Measurement of Air-Water Transfer Velocities

Let us now analyze the information on air-water exchange velocities which has been gained from observations both in the field and in the laboratory. We are especially interested in those extreme situations which are either solely water-phase or solely air-phase controlled, since they allow us to separate the influences of the two phases. We start with the latter case, the air-phase-controlled exchange. 

Transfer Velocities in Air Deduced from Evaporation of Water 

Traditionally, water is used as the test substance for determining v,a. Its air-water partition constant at 25°C is A)a/w = 2.3 x 10 5, which is much smaller than Kac cal of Eq. 20-4. Thus, the exchange of water vapor at the air-water interface is solely controlled by physical phenomena in the air above the water surface. The flux of water into air (evaporation) is given by (see Eqs. 20-6, 20-7, 20-9a)  

In the experiments used to draw Fig. 20.2, wind speeds were measured at different heights above the water surface. Since wind speed generally decreases when approaching the water surface, these experiments can be compared only if we find a means to transform the wind speeds to a standard height (usually 10 m). Mackay and Yeun (1983) use the standard boundary layer theory with a roughness height of 0.03 cm and a wind stress coefficient of 1.5 x 10 3 to get  

To demonstrate the feasibility of extrapolating such laboratory results to the field, we use Eq. 20-15 to calculate the order of magnitude of the annual evaporation rates from surface waters. Let us assume a typical relative humidity of 80% (RH = 0.8), wind speeds between 0 and 15 m s 1, and a water temperature of 15°C. Water vapor saturation of air at 15°C is C tera= 12.8 x 10 6 g cm 3 (Appendix B, Table B.3). Thus, from Eq. 20-11  

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Calculate the total air-water transfer velocity, v/aAv, of 1,1,1-trichloroethane (methyl chloroform, MCF) and tribromomethane (bromoform, BF) at the surface of the ocean for a wind speed of 15 m s 1 measured 3 m above the water surface at seawater temperatures of 25°C and 0°C, respectively. 

Studies of the air-water gas exchange process by infrared imaging techniques enable local and fast measurements of the heat transfer velocity. Applying Schmidt number scaling, the obtained gas transfer velocities are consistent with mass balance methods and are in good agreement for the... 

Table 20.1 Various Empirical Relationships Between Wind Velocity Measured at Heigth z Above the Water, u7, and Air-Phase Transfer Velocity of Water , va, Deduced from Observations of Water Evaporation Rates b...

The wall-to-bed heat-transfer coefficient in a three-phase fluidized bed was measured by Ostergaard100 and Viswanathan et al.140 The first author measured the wall-to-bed heat-transfer coefficient in an air-water-glass ballotini (0.5-mm-diameter) system in a 7.62-cm-diameter bed. It was found that the heat-transfer coefficient was a strong function of gas velocity but a rather weak function of liquid velocity. Viswanathan et al.140 studied the wall-to-bed heat-transfer coefficient in a 5.1-cm bed of air, water, and quartz particles of 0.649- and... 

On the other hand Bao et al. (2000) reported that the measured heat transfer coefficients for the air-water system are always higher than would be expected for the corresponding single-phase liquid flow, so that the addition of air can be considered to have an enhancing effect. This paper reports an experimental study of non-boiling air-water flows in a narrow horizontal tube (diameter 1.95 mm). Results are presented for pressure drop characteristics and for local heat transfer coefficients over a wide range of gas superficial velocity (0.1-50m/s), liquid superficial velocity (0.08-0.5 m/s) and wall heat flux (3-58 kW/m ). 

Here Va and are the true velocities at the entrance, of gas and liquid, respectively, and do is the critical droplet diameter. The value of the Wee depends on the degree of shock at the entrance section e.g., for smooth liquid injection, 22 was used, and for tee entrances, 13 to 16. Collier and Hewitt (C6) also measured entrainment in air-water mixtures, and have extended the same correlation to much wider ranges, using We — 13 in the case of jet injection with the results shown in Fig. 9. Anderson et al. (A5), during mass-transfer studies in a water-air-ammonia system, found en-... 

The concentration term for DMS (S) is calculated using the mean of the average DMS concentrations found on cruises between April to September and is equal to 8.8 nmol DMS (S) H. Air concentrations are of the order of 3 nmol DMS (S) nr3 (1) and are assumed to be negligible, hence the concentration difference is equal to the mean DMS concentration in water. The transfer velocity, k, was calculated from the equations of Liss and Merlivat (14) using the mean wind speeds measured on board ship, which procedure yields a value of 15.4 cm h 1. Therefore DMS emission is equal to ... 

Both the heat and mass transfer coefficients are functions of air velocity. However, at air speeds greater than about 15 ft/s (4.5 m/s), the ratio h kgis approximately constant. The wet-bulb depression is directly proportional to the difference between the humidity at the surface and the humidity in the bulk of the air. In the wet- and dry-bulb hygrometer, the wet-bulb depression is measured by two thermometers, one of which is fitted with a fabric sleeve wetted with water. These thermometers are mounted side by side and shielded from radiation, an effect neglected in the derivation above. Air is drawn over the thermometers by means of a small fan. The derivation of the humidity from the wet-bulb depression and a psychrometric chart are discussed later. 

The primary variable that determines whether the controlling resistance is in the liquid or gas film is the H or Henry constant. As shown in Figure 5.15, and as is apparent from equation 39, for small values of H the water phase film controls the transfer, and for high values of H the transfer is controlled by the air phase film. Gas transfer conditions that are liquid film controlled sometimes are expressed in terms of thickness, Zw, of the water film. As indicated by equation 38, this can be done from a measured value of (or K,o,) and the diffusion coefficient of the substance Zw decreases with the extent of turbulence (current velocity, wind speed, etc.). Typical values for are in the range of micrometers for seawater, a few hundred micrometers in lakes and up to 1 nun in small wind-sheltered water bodies (Brezonik, 1994). 

The Radon Deficiency Method. This is based on determining the radioactive disequilibrium between Rn and its precursor, Ra [63]. Away from the air-sea and sediment-water interfaces, the two radioisotopes are generally in decay equilibrium. Deficiency of Rn activity in the surface mixed layer is due to loss of the gas to the atmosphere, and from this disequilibrium between nuclides a transfer velocity can be calculated. One requirement of this method is that winds be steady for several days - a condition that often is not met at sea. In addition, the method measures evasion rates only. 

An experimental stu% was performed to determine fee effect of small water droplets incorpmated into a single-phase stagnation-point flow on heat transfer. Steady state and transient cooling heat transfo erqieriments were carried out to analyze fee characteristics of single-phase and two-phase flows. PIV measurements were made for different air velocities to determine the characteristics of the flow. Water droplets size distribution was also measured. The following conclusions can be made fiom this study ... 

IS An air-water-vapor mixture, 1 std atm, 180 C, flows in a duct (wall temperature 180 Q at 3 m/s average velocity. A wet-bulb temperature, measured with an ordinary, unshielded thermometer covered with a wetted wick (9.5 mm outside diameter) and inserted in the duct at right angles to the duct axis, is-52 C. Under these conditions, the adiabatic-saturation curves of the psychromctric chart do not approximate wet-bulb lines, radiation to the wet bulb and the effect of mass transfer on heat transfer are not negligible, and the k-type (rather than F) mass-transfer coefficients should not be used. 

There is clearly a need to better measure and document mass transfer coefficients (MTCs) or velocities in the 41 individual processes described in this handbook. It would be very useful to have available compilations of MTCs for specific chemicals in specific environmental settings thus providing guidance as to the likely range of values. It is understandably difficult to measure MTCs in the highly variable natural environment, even for example, in a relatively simple system such as the water-air interface of a small lake. Complications result from thermal and meteorlogical variability and the presence of particles. These variables can be better controlled in the laboratory in wind-wave tanks but this introduces problems of scale, wind-driven currents, and fetch. What is needed are careful experimental measurements in both... 

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