Experimental Determination of the Diffusion Coefficient of Dimethylsulfide in Water

Estimates of the sea-to-air flux of dimethylsulfide (DMS) are based on sea surface concentration measurements and gas exchange calculations. Such calculations are dependent on the diffusivity of DMS (DDMs), which has never been experimentally determined. In this study the diffusivity of DMS in pure water was measured over a temperature range of 5ø-30øC. The measurements were made using a dynamic diffusion cell in which the diffusing gas flows over one side of an agar gel membrane and the inert gas flows over the other side. The diffusion coefficient can be estimated from either time dependent or steady state analysis of the data, with an estimated uncertainty of less than 8% (1 rr) in each measurement. A best fit to all the experimental results yields the equation DDM s (in cm2 sec = 0.020 exp (-18.1/RT), where R = 8.314 x 10 -3 kJ mole -1 K -(cid:127) and T is temperature in kelvin. The values of DDMS obtained in this study were 7-28% larger than estimates from the empirical formula of Hayduk and Laudie (1974) which has previously been used for DMS in gas exchange calculations. Applying these values to seawater results in an increase of less than 5% in the global oceanic flux of DMS.

where K is the gas exchange coefficient or piston velocity (expressed on a liquid or gas phase basis), C is the concentration in the liquid or gas phase, and a is the dimensionless solubility of the gas in seawater [Liss and Slater, 1974]. The gas exchange coefficient contains both liquid and gas phase components (k I and k a) as follows:

KI kl ak a
Experimental studies have shown that k a >> k I under natural conditions [Liss, 1973]. Therefore gas exchange is dominated by resistance in the liquid phase for slightly soluble gases. This is also the case for DMS, which has intermediate solubility in water. It has also been demonstrated experimentally that k I is dependent on the diffusivity of the diffusing gas D with a functional form of k I =f(Sc -n) =f(D n) where n may vary from 1/2-2/3 depending on the sea state [Liss and Merlivat, 1986 In this study we experimentally determine the diffusion coefficient for DMS, compare the measured and calculated values, and discuss the implications for the global flux of DMS. We also determined the diffusion coefficient of methane in order to evaluate systematic errors introduced by the experimental apparatus and to compare our results to diffusivities reported in the literature for other gases.

EXPERIMENTAL METHOD
The experimental approach used in this study is a variation on the method of Barter [1941], and the apparatus was modified from the design of Jiihne et al. [1987a]. The diffusion cell consists of a stainless steel housing with two chambers on either side of an aqueous gel membrane (Figure l a). At the onset of the experiment, a flow of DMS in nitrogen is introduced on the ::high-concentration" side of the membrane (referred to as chamber 1), while pure nitrogen flows on the "low-concentration" side of the membrane (referred to as chamber 2). The experiment consists of measuring the ratio of the DMS concentrations in the gas flows from each chamber as a function of time from the start of the experiment or after equilibration of the membrane. In this section we briefly discuss the use of diffusion theory to model the experimental results and describe the experimental procedure.

16,481
l where I is the membrane thickness, C• and C2 are the concentrations at x -0 and x = 1, respectively, and Co is the concentration in the sheet at t -0, which is assumed to be uniform throughout the sheet.

Measuremen t
As described above, the experimental quantity of interest is the ratio of the gas flux through the "low-concentration" surface of the membrane to the gas concentration at the "high-concentration" side of the membrane. This is given by el) c2f2 •'• = Claa A (lO) where cI) is the flux out of the membrane, C2a and C la are the gas phase concentrations on either side of the membrane, f2 is the gas flow on the low-concentration side of the membrane, a is the dimensionless Ostwald coefficient for DMS in water (ratio of aqueous phase to gas phase concentration), and A is the cross-sectional area of the membrane.
The experimental apparatus is shown in Figure 1 b. The cell is immersed in a stirred, thermostated water bath which was varied at 5 ø intervals from 5 ø to 30øC over the course of the experiments. The nitrogen gas supplies were passed through glass-fritted bubblers immersed in the water bath to saturate them with water vapor prior to entering the cell. The temperature of the cell was monitored using a thermocouple sensor placed in a well drilled near the center of the cell. DMS was introduced into chamber 1 by passage over a small glass bulb containing liquid DMS (purity >99%, Aldrich, Milwaukee, Wisconsin). The concentration on this side of the cell is therefore slightly undersaturated with respect to pure DMS. For methane runs, the glass bulb was removed, and the pure gas (purity 99.0%, Liquid Carbonic, Chicago, Illinois) was introduced into the bubbler in place of the nitrogen. Gas flow rates of 10 cm3 min-• and 20 cm 3 min-• were used on the high-and low-concentration sides of the membrane, respectively, during the experiments. The membrane is an agar gel (0.5%) which is 3.8 cm in diameter and approximately 0.6 cm thick. Agarose gels have been used in many previous studies of diffusion through a liquid membrane [Schantz and Lauffer, 1962;Spalding, 1969;Langdon and Thomas, 1971]. Jiihne et al. [1987a] compared gas diffusion through agarose gels to wetted frit diaphragms. Their results demonstrated agreement between the two methods, with more reproducible results from the gels. This is presumably because convective or other turbulent motion is inhibited in the gels. Two small corrections must be accounted for when calculating aqueous diffusion coefficients from measurements made in gel membranes. The first is the reduction of solubility of the diffusing gas due to the lowering of the activity of water. Second, there is a hindrance to the diffusion path due to the formation of a three-dimensional network not found in pure water. Langdon and Thomas [1971] estimated that both effects reduce the diffusion coefficient for a substance through a gel in comparison to pure water by 1.36% for a 0.5% gel.
The gel in our apparatus rests directly on a sheet of porous polytetrafluoroethylene filter membrane 0.13 mm thick with mean pore size 10-20/am (Zitex, Norton Company, Wayne, New Jersey). The sheet is supported by a porous polyethylene sheet 1.59 mm thick with mean pore size 15-45 tam (X-4900, Porex Corporation, Fairburn, Georgia). The porosity of both sheets is sufficiently large that they make a negligible contribution to the resistance of the membrane to gas diffusion. The gel is cylindrical in shape, but for a small portion of its total length the gel diameter is slightly increased by the presence of a small (0.79 mm x 0.40 mm) groove machined in the cell wall. This groove provides friction for the gel to prevent it from sliding upward in the event of a slight pressure gradient between the two sides during setup. The presence of a groove of these dimensions has a negligible effect on the diffusion of gases through the cell, as demonstrated by Barrer et al. [1962].
The gel thickness used in each experiment was calculated from the gel weight and the known diameter of the cell. The gel density was determined experimentally to be 0.992 g cm -3 (ltr = 0.05%) at 25øC. The uncertainty involved in determining the gel thickness has two components. The first is the uncertainty in the physical measurement of the thickness, which is largely due to the uncertainty in the determination of the density of the gel. The second results from the loss of some of the gel to evaporation during the course of the experiment, which was greatest at the higher temperatures. The combined uncertainty in the measured thickness is less than 5%. For steady state calculations the latter uncertainty was removed through the measurement of the gel thickness at the conclusion of the experiment. Temperature (degrees C)

Data Analysis
There are two approaches to calculating the diffusion coefficient from the experimental data. The first is simply to allow the experiment to run until the membrane approaches a steady state condition, that is, constant flux. In this case,  Table 1.
The diffusivities reported in this paper include only the steady state values. The steady state proved to be more reproducible than the time-resolved diffusivities. The timeresolved method provided confirmation that the experiment was proceeding correctly and that the gel was intact during the experiment. Both the steady state and time-resolved diffusivities have been corrected for the gel effects discussed earlier. Each value was increased by a factor of 1.36% [Langdon and Thomas, 1971].

Methane
In order to test the reliability of our technique we first  Rackett [1970] and modified by Spencer and Danner [1972]. This value for the molar volume is slightly different from that previously used to estimate DDM s in the gas exchange literature (73.96 cm 3 mole-I), which was taken from the density at 20øC [Bates et al., 1987;Andreae, 1990]. Figure 4 demonstrates that the diffusivities obtained in this study are larger than those predicted by Wilke and Chang [1955] and Hayduk and Laudie [1974]. A discrepancy of 7-28% is observed between this study and the Hayduk-Laudie study. The magnitude of the disagreement with the Wilke-Chang results depends on the value of the association factor chosen. Hayduk and Laudie, using a larger data set, recommended an adjustment of the association factor for water from 2.6 to 2.26. The diffusivities calculated using this new association factor are 12-20% lower than this study, but the values obtained using the original association factor are only 6-14% lower. Another difference is the temperature dependence of the diffusivities. As expected, the Wilke-Chang correlation gives a better agreement with the temperature dependence observed in this study than the Hayduk-Laudie correlation. The results for methane were similar, with the Wilke-Chang expression using the original association factor providing the best agreement of the three estimations with the data from this study.
The diffusion coefficients determined in this study were measured using gels made with pure water. A correction is needed in order to apply these results to seawater for the calculations of the sea-to-air flux of DMS. Jiihne et al.
[1987a] measured the diffusivities of H2 and He in pure water and 35.5%0 NaC1 gels and found the diffusivities in NaC1 to be lower by 6%. We made a similar comparison for methane, which is much closer in molar volume and diffusivity to most gases of atmospheric interest. Three runs made with a 35%0 NaC1 gel at 15øC gave a mean D CH4 of 1.47 x 10 -5 (lcr = 0.02 x 10-5), and the four pure water 15øC runs (shown in Figure 3) gave a mean of 1.53 x 10 -5 (lcr = 0.02 x 10-5). These results suggest that DCH 4 in seawater is 3.9 + 1.4% lower than that in pure water, a difference which is significant at the 98% confidence level according to the t test [Havilcek and Crain, 1988]. This factor was used to calculate DDM S in seawater. We obtained the appropriate Schmidt numbers for diffusion of DMS in seawater using the kinematic viscosity, v (in cm2 sec-•) of seawater as a function of temperature. The kinematic viscosity (viscosity/ density) is calculated using the viscosity of seawater from Millero [1974] and the density of seawater from Millero and Poisson [1981]. The resulting Schmidt numbers are given in Table 2 for the temperature range 5ø-30øC. A least squares third-order polynomial fit to the data gave the equation $c-2674.0-147.12t + 3.726t 2-0.038t 3 (15) where t is temperature (in degrees Celsius). The mean estimated uncertainty of this fit is 0.27% (1 or).
In previous global flux studies [Bates et al., 1987;Erickson et al., 1990;Andreae, 1990] the diffusivity of DMS has been estimated using molar volume and viscosity in the Hayduk- Laudie correlation. Despite the large differences between those estimates and the experimentally determined diffusivities (7-28%), the global flux of DMS is not greatly affected.
Since the square root of the diffusivity is used in the flux calculation, the global flux should increase on the order of 4-5%. A correction to the global flux estimate of these studies cannot be made with only a single calculation, because the difference in diffusivity is temperature dependent. The correction must be made for the flux at individual locations and then factored into the global flux estimate.

SUMMARY
In this study the diffusion coefficient of DMS in pure water was experimentally determined in order to provide a basis for sea-to-air gas exchange calculations. The measured diffusivities agree reasonably well with empirical estimates, with the closest agreement provided by the Wilke and Chang [1955] correlation using the original solvent association factor. Diffusivities calculated using the Hayduk and Laudie [1974] expression, which are commonly used in the gas exchange literature, were lower than the experimental results by 7-28%, depending on the temperature. Using the measured diffusivities results in an increase in the global DMS sea-to-air flux estimate of approximately 5%. The diffusivities are used to derive a set of Schmidt numbers for DMS in seawater which are recommended for use in gas exchange calculations.