Evaporation Kinetics of Polyol Droplets: Determination of Evaporation Coefficients and Diffusion Constants

In order to quantify the kinetics of mass transfer between the gas and condensed phases in aerosol, physicochemical properties of the gas and condensed phases and kinetic parameters (mass/thermal accommodation coefficients) are crucial for estimating mass fluxes over a wide size range from the free molecule to continuum regimes. In this study, we report measurements of the evaporation kinetics of droplets of 1‐butanol, ethylene glycol (EG), diethylene glycol (DEG), and glycerol under well‐controlled conditions (gas flow rates and temperature) using the previously developed cylindrical electrode electrodynamic balance technique. Measurements are compared with a model that captures the heat and mass transfer occurring at the evaporating droplet surface. The aim of these measurements is to clarify the discrepancy in the reported values of mass accommodation coefficient (αM, equals to evaporation coefficient based on microscopic reversibility) for 1‐butanol, EG, and DEG and improve the accuracy of the value of the diffusion coefficient for glycerol in gaseous nitrogen. The uncertainties in the thermophysical and experimental parameters are carefully assessed, the literature values of the vapor pressures of these components are evaluated, and the plausible ranges of the evaporation coefficients for 1‐butanol, EG, and DEG as well as uncertainty in diffusion coefficient for glycerol are reported. Results show that αM should be greater than 0.4, 0.2, and 0.4 for EG, DEG, and 1‐butanol, respectively. The refined values are helpful for accurate prediction of the evaporation/condensation rates.


Introduction
Understanding and quantifying the kinetics of mass transfer between the gas and condensed phases in aerosol is important for predicting mass concentrations, size distributions, and compositions with consequences for ambient aerosol processes, impacts, and fates (Riipinen et al., 2011Topping et al., 2013;Tröstl et al., 2016). Predictions of condensation and evaporation rates depend on accurate knowledge of physicochemical properties of the gas and condensed phases, such as vapor pressures, diffusion constants, and thermal conductivities (Miles et al., 2012), and kinetic parameters such as mass/thermal accommodation coefficients, which are crucial for estimating mass fluxes over a wide size range extending from the free molecule to continuum regimes (Kolb et al., 2010;Vehkamäki & Riipinen, 2012). These quantities are generally much less well known for condensing and evaporating organic vapors than for water (Kolb et al., 2010). In addition, many of these same quantities and processes must be accurately represented in the design and interpretation of data from analytical instruments such as the condensation particle counter (CPC) and the hygroscopic tandem differential mobility analyzer.
The CPC is the most commonly used technique for ultrafine-particle concentration measurements in laboratory and field measurements (McMurry, 2000). Inside the CPC, a gas phase supersaturation of a condensing species is generated through which the introduced particles are activated and grow to sizes that are large enough for optical detection. Various types of laminar, continuous flow CPCs have been developed as commercial instruments using different working fluids, e.g., 1-butanol (Agarwal & Sem, 1980), water (Hering & Stolzenburg, 2005), and diethylene glycol (Iida et al., 2009). Iida et al. (2009) investigated the dependence of the size-dependent activation efficiency on the working fluid, considering ethylene glycol, diethylene glycol, propylene glycol, oleic acid, and dioctyl sebacate. Diethylene glycol (DEG) was recommended as the most effective working fluid in new CPC designs, improving the performance of sub-2 nm particle detection. Furthermore, several CPC-based techniques, such as Pulse Height Analysis Mode (Saros et al., 1996), the CPC battery (Kulmala et al., 2007), and the Nano-CPC battery (Kangasluoma et al., 2014), have been proposed to obtain more information in atmospheric nanoparticles measurement other than just the particle concentration. The calibration and application of different types of CPC show that the detection efficiency is dependent not only on the instrumental operating conditions (pressure, flow rate, and temperature) but also on the particle properties (initial size, polarity, chemical composition, and morphology) (Giechaskiel et al., 2011;Hering & Stolzenburg, 2005;Kangasluoma et al., 2015;Kulmala et al., 2007;Tuch et al., 2016;Wiedensohlet et al., 1997;Zhang & Liu, 1990). Therefore, numerical simulations of condensational growth of particles inside the CPC are essential for instrument development and data interpretation (Ahn & Liu, 1990;Hering & Stolzenburg, 2005;Iida et al., 2009;Saros et al., 1996;Zhang & Liu, 1990).
The supersaturation profile of the working fluid vapor inside the condenser of a CPC is calculated from the vapor species and temperature distributions, both of which are calculated from flow field simulations. Equations satisfying heat balance have been developed to describe the particle growth process (Ahn & Liu, 1990;Zhang & Liu, 1990). Transition regime corrections are taken into account (Seinfeld & Pandis, 2006) to ensure that the equations are valid for the entire particle size range sampled. In the free molecule regime, mass accommodation coefficient (α M ) and thermal accommodation coefficient (α T ) are the two parameters that fundamentally influence the interaction of the vapor with growing droplets (Seinfeld & Pandis, 2006;Winkler et al., 2004). A value of α M < 1 has the implication that the actual final size of a droplet is smaller than the predicted value when assuming that α M = 1. Kinetic calculations show that the time dependence of water droplet growth is more sensitive to α M than α T (Miles et al., 2012) for particle sizes in the CPC measurement size range. Therefore, α M is a key parameter that must be known to fully understand and quantify the condensational growth of particles. The mass accommodation coefficient (α M ) and evaporation coefficient (γ) are referred to in condensation and evaporation studies, respectively. However, the values of α M and γ are assumed to be identical based on microscopic reversibility (Miles et al., 2012).
For water, many studies have reported α M through measurements of evaporation/condensation kinetics Hołyst et al., 2013;Langridge et al., 2016;Marek & Straub, 2001;Miles et al., 2012;Raatikainen et al., 2012;Tsuruta et al., 1994;Winkler et al., 2006). Results from experiments using a variety of ensemble and single-particle techniques confirm that α M is greater than 0.2 (Langridge et al., 2016;Miles et al., 2012) and even close to 1 Raatikainen et al., 2012;Winkler et al., 2006). α T is usually assumed to be unity, which agrees with simulation and experimental results (Hołyst et al., 2013;Winkler et al., 2004;Zientara et al., 2008). The temperature dependence of the vapor pressure of water Murphy & Koop, 2005) and the diffusion coefficient of water in the gas phase are well established (Miles et al., 2012). In this work, further measurements of the evaporation kinetics of pure water are only reported to verify model performance.
For 1-butanol, Ahn and Liu (1990) assumed α M = 1 in their simulations of condensational growth inside a 1-butanol CPC. However, this assumption cannot be verified based on current design because the droplet size as a function of time could not be adequately resolved. Very few studies to determine α M for 1-butanol have been reported. Only the product of diffusion coefficient and vapor pressure (D × p v ), which is a constant under quasi-steady state conditions (Fuchs, 1959), was determined by Erbil and Dogan (2000) for some liquids from hanging droplet evaporation measurements, including 1-butanol. Taking into account the temperature suppression at the droplet surface but not α M , the reported value of D × p v for 1-butanol at 14.9°C was 0.435 cm 2 s À1 mmHg. This value is 52% higher than the product of D and p v both at 14.9°C presented in the same paper, which suggests that there is a large error in the determined value of D × p v . Tsuruta et al. (1994) determined the α M of ethylene glycol (EG) and water using a dropwise condensation method. They reported that the α M value for EG is in the range of 0.17-0.45 at 0.24-1.57 kPa. Jakubczyk et al. (2010) investigated the evaporation kinetics of some low-volatility organic (EG, DEG, and TEG) droplets in nitrogen. Their results suggested that the evaporation coefficient for EG at 298 K is as low as 0.035 ± 0.012.
The evaporation rates of DEG, TEG, and glycerol into vacuum have been measured in the temperature range 5-50°C using a microbalance (McFeely & Somorja, 1972). Results suggested that the value of evaporation coefficient for DEG at 300 K is 0.05. Lednovich and Fenn (1977) measured the absolute evaporation flux of some polar and nonpolar liquids (including DEG and glycerol) from clean surface by means of a mass spectrometer. The values of evaporation coefficient were reported to be close to unity (0.98-1.2 for DEG at 4.5-37.3°C) and independent of temperature. However, the value determined in later experimental work was only 0.082 ± 0.035 for DEG at 298 K (Jakubczyk et al., 2010). Recently, Hołyst et al. (2013) used molecular dynamics simulation and single-particle technique to investigate the interfacial transport of energy and mass during evaporation of liquid droplets of water, DEG, TEG, and glycerol into inert gas. They found that α M for DEG lies within the range of 0.74-0.9.
In this study, we aim to clarify the discrepancy in α M values for 1-butanol, EG, and DEG and improve the accuracy of D for glycerol. The order of volatility of decreasing volatility is 1-butanol, EG, DEG, and glycerol. We will use a model based on the work of Ahn and Liu (1990) (referred to as the Liu model below) to describe the heat and mass transfer at the evaporating droplet surface. In order to verify a newly developed program based on the Liu model, the evaporation kinetics of pure water droplets under different relative humidities (RHs) are simulated and compared with cylindrical electrode electrodynamic balance (EDB) measurements and with a further model that we have used previously (Miles et al., 2012). The sensitivity of the evaporation kinetics of 1-butanol to the value of α M is also analyzed. Then, we will report the evaporation profiles of 1-butanol, EG, DEG, and glycerol droplets under well-defined conditions (gas flow rates and temperature) using the previously developed EDB technique (Davies et al., 2013(Davies et al., , 2012Rovelli et al., 2016). For single-component organic droplets, the time-resolved radius recorded from experiments is fit using Liu model with varying experimental conditions (e.g., gas velocity, V g ) and differing treatments of the key thermophysical properties (specifically, the evaporation coefficient, α M , and the relative error in the literature value of diffusion coefficient at 298 K, ΔD 298 /D 298 ). The fitted values of (α M , V g , and ΔD 298 /D 298 ) corresponding to the best agreement between model prediction and experimental data (minimum residual) are obtained. With knowledge of uncertainties in the thermophysical and experimental parameters, the plausible ranges of the evaporation coefficients for 1-butanol, EG, and DEG as well as uncertainty in D for glycerol are reported.

Evaporation/Condensation Model
Models for predicting evaporation/condensation rates of unary, binary, and more complex droplets have been developed by a number of authors (Jakubczyk et al., 2010;Kulmala et al., 1993;Persad & Ward, 2016;Seinfeld & Pandis, 2006). If the temperature suppression at the evaporating droplet surface is severe (i.e., the temperature difference between the droplet surface and the surrounding gas, T d À T ∞ , is greater than À3 K), the semianalytical framework of Kulmala et al. (1993) is not accurate (Kulmala et al., 1993;Rovelli et al., 2016). Considering the simplicity of the treatment for a single-component droplet while capturing the possible coupling of heat and mass transport, the Liu model (Ahn & Liu, 1990) is compared with our measurements. The radius (r) of the evaporating/condensing single-component droplet as a function of time (t) can be described as where D is the diffusion coefficient of the evaporating/condensing vapor in the surrounding gas (pure nitrogen in this work). M v and ρ are the vapor's molar mass and liquid phase density, respectively. R is the gas constant. p d and p ∞ are the partial pressures of the evaporating/condensing vapor at the droplet surface and far from the surface, respectively, and T d and T ∞ are the corresponding temperatures. K g is the thermal conductivity of the surrounding gas, and L is the latent heat (enthalpy of vaporization) of the evaporating/condensing vapor. β M and β T are the Fuchs-Sutugin transitional correction factors for mass Journal of Geophysical Research: Atmospheres 10.1002/2017JD027111 and heat transfer, respectively. β M and β T are expressed as (Kulmala et al., 1993;Miles et al., 2012;Seinfeld & Pandis, 2006;Winkler et al., 2004) Kn M and Kn T are the Knudsen number for mass and heat transfer, respectively (Ahn & Liu, 1990;Wagner, 1982). λ M and λ T are the effective mean free paths for mass and heat transfer, respectively (Seinfeld & Pandis, 2006).
c v and c g are the mean speeds of vapor and gas molecules at temperature of T, respectively. M g is the molar mass of the surrounding gas. Finally, where S is the saturation fraction of vapor in the flowing gas far from the droplet surface, a solute and a Kelvin are correction factors taking into account the solute effect and Kelvin effect, respectively, and p v (T ∞ ) and p v (T d ) are vapor pressures of the evaporating vapor at T ∞ and T d , respectively (Seinfeld & Pandis, 2006).

Modifications and Corrections
The mass flux of a pure (single-component) droplet during evaporation/condensation is defined by When both sides of equation (1) are multiplied by r, the left side is proportional to the mass flux, I, as shown in equation (13). Taking into account the enhanced mass transfer due to the relative movement of the droplet and gas phase, the right sides of equations (1) and (2) are scaled as The Sherwood number, Sh, is defined as a function of other dimensionless parameters (Seinfeld & Pandis, 2006) Sh ¼ 2 þ 0:6 Re 1=2 Sc 1=3 Sc where Re is the Reynolds number, V g is the gas flow velocity, ν g is kinematic viscosity of gas, and Sc is the Schmidt number. This correction is the same as used by previous researchers (Davies et al., 2012;Devarakonda & Ray, 2000;Hopkins & Reid, 2005).

Properties of Nitrogen and Organic Vapor
The thermal conductivity (K g ) and kinematic viscosity (v g ) for nitrogen have been well characterized, and the parameterizations are given by Lemmon and Jacobsen (2004). By fitting the data from these parameterizations, simpler forms are obtained for easy use (Davies, 2014) and will be used in this work as K g = 3.95 × 10 À4 + 9.805 × 10 À5 T À 4.3032 × 10 À8 T 2 , and ν g = 8.263 × 10 À8 T À 8.722 × 10 À6 . The main physicochemical properties of compounds investigated in this work are listed in Table 1. For 1-butanol, although many parameterizations of vapor pressure (p v ) have been presented, the relative differences among the calculated values are several percent or even higher. The parameterization of p v from Yaws (1994) was used for simulation in this work because the predicted value at 298 K (940 Pa) matches the most recent experimental value (Garriga et al., 2002).
The temperature dependence of D is described as (Tang et al., 2015a) where D 298 is the diffusion coefficient at 298 K, as shown in Table 1.
Under the conditions investigated (S ≈ 0), the temperature difference (T d À T ∞ ) for an evaporating 1-butanol droplet is~À3 K, while the (T d À T ∞ ) values are smaller than À0.075, À3 × 10 À3 , and À2 × 10 À4 K for evaporating EG, DEG, and glycerol droplets, respectively. For 1-butanol, the temperature dependences of density and latent heat were taken into account, and the parameterizations from Haynes (2016) and Poling et al. (2008), respectively, were used in this study, as shown in Table 1. The densities for EG, DEG, and glycerol at 20°C (Haynes, 2016) were used throughout in the simulation. As their latent heat is insensitive to temperature in the range of interest (15-25°C), the values at 25°C from database (Haynes, 2016, https://pubchem.ncbi. nlm.nih.gov) are used directly in the simulation.
Comparative kinetic measurement for hygroscopicity determination of aerosol using the EDB has been described previously (Davies et al., 2013;Rovelli et al., 2016). Similarly, we use the size of an equilibrated sodium chloride droplet to determine the RH in the gas phase and measure the evaporation kinetics of a pure water droplet into a gas phase of varying RH for comparison. The sodium chloride droplet, starting with known initial solute concentration, and a pure water droplet were sequentially generated and introduced into the chamber as probe and sample droplets, respectively. The equilibrated size following evaporation of the aqueous NaCl droplet can be used to determine the gas phase RH (Davies et al., 2013;Rovelli et al., 2016). For example, in Figure 1, the gas phase RH determined using NaCl probe is 0:888 þ0:003 À0:004 . Then, the evaporation profile of a pure water at RH = 0.888 is predicted using Kulmala and Liu models, as shown in Figure 1. The simulated evaporation profile using the Kulmala model agrees well with the experimental results. Although the Liu model used in this study slightly overestimates the evaporation rate, the simulated curve still matches the experimental curve within the uncertainty envelope. The expressions of the Liu model are simple and explicit, and it is for this reason that the Liu model is used throughout in the work. The comparison in Figure 1 serves as a validation of our implementation of the Liu model, clearly demonstrating that it is sufficiently accurate to describe the evaporation/condensation kinetics of compounds investigated in this work. Figure 2 shows simulated evaporation profiles of a pure 1-butanol droplet assuming T = 293.15 K, V g = 3 cm/s, and S = 0 in the nitrogen flow. The sensitivity of evaporation kinetics of a pure 1-butanol droplet to mass accommodation coefficient (α M ) is illustrated by varying α M = 0.1, 0.2, 0.4, 0.6, and 1 in calculations using the Liu model. As shown in Figure 2, the evaporation rate increases with α M . Limited by the size accuracy in present EDB measurement (±100 nm) (Davies, 2014, Rovelli et al., 2016, it would not be possible to resolve the difference between α M = 0.6 and 1 experimentally, as the error envelopes overlap. By using equations (5), (7), and (8), the effective mean free path for mass transfer is estimated to bẽ 90 nm under the conditions investigated, which is 2 orders of magnitude smaller than the droplet radius recorded by the EDB (9-30 μm) in this study. Thus, the evaporation kinetics of organics investigated in this study are always in the continuum regime with values of Kn < 0.01. As the evaporation rates of EG, DEG, and glycerol are several orders of magnitude lower than that of 1-butanol, their evaporation kinetics are less sensitive to α M . In the following model predictions for EG, DEG, and glycerol, α M is also varied at 0.1, 0.2, 0.4, 0.6, and 1 to resolve its influence. However, only the results at α M = 0.1, 0.2, 0.4, and 1 are presented and discussed.

Reagents
For EG (>99%, Acros Organics), DEG (>99%, Alfa Aesar), and glycerol (>99.5%, Acros Organics) solutions, high-performance liquid chromatographygrade water (VWR Chemicals) was used. Solutions were prepared up to the solubility limit of each solute considered. For 1-butanol (>99%, Fisher) solution, an ethanol-H 2 O mixture with volume ratio of unity (v/v = 1) was used as the solvent as 1-butanol is insoluble in water but miscible in ethanol. The solute concentrations of the solutions prepared in this study are listed in Table 1.

Time-Resolved Evaporation Profiles of Single Droplets
The EDB measurement procedures used in this study have been discussed in previous works (Davies et al., 2012(Davies et al., , 2013Rovelli et al., 2016). The electrodynamic potential is provided by a pair of concentric cylindrical electrodes, and the trap is operated at atmospheric pressure and can access a temperature range from 248 to 340 K. A gas flow passes through the cylindrical electrodes, and the environmental conditions (flow rates, relative humidity, and temperature) are known and well controlled. More specifically, a dry or humidified nitrogen flow controlled by mass flow controller (MKS 1179A) is introduced into the chamber through the space between the inner electrode and the outer electrode. The temperature of the chamber body is controlled with high precision by a recirculating water/EG mixture (v/v = 1) from a thermostatic water bath (Julabo, F32). Single droplets generated on demand by a microdispenser (Microfab MJ-ABP-01) are charged using an induction electrode then introduced into the chamber and finally trapped in the central region between the electrodes within 100 ms. After careful collimation, the trapped droplet is illuminated by a green laser (λ = 532 nm). The elastic scattering pattern is recorded with high time resolution down to 10 ms. The levitated droplets remain spherical during measurement because the droplets are sufficiently small enough that capillary forces dominate the gravitational force (Reid et al., 2011). The Geometric Optics Approximation (GOA) method is used to calculate the droplet radius as time evolves (Davies et al., 2012).
In this work, full evaporation profiles of EG/water, DEG/water, and glycerol/water droplets (referred to as EG, DEG, and glycerol droplets later) at 20°C and under different flow rates (50, 100, and 200 cm 3 /min) were recorded with a time resolution of 10 ms, as shown in Figures 3a-3c. Because of the high volatility of 1-butanol, evaporation profiles of 1-butanol/ethanol/water (referred to as a 1-butanol droplet) droplet at lower temperatures (12 and 15°C) were also recorded to collect more data for fitting, as shown in Figure 3d.
The reported values of refractive index at 589 nm were used in the GOA method, as they are very close to   Table 1.

Journal of Geophysical Research: Atmospheres
10.1002/2017JD027111 those at 532 nm and can easily be found in the Haynes (2016). Repeated measurements were performed for ten 1-butanol droplets, three EG droplets, two DEG droplets, and two glycerol droplets for each set of environmental conditions.
For EG, DEG, and glycerol droplets evaporating in a pure dry nitrogen flow, the solvent (water) evaporates at least 2 orders of magnitude faster than that of the solute because of the high values of p v and D for water. An inflection point in the r-t curve is easily observed (Figures 3a-3c) at around 2 s when water evaporation is nearly complete, and the evaporation kinetics become dominated by the low-volatility solute (Krieger et al., 2012). Therefore, only data beyond 30 s are considered for fitting to avoid the interference of solvent (water) evaporation and temperature suppression.
In the case of a 1-butanol droplet, the evaporation rates of cosolvents (ethanol: H 2 O) are several times higher than that of 1-butanol although some residual water or ethanol might still remain in the droplet. As shown in Figure 3d, the inflection point in the r-t curve is not significant. Although the solute concentration is very high and the value is close to the density of pure 1-butanol (810 g/L), it is difficult to determine exactly when the mole fractions of ethanol/water become very small. Assuming that the solvents evaporate completely while 1-butanol remains in the droplet, the corresponding radius should be~25 μm, a size which is reached at 0.5 s. In the fitting procedures, data points beyond 0.8, 1.0, and 1.5 s (total evaporation time of around 2.5 s at 15°C) were used for fitting, respectively. The effect of the selected data range on the fitting results will be discussed later. The systematic influences of the gas velocity and temperature on the evaporation rates are clear in these plots, and the small variation with gas flow rate seen in Figure 3d illustrates the high level of precision that can be achieved using this approach.

Fitting of Experimental Data
As no organic vapors were introduced in the nitrogen flow during measurements, the saturation fraction, S, in equation (11) was set to be zero in the simulation. The correction factor for the solute effect (a solute ) equals unity for a single-component droplet. The possible effect of impurities introduced from reagents will be discussed later. For particles larger than 5 μm, the lower limit of experimental measurements in the current study, the correction factor for the Kelvin effect (a Kelvin ) is within the range of 1-1.0008 according to the equation in Hinds (1999). Thus, a Kelvin is set to be unity in all cases. We now present the procedure used to fit the raw evaporation data for single-component droplet.
In a first preprocessing stage, the curves for radius and radius squared as a function of time (r-t and r 2 -t) are considered. A linear regression method is used to obtain the best linear fit of the experimental r 2 -t curve and to remove any outliers in radius. From this fit, the first fitted value of the square of radius (r 2 0;fit ) and its uncertainty range (the lower limit, J 1 , and the upper limit, J 2 , in r 2 0;fit ) are identified. In the following simulation, the trial value of r 0 is scanned in the range of J 1 1/2 -J 2 1/2 to account for this possible error in the initial droplet size determination (typically ±100 nm (Davies, 2014;Rovelli et al., 2016)).
For chosen values of mass accommodation coefficient (α M ) and gas flow velocity (V g ), the droplet temperature at its surface (T d ) is calculated from equation (15) for varying initial radius (r 0 ) and diffusion coefficient (D). For each simulation for different r 0 , Δr 0 is defined as the difference between the stepwise value r 0 and r 0,fit . (D 298 + ΔD 298 ) instead of D 298 from Lugg (1968) is used to calculate D by equation (19), and ΔD 298 is systematically varied to obtain different D for the simulation. Assuming that thermal equilibrium between the droplet surface and the gas very close to the surface is achieved, the temperature dependence of the gasphase properties is evaluated using T d and updated in every time step. Then, a simulated radius as a function of time (r sim (t)) is calculated from the model and compared with experimental values of radius (r exp (t)). The simulation residual, X i r sim t i ð Þ À r exp t i ð Þ À Á 2 , is calculated and plotted as a function of (Δr 0 , ΔD 298 /D 298 ).
This allows the best fitted values of (Δr 0 , ΔD 298 /D 298 ) to be obtained from the combination in values that has the minimum value of simulation residual. Then, r 0 and D are updated and used to simulate the evaporation profile again. The recalculated (r sim À r exp ) and (T d À T ∞ ) as a function of time are evaluated to monitor the simulation procedure. Then, by systematic variation of α M and V g , a comparison between the measurement and simulation leads to a full evaluation of the simulation residuals and an identification of the best fitted values of (α M , V g , Δr 0 , and ΔD 298 /D 298 ). An example of the dependence of the simulation residual on Journal of Geophysical Research: Atmospheres 10.1002/2017JD027111 the three parameters (α M , V g , and ΔD 298 /D 298 ) is shown in Figure 4 for an EG droplet evaporation measurement.

Determination of α M and Diffusion Coefficient
It is observed from monitoring result of the simulation procedure that the value of the Δr 0 is very close to zero and much smaller than the possible error in the size determination (±100 nm (Davies, 2014;Rovelli et al., 2016)).The relative difference of the residual across all trial combinations of fit parameters is less than 2 (equally 0.3 in log scale, as shown in Figure 4) over the range investigated, as shown in Figure 4, suggesting that the Δr 0 and residual are not sufficiently significant to be used as criteria in determination of the plausible range of α M for EG and other organics investigated in this work. Indeed, different combinations of (α M , V g , and ΔD 298 /D 298 ) can essentially lead to the same time dependence in radius within the experimental uncertainty. Thus, α M can only be determined if additional constraints can be imposed on the values of V g and ΔD 298 /D 298 , thereby constraining the retrieved value of α M . V g is only dependent on the well-controlled flow rate in the EDB, while ΔD 298 /D 298 is constant and assumed independent of T and V g .

Evaluation of Gas Velocity Range
In previous work (Davies, 2014), the dependence of the gas flow velocity (V g ) on the gas flow rate for the same EDB has been calibrated carefully by means of force balance method. The determined V g at 50, 100, and 200 cm 3 /min are 0.8, 1.7, and 3.1 cm/s, respectively, with uncertainty of 0.8 cm/s. During evaporation kinetics measurement of single supercooled water droplets, it was confirmed that V g at 50 cm 3 /min is in the range from 0.84 cm/s (assuming α M = 1) to 1.47 cm/s (α M = 0.1) . Assuming linearity in the relationship of V g to the gas flow rate, the possibility of V g < 1.7 cm/s and V g < 3.1 cm/s can be excluded for flow rates of 100 and 200 cm 3 /min, respectively, as V g is in the range of 0.84-1.47 cm/s for 50 cm 3 /min. Therefore, V g at 50, 100, and 200 cm 3 /min in this work should lie in the range of 0.84-1.47, 1.7-2.5, and 3.1-3.9 cm/s, respectively. Lugg (1968) and Tang et al. (2015a) have compiled and evaluated the diffusion coefficients for many organic compounds in air. However, the proposed values of uncertainty do not match well with each other. For the organic compounds of interest, the values of D 298 estimated from the Fuller method (Tang et al., 2015b) are all higher than the experimental values from Lugg (1968) by 5-14%. The deviation, used as the uncertainty in D 298 by Tang et al. (2015a), is also greater than the standard deviation from observations (Lugg, 1968).

Estimation and Evaluation of Diffusion Coefficients
In this work, the diffusion coefficients for the organics of interest at 298 K in nitrogen are estimated by using Chapman-Enskog kinetic theory (Bird et al., 2002). An evaluation of the calculated values of D 298 from different methods, including Wilke-Lee, Fuller and Chapman-Enskog (Erbil & Dogan, 2000;Lugg, 1968;Tang et al., 2015a), and this work is shown in Table 2.
The average of the calculated values of diffusion coefficient for the organics of interest at 298 K agrees with the experimental values (Lugg, 1968) within the expected accuracy of the method of Chapman-Enskog theory (8% (Bird et al., 2002)), as shown in Table 2. The slight difference between the calculated values for 1-butanol from different studies even using the same method is likely attributed to the difference in properties used. For example, the average values of the calculated values of diffusion coefficients for 1-butanol, EG, and DEG at 298 K are 8.64 × 10 À6 , 1.02 × 10 À5 , and 7.53 × 10 À6 m 2 /s with relative standard deviation (RSD) of 4.5%, 10.1%, and 8.7%, respectively, as shown in Table 2. The relative deviations of these average values with respect to the experimental values are 0.39%, 0.84%, and 3.2%, which are much smaller than the RSD of the average values. This suggests that the experimental values from Lugg (1968) are accurate.
Using the RSD value of D 298 from Lugg (1968) (referred to as u(D 298 )/D 298 ), a range on ΔD 298 /D 298 is used as a constraint to determine the plausible range of α M for 1-butanol, EG, and DEG. For glycerol, the calculated D 298 obtained in this work is 7.63 × 10 À6 m 2 /s. As no experimental value has been reported, the claimed accuracy of the method is~8% (Bird et al., 2002) and will be improved later.

Results and Discussion
In this part, we will present the plausible ranges of α M for EG, DEG, and 1-butanol, respectively, and then the uncertainty in the diffusion coefficient of glycerol.  Figure 5. For the three repeated experiments, the standard deviations of ΔD 298 /D 298 at each trial value of V g are better than 0.006 and are plotted as error bars.
As described in section 3.4.1, V g at 50, 100, and 200 cm 3 /min should lie in the range of 0.84-1.47, 1.7-2.5, and 3.1-3.9 cm/s, respectively. As discussed in section 3.4.2, ΔD 298 /D 298 for EG should lie in the range of À0.038 and 0.038 taking the proposed RSD value of D 298 (u(D 298 )/D 298 ) from Lugg (1968). The plausible ranges of (V g and ΔD 298 /D 298 ) at 50, 100, and 200 cm 3 /min are indicated in Figure 5. When α M equals 0.1 and 0.2, the curves obtained from fitting of experimental data do not all simultaneously intersect with the allowed ranges in ΔD 298 /D 298 , indicated by the corresponding rectangle regions, as shown in Figures 5a and 5b. Therefore, α M < 0.2 can be easily excluded for EG.

Effect of Accuracy of the Vapor Pressure
The parameterization of vapor pressure (p v ) of EG from Yaws (1994) is used in this study to calculate p v at 298 K (7.45 Pa). Furthermore, the parameterizations and experimental vapor pressure values for EG at 20°C and 25°C reported in the literature (Ambrose & Hall, 1981;Ethylene Glycol Product Guide, 2008;Hales et al., 1981;Yaws, 1994) were evaluated. The average predicted value of p v at 20°C is 7.50 Pa with RSD of 1.74%. The value of p v used in this study is 0.74% greater than the experimental value (7.4 Pa) (Hales et al., 1981) and À0.56% smaller than the average value calculated above. Therefore, the RSD of p v for EG at 20°C is set conservatively to be ±0.8% in this study. Because temperature suppressions during the evaporation process and the saturation fraction of vapor in the flowing gas (S) can be neglected, equation (14) is simplified as  (Erbil & Dogan, 2000) 9.07 × 10 À6b (Erbil & Dogan, 2000) 8.24 × 10 We have attempted to further constrain the best fit α M range by taking into account the interference from moisture and the effect of impurities. In Figures 5c and 5d, the fitted V g at 50 cm 3 /min is below the expected range (marked in light blue) when the fitted V g at the other two flow rates fall in their expected ranges. This phenomenon could perhaps arise from moisture interference from environment during EDB measurement. When the flow rate was set to be 50 cm 3 /min, the gas velocity of the flow surrounding the evaporating droplet was low. Moisture from the environment could possibly penetrate through the flow, and water vapor could be absorbed by the trapped droplet. Based on the hygroscopicity of EG (EG Product Guide, 2008), the mass percent of water in the droplet at equilibrium at low RH (<25%) is below 10%. Thus, the actual a solute in the measurement could be several percent lower than unity which is used in the fitting. Thus, according to equation (20), the ΔD 298 /D 298 presented here is underestimated by several percent. Correcting for moisture content would shift the ΔD 298 /D 298 -V g curve upward at 50 cm 3 /min.
The possible effect of impurities introduced from reagents must also be considered. When the radius of the evaporating EG droplet decreases from 22 μm to 10 μm, the concentration of impurities in the droplet would be expected to increase from <1% to <8% based on the reported purity of EG reagent (>99%). The existence of an impurity at this content level would suppress the evaporation rate of solute, leading to an underestimate of ΔD 298 /D 298 in Figure 5. This would suggest that the impact of impurities would act to shift the ΔD 298 /D 298 -V g curves upward, suggesting that our reported lower limits on α M should be considered very much as lower bounds on the value. Marek and Straub (2001) summarized that impurities (such as dissolved glass components, fatty acids, and surfactants) in water could cause a strong reduction in the observed evaporation coefficient of water. As the detailed composition of EG reagent is unknown, it is very challenging to estimate the effect of impurities further.  Tsuruta et al. (1994). Limited by the accuracies of D 298 for EG and V g in the EDB measurement, it is difficult to constrain the α M range further in this study. In Figures 5c and 5d, the fitted points of (V g and ΔD 298 /D 298 ) falling within the rectangle regions are all above the zero line (ΔD 298 /D 298 = 0). This indicates that the true value of D 298 might be a little higher than the present value used in this study.

Determination of α M for DEG
DEG evaporates much more slowly than EG under the same conditions, and its evaporation rate increases with gas flow rate, as shown in Figure 3b. Experimental data from two DEG droplets were processed. ΔD 298 /D 298 for DEG as a function of V g are reported in Figure 6 assuming that α M = 0.1, 0.2, 0.4, and 1. As described in section 3.4.1, V g at 50, 100, and 200 cm 3 /min should lie in the ranges of 0.84-1.47, 1.7-2.5, and 3.1-3.9 cm/s, respectively. As discussed in section 3.4.2, ΔD 298 /D 298 for DEG should lie in the range of À0.01 and 0.01 taking the proposed RSD value of experimental value of D 298 (u(D 298 )/D 298 ) from Lugg (1968). The acceptable ranges of (V g and ΔD 298 /D 298 ) at 50, 100, and 200 cm 3 /min are indicated by the rectangular regions in Figure 6. When α M equals 0.1, the curve obtained from fitting of experimental data does not cross the corresponding rectangle, as shown in Figure 6a. Thus, α M < 0.1 can be easily excluded.
In this work, the parameterization from DiEthylene Glycol Product Guide (2005) was used to estimate the vapor pressure (p v ) of DEG at 20°C (as shown in Table 1) and is 3% higher than the value predicted by Ambrose and Hall (1981). This would possibly introduce error in the fitted ΔD 298 /D 298 according to equation (20). The phenomenon caused by the moisture interference during measurement is also observed for DEG evaporating at 50 cm 3 /min, as shown in Figures 6b and 6c.  Figure 6b. This range is higher than previous experimental results (Jakubczyk et al., 2010) but consistent with later simulation and experimental results (Hołyst et al., 2013). If the accuracy of D 298 and p v for DEG could be improved, it would be possible to refine the range of α M .
4.3. Determination of α M for 1-Butanol 4.3.1. The Plausible Range of α M for 1-Butanol Experimental data of ten 1-butanol droplets beyond 1.5 s (total time of around 2.5 s) were processed, and the fitted ΔD 298 /D 298 as a function of trial V g are reported in Figure 7 assuming that α M = 0.1, 0.2, 0.4, and 1, respectively. Comparing with EG and DEG, the 1-butanol droplet evaporates much faster. Thus, the number of data points available for fitting is much less and the precision of the fitted ΔD 298 /D 298 for 1-butanol is worse. As described in section 3.4.1, V g at 50, 100, and 200 cm 3 /min should lie in the range of 0.84-1.47, 1.7-2.5, and 3.1-3.9 cm/s, respectively, while ΔD 298 /D 298 for 1-butanol should lie in the range of À0.011 and 0.011, taking the proposed RSD value of D 298 from Lugg (1968). The acceptable ranges of (V g and ΔD 298 /D 298 ) at 50, 100, and 200 cm 3 /min are marked by the rectangle regions with colors of light blue, light red, and gray, respectively, as shown in Figure 7. Values of the mass accommodation coefficient (α M ) less than 0.2 can be easily excluded according to Figures 7a and 7b.

Refinement of α M Range for 1-Butanol
The effect of temperature suppression caused by solvent evaporation, residual water or ethanol in the droplet, moisture interference in the gas phase, and impurities from reagents will be taken into account to refine α M range for 1-butanol.
As the solvents (ethanol and water) evaporate much faster than the solute and the resulting temperature suppression is severe, the droplet may not be able to recover fully on the experimental timescale to achieve a thermal equilibrium. These suggest that the actual T d in the measurement may be lower than the estimated It is difficult to determine exactly when the mole fractions of ethanol and water become very small; instead, data points beyond t fitted = 0.8, 1.0, and 1.5 s were only extracted from the evaporation profiles for fitting and the outcomes were compared. The obtained ΔD 298 /D 298 -V g curve shifts upward as t fitted decreases from 1.5 s to 0.8 s and the absolute variance is around 1% for 200 cm 3 /min, as shown in Figure 8. This might be attributed to the evaporation of residual solvents in the droplet. A larger t fitted was not chosen as less than 100 data points were extracted, and the precision of the fitted result became worse. The overall consequences of this comparison suggest that a value of α M = 1 becomes more consistent with the date as earlier parts in the evaporation are excluded from the fitting.  The predicted values of vapor pressure (p v ) of 1-butanol from different parameterizations (Munday et al., 1980;Schmeling & Strey, 1983;Riddick et al., 1986;Gregorowicz et al., 1987; http://ddbonline.ddbst.com/ AntoineCalculation/AntoineCalculationCGI.exe; Ahn & Liu, 1990;Dean, 1992;Yaws, 1994;Liley et al. 1999;Poling et al., 2008;Yaws, 2015) are not consistent and do not match the experimental values (Butler et al., 1935;Puck & Wise, 1946;Kemme & Kreps, 1969;Ambrose & Sprake, 1970;Gracia et al., 1992;Garriga et al., 2002) well, as shown in Figure 9. As described in section 2.1.2, the parameterization from Yaws (1994) was used to estimate p v for 1-butanol in this study. Experimental values of p v at 298 K obtained by other researchers (marked with circles) are 4.3% and 8.5% lower than the used value. Using the parameterization from Ahn and Liu (1990), the predicted value of p v at 298 K agrees well with the value from Haynes (2016). If this parameterization is used instead of Yaws's for fitting, the fitted ΔD 298 /D 298 would increase by 0.085 with respect to the value shown in Figure 7. The ΔD 298 /D 298 -V g curves would be shifted upward by 0.085 and beyond the rectangle region even when α M equals unity. This indicates that the value of p v at 298 K from Haynes (2016) might be lower than the true value.

Summary
It is confirmed that α M < 0.2 can be excluded. Taking into account the possible underestimation of fitted ΔD 298 /D 298 caused by thermal nonequilibrium and impurity during measurement, α M should be greater than 0.4. The proposed value of p v at 298 K from Haynes (2016) might be lower by several percent.

Determination of Diffusion Coefficient for Glycerol
As the reported values of α M for glycerol are greater than 0.34 (McFeely & Somorja, 1972) and even larger (Cammenga et al., 1977;Lednovich & Fenn, 1977), sensitivity analysis shows that the evaporation kinetics should be more sensitive to the diffusion coefficient than to α M . Therefore, measurements under only the commonly used condition of EDB (20°C, 200 cm 3 /min) were performed. Experimental data for two glycerol droplets were processed, and the 2-D contour of ΔD 298 /D 298 as a function of (α M and V g ) is reported in Figure 10. The fitting of  data of two glycerol droplets show that the standard deviation of fitted ΔD 298 /D 298 at given (α M andV g ) is less than 0.007. The parameterization of vapor pressure for glycerol from Cammenga et al. (1977) was used in this study and compared with that from Coker (2010). The relative difference between the predicted values of p v at 20°C from the two parameterizations is 0.73%, comparable with the absolute accuracy claimed in Cammenga et al. (1977).
As discussed before, V g at 200 cm 3 /min should lie in the range of 3.1-3.9 cm/s. When α M greater than 0.34 (McFeely & Somorja, 1972) is used as a constraint, the possible range of (α M and V g ) is marked by the black shaded box, as shown in Figure 10. The likely range of fitted ΔD 298 /D 298 is between À3% and 1%. If α M is constrained to have a value greater than 0.9 (Lednovich & Fenn, 1977), the possible range of (α M and V g ) is marked by the red rectangle with oblique line. The likely range of fitted ΔD 298 /D 298 is between À3% and À1%. We conclude that the RSD of D 298 should lie in the range of À3% and À1%, which is much better than the expected accuracy of the method from Chapman-Enskog theory (8 % (Bird et al., 2002)).

Conclusions
In order to accurately quantify the kinetics of mass transfer between the gas and condensed phases in aerosol, physicochemical properties of the gas and condensed phases as well as kinetic parameters are crucial for estimating mass fluxes over a wide size range. Comparing with physicochemical properties, the kinetic parameters such as mass accommodation coefficient/evaporation coefficient remain to be accurately determined. In this work, we aim to clarify the discrepancies in the reported values of evaporation coefficient (α M ) for 1-butanol, ethylene glycol (EG), and diethylene glycol (DEG) and improve the accuracy of diffusion coefficient for glycerol.
Simulations based on Liu model (Ahn & Liu, 1990) have been used to describe the heat and mass transfer at the evaporating droplet surface. We have first verified this model by comparing predictions for the evaporation of pure water droplets with measurements using the cylindrical electrode electrodynamic balance (EDB), along with a comparison with predictions from the Kulmala model (Kulmala et al., 1993). This demonstrates that Liu model is sufficiently accurate to describe the evaporation/condensation kinetics of compounds investigated in this work. The sensitivity of evaporation kinetics to the value of α M for 1-butanol has been evaluated using this approach. The evaporation rate increases with α M , and the experimental error envelop overlaps with simulations when α M is greater than 0.6, suggesting that this is an upper limit for determination using the EDB approach if all other quantities are known exactly. Clearly, uncertainties in the other physicochemical parameters further lower the accessible limit below which values of α M can be directly determined.
We report evaporation profiles of 1-butanol, EG, DEG, and glycerol droplets under well-determined conditions (gas flow rates and temperature) using the EDB technique with a time resolution of 10 ms. For singlecomponent organic droplets, the time-resolved radius recorded from experiments is fitted using Liu model with varying experimental conditions (e.g., gas velocity, V g ) and differing treatments of the key thermophysical properties (the evaporation coefficient, α M , the diffusion coefficient at 298 K). The fitted values of (α M , V g , and ΔD 298 /D 298 ) corresponding to the best agreement between model prediction and experimental data are obtained.
The uncertainties in the thermophysical and possible errors in experimental conditions were carefully evaluated. The calculated values of D 298 from different methods, including Wilke-Lee, Fuller, and Chapman-Enskog, in the literature and this work were evaluated and compared with experimental values. This comparison demonstrates that the experimental values from Lugg (1968) are accurate. The gas velocities (V g ) at three gas flow rates were evaluated based on previous studies, and the plausible ranges were obtained. With these constraints on the accuracy of D 298 and V g , the impossible range of α M could be easily excluded. The possible error in experimental conditions, such as moisture interference and impurities effect, was taken into account to refine the range of α M further. Results show that α M should be greater than 0.4 for EG. This range is beyond the result from Jakubczyk et al. (2010) and agrees with the result from Tsuruta et al. (1994). The fitted points of (V g and ΔD 298 /D 298 ) falling within the rectangle regions are all above the zero line (ΔD 298 /D 298 = 0), which indicates that the true value of D 298 might be a little higher than the present value used in this study. For DEG, α M should be greater than 0.2. This range is higher than previous experimental results (Jakubczyk et al., 2010) but consistent with their later simulation and experimental results (Hołyst et al., 2013). For 1-butanol, α M should be greater than 0.4, while the proposed value of vapor pressure at 298 K from CRC handbook might be lower by several percent. For glycerol, the likely range of fitted ΔD 298 /D 298 is between À3% and 1% when α M greater than 0.34 (McFeely & Somorja, 1972) is used as a constraint. If α M is constrained to have a value greater than 0.9 (Lednovich & Fenn, 1977), the likely range of fitted ΔD 298 /D 298 is between À3% and À1%. Therefore, the accuracy of D 298 is much improved comparing with the expected accuracy of the method from Chapman-Ensokog theory (8%) (Bird et al., 2002).