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The two-film model is often used to describe the volatilization of organic substances from water. This model assumes uniformly mixed water and air phases separated by thin films of water and air in which mass transfer is by molecular diffusion. Mass-transfer coefficients for the films, commonly called film coefficients, are related through the Henry's law constant and the model equation to the overall mass-transfer coefficient for volatilization. The films are modeled as two resistances in series, resulting in additive resistances.
The two-film model and the concept of additivity of resistances were applied to experimental data for acetone and t-butyl alcohol. Overall mass-transfer coefficients for the volatilization of acetone and t-butyl alcohol from water were measured in the laboratory in a stirred constant-temperature bath. Measurements were completed for six water temperatures, each at three water mixing conditions. Wind-speed was constant at about 0.1 meter per second for all experiments. Oxygen absorption coefficients were measured simultaneously with the measurement of the acetone and t-butyl alcohol mass-transfer coefficients. Gas-film coefficients for acetone, t-butyl alcohol, and water were determined by measuring the volatilization fluxes of the pure substances over a range of temperatures. Henry's law constants were estimated from data from the literature. The combination of high resistance in the gas film for solutes with low values of the Henry's law constants has not been studied previously.
Calculation of the liquid-film coefficients for acetone and t-butyl alcohol from measured overall mass-transfer and gas-film coefficients, estimated Henry's law constants, and the two-film model equation resulted in physically unrealistic, negative liquid-film coefficients for most of the experiments at the medium and high water mixing conditions. An analysis of the two-film model equation showed that when the percentage resistance in the gas film is large and the gas-film resistance approaches the overall resistance in value, the calculated liquid-film coefficient becomes extremely sensitive to errors in the Henry's law constant. The negative coefficients were attributed to this sensitivity and to errors in the estimated Henry's law constants.
Liquid-film coefficients for the absorption of oxygen were correlated with the stirrer Reynolds number and the Schmidt number. Application of this correlation with the experimental conditions and a molecular-diffusion coefficient adjustment resulted in values of the liquid-film coefficients for both acetone and t-butyl alcohol within the range expected for all three mixing conditions. Comparison of Henry's law constants calculated from these film coefficients and the experimental data with the constants calculated from literature data showed that the differences were small relative to the errors reported in the literature as typical for the measurement or estimation of Henry's law constants for hydrophilic compounds such as ketones and alcohols.
Temperature dependence of the mass-transfer coefficients was expressed in two forms. The first, based on thermodynamics, assumed the coefficients varied as the exponential of the reciprocal absolute temperature. The second empirical approach assumed the coefficients varied as the exponential of the absolute temperature. Both of these forms predicted the temperature dependence of the experimental mass-transfer coefficients with little error for most of the water temperature range likely to be found in streams and rivers.
Liquid-film and gas-film coefficients for acetone and t-butyl alcohol were similar in value. However, depending on water mixing conditions, overall mass-transfer coefficients for acetone were from two to four times larger than the coefficients for t-butyl alcohol. This difference in behavior of the coefficients resulted because the Henry's law constant for acetone was about three times larger than that of
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Application of the two-film model to the volatilization of acetone and t-butyl alcohol from water as a function of temperature