short amount of time in which the liquid is static in the tip, can increase the concentration in droplets compared to the bulk solution.24 We can ensure that the droplets emerge with the concentration of the bulk solution by maintaining a constant pulse sequence to the microdispenser resulting in continual droplet creation. This prevents concentration gradients from developing in the solution in the capillary tip as water evaporates when not generating droplets. In order to introduce droplets into their bihyperboloidal EDB, Shulman et al. generated an electrospray from a droplet suspended from a needle, creating a mist of charged droplets which may influence gas phase conditions in the chamber. No indication is given as to the time scale for droplet confinement, and it appears to be assumed that the first timeresolved size measurement relates to a concentration equivalent to the bulk solution. On the basis of our previous work, we suggest that this would result in an underestimate of the solute concentration when the first size measurement was made as significant water loss would have already occurred. In addition, no mention of the effect of the charge on the droplet is made, and in this procedure it is likely that droplets will be highly charged. Indeed, it is noted that some droplets suffered from mass loss due to charge-induced explosions. In our experiments we have tried to address a number of these issues, particularly the certainty with which the starting composition of the droplet can be known and the influence of droplet charge on the evaporation rate. The charge on our droplets is likely to be significantly less, on the order of 20 to 50 fC, and we have accounted for the effect of charge on mass transfer in the kinetic simulations based on the work of Nielsen et al.44 In addition, we have already described how the droplet concentration is established in our measurements and have shown that it is well-defined. The gas phase conditions in our chamber are controlled by a nitrogen gas jet and by introducing single droplets into the trap, we cause minimal perturbation to the expected humidity. In summary, our results support the conclusion that these organic species do not influence mass transfer due to surface effects and behave in a way comparable to simple salt species: water evaporation is governed purely by the diffusion rate of water vapor away from the droplet surface, and the droplets rapidly approach equilibrium. Having concluded that the organic acids studied in this work do not have an observable influence on the surface kinetics occurring during evaporation, it is important to determine under what conditions we may expect to see an influence. The evaporation (or mass accommodation) coefficient, α, has been established as a parameter that defines the surface kinetics occurring during mass transfer. The range of this value in the literature spans orders of magnitude,45 and numerous studies have reported values. A comprehensive review of surface accommodation coefficients has recently been published by Kolb et al.6 One study, similar in many ways to the work reported here,29 reports a temperature-dependent value of the evaporation coefficient for pure water of between 0.18 and 0.13 for droplets on the order of 10 μm and at ambient pressure. On the basis of the uncertainty in the thermophysical parameters associated with diffusion and thermal conductivity, we are insensitive to any value of evaporation coefficient above 0.1, and when the experimental uncertainties are accounted for, we are insensitive to the value of the evaporation coefficient if it is above around 0.05, as illustrated in Figure 4. These limitations are not unique to our experiment, indeed any measurement made on droplets on the order of ca. >5 μm at atmospheric

Figure 4. An enlarged view of the data reported in Figure 1b indicating the effect of the evaporation coefficient, α, on the evaporation profile. The dark envelope represents the thermophysical uncertainties, while the light gray includes uncertainties in both experimental and thermophysical values. The dash line represents the simulation using decreasing values of the mass accommodation coefficient, from 1.0 to 0.01.

pressure will be insensitive to a value of α greater than 0.1, and likely the sensitivity will be significantly less when uncertainties associated with humidity are considered. Thus, we can conclude that, within the uncertainties of the thermophysical parameters and experimental conditions, the evaporation coefficients from the aqueous droplets discussed above must be larger than 0.05. 3.3. Evaporation of Solution Droplets to Kinetically Arrested and Amorphous States. It has previously been suggested that a number of solute systems can form kinetically arrested states upon losing water or amorphous states that retain water. These can include glasses, which can be considered as a highly viscous phase through which water diffusion is restricted, and gels, which are two-phase states consisting of an insoluble network containing pores and channels in which aqueous solution resides.46 The effect of the formation of these states on water transport is investigated here utilizing the same techniques that have already been discussed. 3.3.1. Glass Formation during Evaporation under Dry Conditions. The formation of a glassy, highly viscous state in sucrose droplets has been noted on numerous occasions8,10,12,47 and will be discussed only briefly here. In Figure 5a, we compare the evaporation of sucrose (Sigma Aldrich >99.5%) solution droplets at high RH and low RH. Under high RH conditions, droplets achieve an equilibrium size, while at low RH a substantial decrease in evaporation rate was observed but with further loss of water continuing over many hours (note the inset of Figure 5a is on a log time axis). These data suggest that a kinetically arrested state has been achieved (i.e., a glass) and that the particle continues to lose water to move toward equilibrium but only very slowly. Under such conditions, the evaporating flux of water is governed by the slow diffusion of water through the glassy sucrose matrix. The droplet concentration at the point at which the evaporation rate suddenly declines under dry conditions is explored in greater detail in Figure 5b,c for measurements made on droplets at four different starting concentrations. The concentration at these points is less than what would be 10992

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within the particle as lower water activities are achieved can be estimated from the Stokes−Einstein equation.12 D=

kT 6πaν

(1)

where T is the temperature in K, a is the diffusing molecule size (assumed to be 0.2 nm for H2O), and υ is the viscosity in Pa s. The time scale, τ, for the particle to achieve a homogeneous composition due to diffusion can be estimated from eq 2, where r is the droplet radius.48 τ=

r2 π 2D

(2)

Figure 6 illustrates how the time scale for achieving homogeneous mixing by diffusion depends on the particle

Figure 6. A plot of droplet radius versus diffusional time scale for sucrose droplets of increasing viscosity, according to eqs 1 and 2 (from bottom to top; water activity = 0.8, 0.6, 0.5, 0.4, 0.35, 0.30, 0.25, 0.20 with corresponding viscosities = 0.06, 1.1, 6.2, 50, 180, 830, 550, 63800 Pa s). The arrow indicates the approximate path a droplet initially of 50 g/L sucrose evaporating into dry conditions would traverse, clearly showing diffusional limitations due to increased viscosity as the size reaches 8−9 μm.

radius, estimated for particles that have the viscosity of sucrose solutions at various water activities. The dependence of viscosity for sucrose solutions on water activity has been discussed in our previous work.12 Also shown in Figure 6 is a typical trajectory in water activity/bulk viscosity taken by a sucrose droplet similar to those presented in Figure 5. Clearly, the evaporating droplet rapidly accesses values of the viscosity that slow the mass transport considerably. In particular, the surface layer will become depleted of water and increase in viscosity ahead of the bulk, creating a diffusion-barrier to evaporation. This occurs before the whole droplet forms a glassy state and the arresting of evaporation is thus observed at a lower overall droplet concentration than expected for glass formation. Similar behavior is noted for all initial concentrations investigated. 3.3.2. Gel Formation during Evaporation under Dry Conditions. The time-dependence in the size during evaporation of water from aqueous magnesium sulfate (Fisher Scientific 62−70%) droplets, shown in Figure 7a, deviates from the typical evaporation and efflorescence behavior observed for inorganic solutions and resembles the formation of an

Figure 5. (a) Evaporation of 50 g/L (0.15 M) sucrose droplets into different conditions, from right to left before 10 s, 80%, 50%, 30% and 0% RH. (Inset) Expanded view of evaporation at low RH showing a change in size over an extended time. (b) Evaporation of sucrose solution droplets of concentration, from top to bottom at long time, 200 g/L, 100 g/L, 50 g/L, and 20 g/L, into dry conditions. (c) The concentration at which a sudden decrease in the evaporation rate occurs (black) and at around 8 s (gray). The dash line indicates the concentration previously found to be associated with a glass transition.10

expected based on the water mass fraction at the point of glass formation, assuming additivity rules.10 The probable cause of this difference is likely due to the formation of radial inhomogeneities as a result of increasing viscosity as the glass transition point is approached, with the concentration of the solute averaged across the droplet volume lower than at the surface. The decrease in the diffusion constant of water, D, 10993

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Under dry conditions, evaporation of water is shown to occur at a rate similar to that which would be expected for any common salt solution over the first 1 s of evaporation (Figure 7b,c). However, a marked slowing in the rate occurs after 1 s. Unlike the evaporation of solution droplets into a gas phase of high RH where the droplets reach an equilibrium size, under dry conditions, water does continue to be lost from the particle but only very slowly. Such behavior is consistent with previous observations of a significant decrease in mass transfer rate for magnesium sulfate droplets, attributed to formation of an inorganic gel phase consisting of a network of complex contact ion pairs between Mg+ and SO42− ions.49 The concentration at which this decrease in rate occurred was estimated from a series of measurements that started with solute concentrations spanning more than an order of magnitude, and the results are shown in Figure 7c. This analysis is similar to that performed for sodium chloride droplets for which the phase change was crystallization of the salt. The gel phase forms when the RH is below between 30 and 40%, corresponding to a solute concentration of 8.4 to 7.6 M assuming a simple additivity rule for treating the density and using water activity/mass fraction data of Ha and Chan.50 The concentration at which we observe a decrease in rate is less than this, indicating the likely formation of the gel at the droplet surface prior to the bulk, as noted for glass formation in sucrose. This has been investigated by Li et al.11 using a microRaman microscope to probe surface and bulk gel formation in MgSO4 droplets on a coverslip, noting significant gel formation at the surface ahead of the bulk phase and supporting our observations. To more fully examine the mass transfer limitations imposed due to the formation of a gel phase, a number of rapid RH changes were imposed on a confined droplet. By switching the gas flow using a four-way valve between two flows of constant RH, the time scale for the RH change was minimized and was measured to occur over 20−30 s for a lithium chloride solution droplet confined in the gas flow. As a result, any response in droplet size on a time scale longer than this could be assumed to result from impeded water transport in the particle rather than the change in RH in the chamber. Figure 8 shows a droplet exposed to a number of RH changes, with a very slow response noted for changes below ∼40% RH. In order to obtain information on the changes in water flux, the timeresponse in droplet size was fitted to a first-order exponential decay and a time-constant estimated. These time-constants are reported in Figure 8 and are qualitatively consistent with the time scales noted for changes in peak intensity in the Raman spectra of Li et al.11 indicative of gel formation. A significant amount of water loss occurs after the onset of gel formation, although the rate of mass transport is very slow. Indeed, the time scales for uptake (Figure 8j) and loss (Figure 8i) of water at RH below 20% are on the order of hours. It can be seen in Figure 8e on increasing RH that the size does not increase, but instead appears to arrest. This is similar in principle to effects noted by Li et al.11 where a slow increase in the RH continued to result in gel formation in the core of the droplet. This is due to the water activity at the center remaining elevated compared to the conditions to which the surface is exposed, thus water loss and gel formation continue. On further increase in RH (Figure 8f,g), above 40%, the gel rapidly breaks down and the droplet response follows the humidity in the chamber.

Figure 7. (a) Evaporation of 35 g/L (0.29 M) MgSO4 droplets into different conditions, from right to left before 10 s, 80%, 50%, 30% and 0% RH. The formation of a gel is apparent in the deflection in rate observed under low RH conditions. (b) Evaporation into dry conditions of aqueous MgSO4 solution droplets of concentration, from top to bottom at long time, 150 g/L, 70 g/L, 35 g/L and 20 g/L. (b, inset) Loss of water continues over many hours. (c) The concentration at which a sudden decrease in evaporation rate occurs and after ∼6 s. The gray envelope indicates the expected concentration for onset of gel formation as described in the text.

amorphous state, such as that of a glass for sucrose aerosol. For evaporation into low RH conditions, a sharp change in evaporation rate occurred followed by a steady size decrease, roughly linear on a logarithmic time scale, reminiscent of the time-dependencies observed for the evaporation of sucrose droplets. At higher RH, equilibrium was achieved, and a steady size remained. 10994

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over 2 min, and within a further minute up to five droplets containing 10 mM SDS were studied. The rapid switching between these two systems allows us to assume identical conditions, particularly the same RH and temperature in the gas flow. Thus, the evaporation events measured for water droplets can be treated as a control measurement against which droplets of SDS solution could be compared. The results are shown in Figure 9. Agreement between the radius-squared rate of

Figure 9. A direct comparison of the evaporation of a pure water droplet (black), 41.5 μm2 s−1, and 0.01 M solution of SDS (gray), 41.7 μm2 s−1, into identical conditions in a pseudo-simultaneous experiment.

Figure 8. The effect of changing RH on a droplet of MgSO4 held in the EDB. The black line indicates the size and the dash line indicates the RH. The light gray shaded region indicates where response is consistent with an aqueous solution, while the dark gray shading indicates response associated with a gel. (Note the axis break and scale change after 12,500 s.) The lower panel indicates the exponential time constant in droplet response associated with selected RH changes.

evaporation was within 0.5% for the two cases, thus demonstrating that there is no measurable effect on the evaporation rate despite the droplet concentration becoming far in excess of that required for complete surface coverage by the surfactant. The evaporation coefficient is not significantly affected by the presence of SDS molecules in the droplet and therefore must remain larger than 0.05. This result was highly repeatable, and many hundreds of droplets of SDS and water, under numerous RH conditions, displayed no inhibition of water transport, consistent with previous work done on much larger droplets,53 but contrary to data presented in the work of Shulman et al.19 and Taflin et al.22 An interesting effect became apparent when the initial concentration of SDS was increased (Figure 10). When the surfactant concentration reached around 3.0−3.5M, consistent across measurements made on starting solutions of widely different concentration, a sharp change in rate was observed, similar to that noted for sucrose and magnesium sulfate, and similar to that noted by Shulman et al. and Taflin et al. for this system. The elastic scattering pattern rapidly lost its structure and after this point our ability to accurately determine size was compromised, although it remained possible to observe some water loss after this dramatic slowing in evaporation rate. When considering the phase behavior of water−SDS,54 it is possible that we are encountering a mixed micellar/crystal phase at the point where we observe a decrease in rate, causing bulk transport limitations comparable to a gel. As the mass fraction of SDS increases, a C2 crystal phase develops, which could explain the gradual loss of uniform elastic scattering over tens of seconds. 3.4.2. SDS and NaCl. The effect of the addition of NaCl on evaporation from water and SDS droplets is shown in Figure 11. A retardation of the evaporation rate was observed at a

3.4. Surfactant Effects on Evaporation. We have discussed how limitations in both theoretical descriptions and experimental protocols limit our ability to resolve a value for the mass accommodation coefficient in aqueous systems. It would be possible, however, to measure the effect on mass transfer for a value of the coefficient significantly less than 0.1. It is assumed, through the surface activity of a typical surfactant, that its presence at the surface would provide a surface transfer limitation across the interface, resulting in a lower mass or evaporation coefficient than for a clean surface. We discuss here the use of a surfactant in an attempt to lower the value of the mass accommodation coefficient to a level where significant changes in mass transfer are observed. A number of publications have reported the effects on mass transfer of a molecular film of a surface active species.19−21,51,52 These studies have generally investigated flat water surfaces or very large droplets, except in the case of Shulman et al. It has been proposed that the formation of surface monolayers inhibit evaporation as mass transport across the air/droplet interface is restricted. In order to determine the effects of a surfactant species on mass transfer for droplets in our experiment, the evaporation of aqueous sodium dodecyl sulfate (SDS), an ionic surfactant soluble in water, was studied. 3.4.1. SDS. A direct comparison was made between the evaporation of pure water with and without SDS (Fisher Scientific 99%) at a low concentration (10 mM) under an RH of around 80%. Up to five droplets of pure water were studied 10995

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Figure 11. (a) The effect on the evaporation of 0.08 M SDS solution droplets containing, from top to bottom at long time, 0.2 M, 0.1 and 0 M NaCl. (b) The corresponding time dependence of the concentration of the droplets containing, from top to bottom at long time, 0 M, 0.1 and 0.2 M NaCl.

Figure 10. (a) Evaporation of SDS solution droplets of initial concentration, from top to bottom at long time, 0.2 M, 0.12 M, 0.08 and 0.01 M, into ∼80% RH. (b) The time dependence of the SDS concentration showing a consistent concentration of ∼3.0 M attained before a deflection in the rate occurs, from top to bottom at early time, 0.2 M, 0.12 M, 0.08 and 0.01 M. The lowest concentration was not retained in the trap to a small enough size to observe the change in rate.

crystalline state may be greater, which could explain the observation that crystal formation was seen to occur sooner than in the pure SDS case. Further probing of the phase state would be required to test this hypothesis.

larger size, and thus lower SDS concentration, as a larger mass fraction of NaCl was added. The droplet containing the highest NaCl initial concentration (and no SDS) would be seen to effloresce at around 6 μm, while the size observed at the change in rate was significantly larger. This suggests an interaction between NaCl ions and SDS in solution, with a possible effect on the amorphous structure that develops. The formation of micelles in a solution containing ionic surfactants may be affected by the addition of ionic salts, such as sodium chloride, in an effect known as charge screening. The positive sodium ions are attracted to the negative dodecyl sulfate molecules, allowing them to sit closer. This lowers the critical micelle concentration (CMC) and increases the aggregation number.55,56 Without any additional NaCl, the concentration must reach a certain point in order for the surfactant species to be close enough to interact. By adding further positive ions from NaCl, the interaction can occur over a longer distance as the repulsive interactions are screened. This allows the micellar gel network to develop at a lower concentration, as noted. The degree of uncertainty in the size measurement, due to disturbances in the elastic scattering pattern, suggests a more crystalline structure is formed, which reduces the sphericity of the droplet. With micelles forming more readily the propensity to develop into a

4. CONCLUSIONS In this study we have described how the evaporation rate of water from aerosol may be affected by the presence of dissolved species. We have focused on the change in water activity within a droplet due to the presence of a solute, thus decreasing the surface vapor pressure and rate of evaporation of water, and in some cases leading to the droplet attaining equilibrium with the environmental RH. This is the primary cause of a change in evaporation rate in processes controlled by gas-phase diffusion, and we have shown that inorganic salts (ammonium sulfate and sodium chloride), as well as organic acids (adipic, oxalic and cispinonic), behave in such a way, contrary to previously published work.19 We have presented experimental data and model simulations that are in excellent agreement. Through these simulations, we have introduced the technique of using the equilibrium droplet radius, along with established thermodynamic models, to determine the RH within the experiment to a greater accuracy than common capacitance RH probes. Through a consideration of the uncertainties in the thermophysical parameters used in the model and the experimental uncertainties, we have determined the largest value of the evaporation coefficient resolvable through this 10996

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studentship. A.E.H. acknowledge the EPSRC for the support of a postdoctoral research fellowship, and R.E.H.M. acknowledges NERC for the support of a postdoctoral research fellowship (NE/I020075/1).

technique to be 0.1, with any value greater than this producing an undetectable change in the mass flux. Sensitivity to this parameter is increased under low pressure conditions or with smaller droplets. The formation of amorphous states in aerosol has been further explored, and we report very slow mass transport in sucrose droplets under dry conditions. Rapid evaporation into dry conditions leads to a lower than expected concentration upon entering a glassy state, and we conclude that, due to the surface viscosity increasing ahead of the bulk, water will be trapped in the core, resulting in the overall concentration being less than what would be expected. We report similar mass transport limitations in droplets consisting of magnesium sulfate, with previous work having discussed the formation of a gel network comprised of contact ion pairs. The size response of a single trapped droplet was recorded as the RH was raised and lowered, and we report a significant increase in the response time for changes below around 45% RH, with the response above this point consistent with the change in RH in the chamber. We demonstrate that the surfactant SDS does not affect the evaporation coefficient of water to a degree measurable using this technique. As discussed, our sensitivity to this parameter is limited to values below 0.1, and while the dodecyl sulfate groups are expected to be surface active, the evaporation coefficient must remain above 0.1. Insoluble straight chain alcohols have previously been shown to reduce evaporation rates in large droplets due to the formation of a tight packed insoluble surface monolayer,52 and it seems likely that the dodecyl sulfate head groups, being charged and bulky, will not be present at the surface in a tight-packed structure and so will not produce the same effect. We have shown that SDS in droplets can affect the evaporation rate, but only at high concentrations (∼3 M) consistent with the formation of a mixed micellar/crystal phase. Previous work noting the retardation of water evaporation due to the presence of SDS may have simply been observing the formation of this state. The addition of sodium chloride, in particular the sodium ions, allowed for increased charge screening permitting the dodecyl sulfate head groups to sit closer, reducing the CMC and aggregation number and decreasing the concentration at which the micellar/crystal phase was observed. Although we have demonstrated that heat and mass transfer calculations using a well-established approach can accurately reproduce the experimental trends for evaporating droplets controlled by gas diffusion, providing such a rigorous quantitative model comparison for evaporation from amorphous aerosol remains challenging. Although models have been successfully used in some instances,10,12 we consider that a more general model framework must be established to treat systems where bulk diffusion kinetically limits the partitioning of water between the gas and condensed phases.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.P.R. acknowledges financial support from the EPSRC through the support of a Leadership Fellowship (EP/G007713/1). J.F.D. acknowledges the EPSRC for the award of a Ph.D. 10997

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