Turbulence Effects on Volatilization Rates of Liquids and Solutes

Environ. Sci. Technol. 2004, 38, 4327-4333

Turbulence Effects on Volatilization Rates of Liquids and Solutes J I U N N - F W U L E E , * ,† H U A N - P I N G C H A O , † C A R Y T . C H I O U , * ,‡ A N D M I L T O N M A N E S §,| Graduate Institute of Environmental Engineering, National Central University, Chung-Li, Taiwan 320, Republic of China, U.S. Geological Survey, Box 25046, MS 408, Denver Federal Center, Denver, Colorado 80225, and Department of Chemistry, Kent State University, Kent, Ohio 44242

Volatilization rates of neat liquids (benzene, toluene, fluorobenzene, bromobenzene, ethylbenzene, m-xylene, o-xylene, o-dichlorobenzene, and 1-methylnaphthalene) and of solutes (phenol, m-cresol, benzene, toluene, ethylbenzene, o-xylene, and ethylene dibromide) from dilute water solutions have been measured in the laboratory over a wide range of air speeds and water-stirring rates. The overall transfer coefficients (KL) for individual solutes are independent of whether they are in single- or multi-solute solutions. The gas-film transfer coefficients (kG) for solutes in the two-film model, which have hitherto been estimated by extrapolation from reference coefficients, can now be determined directly from the volatilization rates of neat liquids through a new algorithm. The associated liquidfilm transfer coefficients (kL) can then be obtained from measured KL and kG values and solute Henry law constants (H). This approach provides a novel means for checking the precision of any kL and kG estimation methods for ultimate prediction of KL. The improved kG estimation enables accurate KL predictions for low-volatility (i.e., low-H) solutes where KL and kGH are essentially equal. In addition, the prediction of KL values for high-volatility (i.e., high-H) solutes, where KL = kL, is also improved by using appropriate reference kL values.

Introduction Volatilization from water into the atmosphere is important to the environmental fate of organic chemicals. Up to now, the critical effects of air and water flows on volatilization rates remain to be further understood. According to the conventional two-film volatilization model (1), the interface between bulk liquid and air is bounded by a stagnant transition film on each side, across which the solute moves by diffusion (2, 3). The respective film thicknesses depend on turbulence intensities in the respective phases. The solute concentrations in bulk liquid (usually water) and air phases are considered to be essentially uniform, and thus the combined diffusive transport through the two stagnant films constitutes the principal volatilization resistance. The liquid* Authors to whom correspondence should be addressed. Phone: +886-3-422-6742 (J.-F.L.); (303)236-3967 (C.T.C.). E-mail: jflee@ ncuen.ncu.edu.tw (J.-F.L.); [email protected] (C.T.C.). † National Central University. ‡ U.S. Geological Survey. § Kent State University. | Present address: Amberson Towers (#412), 5 Bayard Rd, Pittsburgh, PA 15213. 10.1021/es0353964 CCC: $27.50 Published on Web 07/08/2004

 2004 American Chemical Society

film and gas-film transfer resistances of a solute are related to the respective mass transfer coefficients, the latter being defined as

J ) kL(Cl - C/l ) ) kG(C/g - Cg)

(1)

where J is the (solute) volatilization flux (mass/area-time); kL is the liquid-film transfer coefficient (length/time); kG is the gas-film transfer coefficient (length/time); Cl is the concentration in the bulk liquid (mass/volume); C/l is the concentration at the liquid side of the interface (mass/ volume); C/g is the concentration at the gas side of the interface (mass/volume); and Cg is the concentration in the bulk air (mass/volume). The kL and kG in eq 1 cannot in general be individually determined because C/l and C/g cannot be measured; the respective values have been estimated by extrapolation from reference coefficients. With the assumption that C/g ) HC/l , where H is the dimensionless Henry’s law constant, eq 1 can be expressed (3-7) as

J ) KL(Cl - Cg/H) = KLCl

(2)

with

KL )

kLkGH kL + kGH

(3)

where KL is the liquid-phase-based overall solute transfer coefficient and Cg/H is the solute concentration in the liquid phase corresponding to Cg in bulk air; the latter term is usually neglected for all vapors except for those (e.g., water vapor) that exist in significant amounts in air. In the case of water evaporation, Cg expresses the air humidity. Equation 3 can be expressed alternatively as

1 1 1 ) + KL kL kGH

(4)

where 1/KL is the overall transfer resistance across the liquidair interface, the sum of the liquid-film resistance (1/kL) and the gas-film resistance (1/kGH). For any given system, kL depends presumably only on stirring (or turbulence) in the liquid phase, and kG depends only on air speed in the gas phase. In extreme cases where 1/kL . 1/kGH, KL approximates kL; conversely, if 1/kL , 1/kGH, then KL approximates kGH. Hitherto the kL and kG have been estimated via empirical correlations. A popular, simple correlation form is that derived on the assumption that the kL or kG of a solute is inversely proportional to the square root of its molecular weight (3, 5-7), namely

kL ) kRL (MR/M)1/2

(5)

kG ) kRG(MR/M)1/2

(6)

and

where kRL and kRG are the respective liquid-film and gas-film transfer coefficients of the reference substances at specified system settings; MR and M are the respective molecular weights of the reference substance and the solute. The measured kL of oxygen and the kG of water have frequently been employed as the respective kRL and kRG for estimating the kL and kG values of solutes under the same turbulence VOL. 38, NO. 16, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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conditions (3, 5-7). However, the precision of eqs 5 and 6 (or other correlation forms) has not yet been substantiated experimentally. In this study we introduce a novel approach, outlined below, to determine directly the kG values of solutes. The associated kL can be obtained from measured KL and kG and solute H by eq 4. The determined kL and kG then allow one to validate the kL and kG estimation methods and provide improved references for estimating the KL values of other solutes under the same overall conditions.

Theoretical Considerations According to Chiou et al. (8, 9), there exists an effective vapor pressure P* for a solution component (say, the solute) immediately above the liquid surface, which corresponds to C/g in eq 1 (i.e., C/g ) P*M/RT, where M is the solute molecular weight and R is the gas constant). The steady-state value of P* (or C/g) for the solute depends in principle on the bulkliquid concentration Cl and the system turbulence intensity. It can be determined by comparing the volatilization flux J of the solute (by eq 2) with the corresponding flux (Jo) of the pure liquid under the same turbulence condition, i.e.,

P*/Po ) C/g/Cog ) J/Jo

(7)

where Po is the saturation vapor pressure and Cog ) PoM/RT is the corresponding vapor concentration of the liquid at temperature T (K). The solute kG can thus be determined as

kG ) J/C/g ) Jo/Cog

(8)

Having determined the kG for a solute with eq 8, one can estimate it for others using the β concept introduced earlier (8, 9) by

kG ) β

RT (2πM )

1/2

(9)

where β (,1) is an empirical factor that accounts for the efficiency of a vapor moving into air at a given setting relative to that into vacuum (where β ) 1) (10, 11). The usefulness of β is that, as will be shown, it is nearly constant for different substances at a given air turbulence level. The associated solute kL can then be obtained through eq 4 from the measured KL and solute H. The dependence of kG on M-1/2 in eq 9 turns out to be the same as that given by eq 6. From eqs 8 and 9 along with C/g ) HC/l and C/l ) RCl, the vapor flux of a solute can be expressed as

RT (2πM )

1/2

J ) Rβ

HCl ) KLCl

(10)

compound

M

H

benzene toluene ethylbenzene o-xylene ethylene dibromide m-cresol phenol

78.1 92.1 106.2 106.2 187.9 108.1 94.1

0.225 0.274 0.357 0.216 2.06E-2 1.60E-5 1.60E-5

a M ) molecular weight; H ) dimensionless air-water Henry’s law constant at 25 °C. Henry’s law constants for benzene, toluene, ethylbenzene, o-xylene, and ethylene dibromide from Mackay and Shiu (12), and those for m-cresol and phenol from Verscheren (13).

phase resistance is greater than the gas-phase resistance, and if R is > 0.5, the opposite holds. For poorly volatile (low-H) solutes, where only kGH is important (i.e., KL = kGH), kG can in principle be estimated with high accuracy from the measured KL, if the solute H is known. However, accurate KL determinations for such solutes are usually time-consuming. Therefore, characterization of β (or kGM1/2) values with pure volatile liquids of known Po or Cog provides a convenient and a priori means to derive kG for various solutes under given turbulence conditions. Similarly, for highly volatile (high-H) solutes, where only kL is important (i.e., KL = kL), kL can be estimated with high accuracy from the measured KL. However, those systems that render accurate estimation of kG are not well-suited for accurate estimation of kL; conversely, systems amenable to accurate estimation of kL are not well-suited for accurate estimation of kG. Significant solute depletion (i.e., R < 1) at the water-air interface usually occurs for highly volatile solutes in poorly stirred solutions (8, 9). For those solutes, water stirring raises R (or kL) and thus enhances KL. For poorly volatile solutes, no significant solute depletion will develop between bulk water and interface (i.e., R = 1); therefore KL should be largely independent of water stirring. The model outlined by eqs 7-12, which provides an essential link between the volatilization of a pure liquid and that of the same substance as a solute, is referred to as the surface-depletion rate-limiting (SDRL) model. As noted with eqs 3, 11, and 12, the SDRL model is mathematically equivalent to the two-film model. Whereas the two-film model is widely accepted, it has yet to be subjected to extensive experimental tests. In this study the KL and respective kGH and kL values for a variety of solutes of high and low volatilities (or H values) have been determined over a wide range of air speeds and water-stirring rates in closely controlled laboratory systems.

Experimental Section

with

KL ) Rβ

RT 2πM

( )

1/2

H ) RkGH

(11)

where KL is as defined earlier and R ) C/l /Cl (e1) characterizes the extent of solute depletion at the liquid surface. Solving eq 1 for C/l /Cl (i.e., R) with C/g ) HC/l and Cg = 0, one arrives at

R)

kL kL + kGH

(12)

From eqs 11 and 12, one notes that kGH ) KL/R and kL ) KL/(1 - R). At R ) 0.5 (i.e., C/l ) 0.5 Cl), kL and kGH are equal (i.e., the transfer resistance in the liquid phase (1/kL) is equal to that in the gas phase (1/kGH)). If R is < 0.5, the liquid4328

TABLE 1. Selected Organic Solutes for Volatilization Studies and Their Propertiesa

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Compounds listed in Tables 1 and 2 (purity >98%) for volatilization measurements, either as neat liquids or as solutes from water, were purchased from Fluka Co. and used as received without further treatment. The experiments were conducted in the laboratory, with the layout shown in Figure 1. A glass dish of 8.0 cm in diameter and 4.0 cm in height was used to hold the neat liquid or the water solution. The liquid or solution depth in the dish was maintained at about 2.2 cm, with the volume being ca. 100 mL. During the experiment, the relative humidity of the ambient air ranged between 85 and 90%. Volatilization fluxes of neat liquids (Jo) were measured at room temperature (26-28 °C) by weight loss against time under different air speeds and liquid-stirring rates, the latter intended to correct for the effect of liquid stirring on the effective air speed. Measurement periods varied between 5

TABLE 2. Measured β × 104 Values (by eqs 8 and 9) for Pure Liquids at Room Temperature (26-28 °C) under Various Air Speeds without Applied Stirringa liquid

0 m/s

0.2 m/s

0.5 m/s

0.8 m/s

1.0 m/s

2.0 m/s

4.0 m/s

6.0 m/s

benzene fluorobenzene toluene ethylbenzene m-xylene o-xylene bromobenzene o-dichlorobenzene 1-methylnaphthalene average standard deviation (SD) 95% t-test confidence

0.178 0.233 0.190 0.196 0.172 0.191 0.192 0.211 0.205 0.196 0.018 0.014

1.89 2.11 1.92 2.06 2.07 2.03 2.10 2.15 2.39 2.08 0.14 0.114

2.52 2.56 2.52 2.55 2.58 2.58 2.86 2.92 3.06 2.68 0.21 0.161

3.39 3.40 3.45 3.59 3.56 3.45 3.47 3.50 3.76 3.51 0.12 0.091

3.99 4.05 4.06 4.04 4.09 4.09 4.16 4.12 4.33 4.10 0.10 0.077

5.16 5.24 4.97 5.36 5.19 5.34 5.22 5.46 5.62 5.28 0.19 0.148

8.12 7.91 8.14 8.29 8.72 8.55 8.23 8.22 9.51 8.41 0.48 0.375

10.4 11.1 9.90 10.2 10.7 10.0 11.1 11.4 12.5 10.8 0.82 0.64

a β ) (2πM/RT)1/2(Jo/Co), where Joand Co are values at liquid temperatures (T). The respective liquid temperatures at selected air speeds of 0, g g 0.2, 1.0, 4.0, and 6.0 m/s are as follows: benzene, 24.8, 21.2, 19.8, 17.5, and 16.8 °C; fluorobenzene, 24.8, 21.8, 20.3, 18.1, and 17.6 °C; toluene, 25.2, 23.8, 21.6, 20.1, and 19.6 °C; ethylbenzene, 25.8, 25.2, 24.3, 23.1, and 22.7 °C; m-xylene, 25.6, 25.0, 24.3, 23.2, and 23.1 °C; o-xylene, 25.6, 25.1, 24.5, 23.5, and 23.2 °C; bromobenzene, 25.4, 25.2, 24.5, 23.8, and 23.6 °C; o-dichlorobenzene, 25.3, 25.0, 24.5, 23.9, and 23.6 °C; and 1-methylnaphthalene, 25.3, 25.2, 25.0, 24.8, and 24.6 °C.

FIGURE 1. Apparatus for volatilization experiments. min and 4 h, depending on the liquid and turbulence setting. Because of evaporative cooling, the fluxes were measured after the liquids reached stable temperatures (usually within 1 min) (i.e., the kG (or β) values were determined using the liquid temperatures and related vapor densities by eqs 8 and 9). A mercury thermometer with its head dipped about 1 cm below the liquid surface was used to monitor liquid temperatures, which showed varying decreases below the room temperature (see Table 2). With a shallow liquid depth (ca. 2.2 cm), the temperature gradient within the liquid was assumed insignificant. Volatilization rates from water solution at various turbulence settings were measured for selected solutes that cover a large range in Henry’s law constant (H) (Table 1). Included are solutes with very low H (m-cresol and phenol), moderately high H (ethylene dibromide), and relatively high H (BTEX: benzene, toluene, ethylbenzene, o-xylene). A series of single-, binary-, and multi-solute solutions were made up with these individual solutes. The solutions were maintained at 25 °C by keeping the vessel in a water bath. Under high air speeds (4.0 and 6.0 m/s), the solution temperature was corrected for a small evaporative cooling (1-2 °C). Initial concentrations were set around 10 mg/L for each solute, and successive decreases with time under experiments were monitored; the solution levels (L) either remained or

were maintained nearly constant (ca. 2.2 cm). The data were used in a first-order plot to determine the volatilization halflife (t1/2). The solute volatilization coefficient (KL) was calculated from

KL ) 0.693L/t1/2

(13)

For high-H solutes with short half-lives (mostly 4 h), the levels were kept nearly fixed by replenishing the evaporative loss of water at hourly intervals. With high ambient humidity, the water loss was relatively small. A mixing blade (1.5 cm wide and 6 cm long) was used to produce various stirring rates, ranging from 0 to 100 rpm. On the basis of the liquid volume and blade dimension, the velocity gradients (G) at given rpm values (14) were calculated (see Appendix A in Supporting Information). At 0, 20, 50, and 100 rpm, as set, the calculated G values are 0, 31, 121, and 344 s-1, respectively. A blower (Hitachi, 0.33 kW) connected to a variable-speed controller (Siemens Ltd) was used to generate a range of air speeds that were measured at a height of 4-5 cm above the liquid surface with a portable anemometer (Sato Keiryoki Mfg. Co., model SK-73D). This height was near the center of the wind span and close to the VOL. 38, NO. 16, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 3. KL (cm/min), kL (cm/min), kGH (cm/min), and r Values of m-Cresol from Its Binary-Solute Solutions with Phenol at 25 °C under Various System Settings and Respective Average β h Values for Pure Liquidsa stirring

KL

r

0 rpm 20 rpm 50 rpm 100 rpm

1.15E-4 1.43E-4 1.62E-4 2.12E-4

1.01 1.04 1.05 1.08


1.16E-3 1.24E-3 1.37E-3 1.46E-3

0.959 0.976 0.979 0.986

FIGURE 2. Dependence of (average) β on air speed (data from Table 2). The error bars are for one standard deviation (SD). Where the error bars are not shown, the SD values are smaller than the symbol sizes.


2.76E-3 3.16E-3 3.30E-3 3.43E-3

0.902 0.916 0.922 0.930

liquid surface so that the effect of air speed on surface stirring could be closely evaluated. The air speed could be controlled accurately from 0.20 to 6.0 m/s. To analyze solute concentrations in water, 1-mL aliquots of the solution were removed and extracted with 1 mL of carbon disulfide. Solute recoveries (by extraction with carbon disulfide) were g90% for benzene, toluene, ethylbenzene, o-xylene, and ethylene dibromide; about 70% for m-cresol; and 50% for phenol. Since only relative concentrations were needed for determining solute KL values, the low recoveries with m-cresol and phenol were inconsequential. The extracted samples were analyzed by GC using a Hewlett-Packard model 5890A gas chromatograph equipped with a FID detector. A packed column with 5% sp-1200/1.75% Bentone on 100/120 Supelcoport, 6 ft × 1/4 in. × 2 mm, was used for solute separation.


4.29E-3 4.40E-3 4.59E-3 4.76E-3

0.879 0.893 0.898 0.905


5.22E-3 5.67E-3 5.76E-3 6.19E-3

0.833 0.872 0.886 0.874

β h × 104

kGH

0.196((0.018) 0.237((0.013) 0.264((0.008) 0.338((0.008)

1.14E-4 1.38E-4 1.54E-4 1.96E-4

kL

Air Speed ) 0 m/s -0.0115 -3.58E-3 -3.24E-3 -2.65E-3

Air Speed ) 0.2 m/s

Results and Discussion We first consider the effect of air speed on the kG or β values of neat liquids (R ) 1), where kG is the only transfer coefficient affecting the volatilization rate. In this case, the use of eqs 8 and 9 for neat liquids enables the determination of kG or β. The observed β values for nine unstirred organic liquids, as listed in Table 2, increase with increasing air speed over the settings of 0, 0.2, 0.5, 0.8, 1.0, 2.0, 4.0, and 6.0 m/s. The average value for the nine liquids at zero air speed, β h ) 1.96 × 10-5 (SD ) (0.18 × 10-5), agrees closely with β h ) 1.98 × 10-5 (SD ) (0.19 × 10-5) derived with 16 organic liquids and water at zero air speed in the earlier study (8). The relation between β and air speed is shown in Figure 2. The vapor pressures of liquids (Po) required for β determination are taken from the literature (15). A correction of Po for temperature drops caused by evaporative cooling was applied. At air speeds g0.5 m/s, the relation between β and air speed is practically linear with a positive β intercept. Below 0.5 m/s, β is more sensitive to the air speed and the relation is nonlinear. However, the measured β values for all liquids at fixed air speeds are highly consistent despite that the Po values vary by almost 2 orders of magnitude. The high invariance of β (or kGM1/2) between vapors, in confirmation of eq 6, suggests that the transport of vapor molecules above the liquid surface is mediated by diffusion through a thin boundary layer, the thickness of which depends on the bulk airflow rate. In all likelihood a minimum stream velocity is necessary to achieve a steady state of the vapor transport. As a consequence, an increase in air speed increases the β value, with the sharpest increase occurring between 0 and 0.2 m/s air speeds, presumably as the system goes from a 4330

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0.0283 0.0517 0.0652 0.104

2.08((0.14) 2.19((0.11) 2.41((0.17) 2.55((0.13)

1.21E-3 1.27E-3 1.40E-3 1.48E-3

Air Speed ) 2.0 m/s 0.0282 0.0376 0.0423 0.0490

5.28((0.19) 5.95((0.29) 6.18((0.23) 6.37((0.25)

3.06E-3 3.45E-3 3.58E-3 3.69E-3

Air Speed ) 4.0 m/s 0.0355 0.0411 0.0450 0.0501

8.41((0.48) 8.49((0.51) 8.80((0.63) 9.06((0.60)

4.88E-3 4.93E-3 5.11E-3 5.26E-3

Air Speed ) 6.0 m/s 0.0313 0.0443 0.0505 0.0491

10.8((0.82) 11.2((0.96) 11.7((1.11) 12.2((0.92)

6.27E-3 6.50E-3 6.79E-3 7.08E-3

a The k values in k H are obtained from eq 9 using the listed average G G β h values of the nine neat liquids (those in Table 2) measured at same air speeds and stirring rates as applied to the solutions. The H values are from Table 1. At given air speeds, small increases in solute kGH (or β h ) with water stirring reflect the effects of stirring on the effective air speeds. With KL and kGH determined, R is obtained by eq 11 and kL is obtained by eq 4. The stirring rates of 0, 20, 50, and 100 rpm correspond to the velocity gradients (G) of 0, 31, 121, and 344 s-1, respectively.

nearly stagnant to a steady state. The constancy of β values at fixed air speeds offers a great advantage in estimating the kG values of poorly volatile chemicals (by eq 6 or eq 9) where direct measurements of their vapor fluxes become difficult because of their low vapor pressures. We evaluate next the KL, kL, and kGH data of low-H m-cresol and phenol, as binary solutes, under various air speeds and stirring rates. The m-cresol data are listed in Table 3, and the phenol data are given in Table S-1 in Supporting Information. For both solutes, one finds that 1/kGH . 1/kL or KL = kGH (i.e., the major transfer resistance is in the air phase). Considering that these two solutes have virtually the same H but phenol has a lower molecular weight (Table 1), the somewhat higher KL values for phenol (by 5-7%) than for m-cresol agree well with the molecular weight dependence of kG in eqs 6 and 9. As anticipated for low-H solutes, the R values are close to 1 in most settings, except those (0.830.90) under high air speeds (4 and 6 m/s). The negative kL values for some systems are artifacts from the small inaccuracy of the KL and kGH data, which causes R to slightly exceed 1 (by eq 11). For low-H solutes (with R = 1), accurate kL can be achieved only with very accurate KL and kGH; however, since 1/kGH . 1/kL, the inaccuracy of kL has little effect on KL. The KL values of m-cresol (or phenol) are sensitive to air speed but are essentially independent of liquid stirring, as expected. For example, in unstirred solutions, the KL increases about 45 times when the air speed increases from 0 to 6 m/s, which is close to that (i.e., 55 times) for pure liquids (where R ) 1) over the same range of air speed. The small difference is attributed to the experimental error and to the R values being somewhat less than 1 under high air speeds. A small

TABLE 4. KL (cm/min), kL (cm/min), kGH (cm/min), and r Values of Benzene from Its Binary-Solute Solutions with m-Cresol at 25 °C under Various System Settingsa r

stirring

KL


9.5E-3 0.0503 0.0752 0.120


kL

kGH

Air Speed ) 0 m/s 5.05E-3 0.0221 0.0297 0.0370

9.5E-3 0.0514 0.0775 0.125

0.0145 0.0521 0.0796 0.122

Air Speed ) 0.2 m/s 7.29E-4 2.48E-3 3.45E-3 4.98E-3

0.0145 0.0522 0.0799 0.123

20.0 21.0 23.1 24.5


0.0256 0.0527 0.0840 0.123

Air Speed ) 2.0 m/s 5.05E-4 9.23E-4 1.42E-3 2.01E-3

0.0256 0.0527 0.0841 0.123

50.7 57.1 59.3 61.1


0.0351 0.0553 0.0886 0.129

Air Speed ) 4.0 m/s 4.35E-4 6.79E-4 1.05E-3 1.48E-3

0.0351 0.0553 0.0887 0.129

80.7 81.5 84.5 87.0


0.0444 0.0559 0.0882 0.134

Air Speed ) 6.0 m/s 4.27E-4 5.18E-4 7.88E-4 1.14E-3

0.0444 0.0559 0.0883 0.134

1.88 2.28 2.53 3.24

FIGURE 3. Dependence of m-cresol KL on water-stirring rate and air speed (data from Table 3).

104 108 112 117

a See footnotes in Table 3 for calculations of k , k H, and R values. L G See also the pure-liquid β h values in Table 3 for calculations of the kG values.

increase in KL with increasing stirring at a given air speed results essentially from the effect of stirring-enhanced air turbulence (i.e., the increased β h ) on kGH (see Table 3). In this study, the volatilization of water (the solvent) was greatly suppressed by the high ambient humidity (85-90% RH), which could explain the small surface depletion for m-cresol (or phenol) when it volatilized with enhanced rates at high air speeds (whereas, by volatilizing into relatively dry air, the solution of m-cresol and water might be enriched in m-cresol at the liquid surface because of the resulting high water-loss rate). We now turn to the KL, kL, and kGH data of benzene (high H) and m-cresol (low H) as binary solutes in water. The results for m-cresol (not shown) are similar to those in Table 3, the differences generally being within (5% of the averages. In contrast with the m-cresol data, one finds for benzene that 1/kL . 1/kGH or KL = kL under all turbulence settings (i.e., virtually all the flow resistance is in the liquid phase (R , 1)). Moreover, except for unstirred solutions, benzene kL (or KL), which increases monotonically with stirring rate, is essentially independent of air speed. For the unstirred systems, benzene KL increases with increasing air speed, but the effect is less than that produced by stirring at 20 rpm (G ) 21 s-1) with zero air speed. The result reflects a small effect of surface stirring on kL by the flow of air under no applied stirring. Finally, the kL data for benzene are much more consistent than the respective data for m-cresol. This is because the accuracy of kGH is not critical to kL for benzene. Comparing the data in Tables 3 and 4, one sees that the relative effects of air speed on kG are similar for benzene and m-cresol and that the relative effects of water stirring on kL are also of the same order, although the calculated kL values for m-cresol are less precise. Evidently, it is the wide disparity in H between the two solutes that accounts for the difference in volatilization behavior; stirring makes little difference to the volatilization of m-cresol (low H), and air speed has little

FIGURE 4. Dependence of benzene KL on water-stirring rate and air speed (data from Table 4). to no influence on the volatilization of benzene (high H). The sharply contrasting effects of air speed and of water stirring on the KL values of m-cresol and benzene are depicted in Figures 3 and 4. In a related study, the KL values of benzene and m-cresol as single solutes have also been determined (not shown); they are practically the same as for the mixture systems, indicating that the volatilization processes of dilute solutes from a multicomponent system are mechanistically independent (16). For multiple high-H solutes, the individual KL values and their responses to turbulence should be similar because virtually all the flow resistance is in the liquid phase (i.e., KL = kL) and because kL is presumably not strongly dependent on the molecular weight (eq 5). The results for BTEX, presented in Table S-2 in Supporting Information, are in keeping with this expectation. The relative KL (or kL) values of BTEX follow approximately the molecular weight dependence of kL given by eq 5. The benzene KL values from the BTEX solution are comparable with those in Table 4, the differences being generally within (6% of the averages. The similar KL values for BTEX and their similar responses to the VOL. 38, NO. 16, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 5. KL (cm/min), kL (cm/min), kGH (cm/min), and r Values of EDB from Its Single-Solute Solutions at 25 °C under Various System Settingsa stirring

r

KL

kL

kGH

6.61E-3 0.0344 0.0691 0.0899

0.111 0.135 0.150 0.192


Air Speed ) 0 m/s 6.24E-3 0.0562 0.0274 0.203 0.0473 0.315 0.0612 0.319


0.0100 0.0316 0.0523 0.0752

Air Speed ) 0.2 m/s 8.48E-3 0.0255 0.0382 0.0519

0.0101 0.0324 0.0544 0.0793

1.18 1.24 1.37 1.45


0.0286 0.0374 0.0595 0.0799

Air Speed ) 4.0 m/s 6.00E-3 7.76E-3 0.0119 0.0155

0.0288 0.0377 0.0602 0.0812

4.77 4.82 5.00 5.14

a See footnotes in Table 3 for calculations of k , k H, and R values. L G See also the pure-liquid β h values in Table 3 for calculations of the kG values.

applied turbulence conform to the characteristics of high-H solutes. The volatilization data of ethylene dibromide (EDB) as a single solute provide a further check on the validity of the model, because EDB has a much higher molecular weight and a significantly lower H than BTEX (see Table 1). It is observed that KL = kL or 1/kL . 1/kGH for EDB with most turbulence settings (Table 5), except under zero air speed with stirring at 50 rpm (G ) 121 s-1) and 100 rpm (G ) 344 s-1), where 1/kL is only about 2-3 times 1/kGH. For most systems, the KL values of EDB are about 40% lower than those of benzene, which, as illustrated below, agree well with the prediction. With the measured KL values for a number of solutes, one can now examine the accuracy of KL predicted via estimated kL and kGH. The kG-β correlation (eq 9), together with H, enables one to estimate the kGH. This approach is particularly helpful for poorly volatile solutes (e.g., m-cresol) when direct kG determinations pose problems. To estimate the kL, we use benzene kL data in Table 4 as the kRL values and employ eq 5 as the correlation method. As illustrated elsewhere (5, 7), an alternative correlation for kL in terms of solute diffusion

coefficients yields comparable results. The kGH values estimated with (average) β h values of the pure liquids (Table 3) are the same as the measured kGH. Here the estimation of kG from β h is more straightforward and less prone to errors than when achieved by using water kG as the reference. This is because acquisition of accurate water kG data requires careful correction of water evaporation for ambient humidity, which may be difficult in some situations. Furthermore, the extrapolation of water kG to solute kG may introduce additional uncertainties. Using the estimation method as described, the predicted KL for toluene, ethylbenzene, and o-xylene from their respective estimated kL and kGH are in good agreement with the measured KL (not shown). Similarly, the predicted KL for m-cresol and EDB (see Table 6) agree well with the experimental KL (see Tables 3 and 5). As illustrated by the BTEX data, when solute H values are sufficiently high (i.e., when KL = kL), the KL values are essentially independent of H but depend primarily on solute diffusion coefficients in the liquid phase, as accounted for by the (MR/M)1/2 term in eq 5. For m-cresol and phenol, the close agreement stems from the improved kGH estimation by eq 9 and the condition that KL = kGH. The satisfactory agreement for EDB further supports the model estimation for KL, because the 1/kGH values of this solute at 50 and 100 rpm stirring under zero air speed (Table 5) also contribute significantly to the resulting KL. These findings suggest that the assumed dependences of kL and kG on molecular weights in eqs 5 and 6 are reasonably accurate. Additional rate data from solutes with comparable kL and kGH would provide a further test on the validity of eqs 5 and 6. In conclusion, the present study shows that (i) the twofilm model and the (equivalent) SDRL model account well for the volatilization rates of a variety of solutes over a wide range of turbulence conditions; (ii) with the aid of the SDRL model, the individual kL and kG can now be determined directly for validation of the estimated values; (iii) the individual solutes in multi-solute systems volatilize independently; and (iv) the use of neat-liquid and referencesolute volatilization data improves the estimation of kL and kG for other solutes.

Acknowledgments We thank the associate editor for suggesting the use of velocity gradient to quantify water turbulence. The use of trade, product, or firm names in this paper is for descriptive

TABLE 6. Estimated KL(est) Values, Based on Estimated kL(est) and Calculated kGH Values, for m-Cresol and EDB at 25 °C under Various System Settingsa m-cresol stirring

kLB

kL(est)


9.5E-3 0.0514 0.0775 0.125

8.07E-3 0.0437 0.0659 0.106


0.0145 0.0522 0.0799 0.123


0.0351 0.0553 0.0887 0.129

kGH

EDB

KL (est)

kL(est)

kGH

KL(est)

Air Speed ) 0 m/s 1.14E-4 1.12E-4 1.38E-4 1.38E-4 1.54E-4 1.53E-4 1.96E-4 1.96E-4

6.14E-3 0.0332 0.0501 0.0807

0.111 0.135 0.150 0.192

5.78E-3 0.0266 0.0376 0.0568

0.0123 0.0443 0.0679 0.105

Air Speed ) 0.2 m/s 1.21E-3 1.10E-3 1.27E-3 1.24E-3 1.40E-3 1.37E-3 1.48E-3 1.46E-3

9.37E-3 0.0337 0.0516 0.0795

1.18 1.24 1.37 1.45

9.30E-3 0.0328 0.0497 0.0754

0.0298 0.0470 0.0753 0.110

Air Speed ) 4.0 m/s 4.88E-3 4.19E-3 4.93E-3 4.46E-3 5.11E-3 4.79E-3 5.26E-3 5.02E-3

0.0227 0.0357 0.0573 0.0833

4.77 4.82 5.00 5.14

0.0266 0.0355 0.0567 0.0820

a The reference benzene k B values are taken from Table 4. The m-cresol k H data are from Table 3, and the similar EDB data are from Table L G 5. The units for kLB, kL, kGH, and KL are all in cm/min.

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purposes only and does not imply endorsement by the U.S. Government.

Supporting Information Available Text showing velocity-gradient calculations and two tables showing phenol and BTEX volatilization data. This material is available free of charge via the Internet at http:// pubs.acs.org.

Literature Cited (1) Whitman, W. G. Chem. Metal. Eng. 1923, 29, 146-148. (2) Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: London, 1970. (3) Liss, P. S.; Slater, P. G. Nature 1974, 247, 181-184. (4) Cohen, Y.; Cocchio, W.; Mackay, D. Environ. Sci. Technol. 1978, 12, 553-558. (5) Schwarzenbach, R. P.; Gschwend, P. M.; Imboden, D. M. Environmental Organic Chemistry; Wiley: New York, 1993; Chapter 10. (6) Rathbun, R. E.; Tai, D. Y. Environ. Sci. Technol. 1987, 21, 248252.

(7) Rathbun, R. E. Am. Soc. Civil Eng., J. Environ. Eng. 1990, 116, 615-631. (8) Chiou, C. T.; Freed, V. H.; Peters, L. J.; Kohnert, R. L. Environ. Int. 1980, 3, 231-236. (9) Chiou, C. T.; Kohnert, R. L.; Freed, V. H.; Tonkyn, R. G. Environ. Int. 1983, 9, 13-17. (10) Langmuir, I. Phys. Rev. 1913, 2, 329-342. (11) Knudsen, M. Ann. Phys. 1915, 47, 697-708. (12) Mackay, D.; Shiu, W. Y. J. Phys. Chem. Ref. Data 1981, 10, 11751179. (13) Verscheren, K. Handbook of Environment Data on Organic Chemicals, 3rd ed.; Wiley: New York, 1996. (14) Tchobanoglous, G.; Burton, F. L. Wastewater Engineering: Treatment, Disposal and Reuse, 3rd ed.; McGraw-Hill: Singapore, 1991; Chapter 6. (15) Weast, R. C.; et al. Handbook of Chemistry and Physics, 68th ed.; CRC Press, Inc.: Boca Raton, FL, 1988. (16) Chiou, C. T.; Manes, M. Environ. Sci. Technol. 1980, 14, 12531254.

Received for review December 15, 2003. Revised manuscript received May 2, 2004. Accepted June 2, 2004. ES0353964

VOL. 38, NO. 16, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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Turbulence Effects on Volatilization Rates of Liquids and Solutes

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