esm222_13_14

esm222_13_14 - ESM 222 Rate-Limited Mass Transfer...

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1 © Arturo A. Kel er ESM 222 Rate-Limited Mass Transfer Between Phases 2 © Arturo A. Kel er Rate-Limited Mass Transfer ± Equilibrium conditions are valid when ± the volumes of the various phases are relatively small ± in experimental conditions ± surface area of the phases in contact is large relative to the volume of one of the phases ± raindrops falling through the atmosphere 3 © Arturo A. Kel er Rate-Limited Mass Transfer ± In many cases, equilibrium conditions do not occur, because a certain amount of time is needed to transfer mass between the phases. ± In some cases (e.g. sorption of pollutants to the soil), we assume that the groundwater flow is so slow that equilibrium conditions are nearly achieved. 4 © Arturo A. Kel er Rate-Limited Mass Transfer ± Mass-transfer limitations are also important when considering the transfer of gases (e.g. O 2 , CO 2 ) from the atmosphere to a water body. ± Examples: ± slow transport of CO 2 from the atmosphere to the deep oceans (centuries) ± O 2 to a river or lake which has become depleted due to excessive biological activity 5 © Arturo A. Kel er Air-Water Exchange ~1 mm ~ 0.1 mm Source: Schwarzenbach et al., 1993 6 © Arturo A. Kel er Air-Water Exchange ± Mixing of a pollutant in the bulk of the phase (e.g. in atmosphere, river or shallow lake) may be fast if there is significant flow and turbulence ± Mixing in the bulk phase is slow when flow is slow and without turbulence (e.g. groundwater), or the bulk phase is very large (e.g. deep lakes or oceans)
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7 © Arturo A. Kel er Air-Water Exchange ± Reduced mixing in the boundary layers due to: ± too much friction at the boundary, ± difficult to form currents in either the air or the water ± surface tension reduces movement of water molecules in boundary 8 © Arturo A. Kel er Air-Water Exchange ± What drives the molecules from one phase to the other? ± Thermodynamic equilibrium ± Molecules of pollutant go from high concentration (polluted phase) to low concentration (“clean” phase) 9 © Arturo A. Kel er Air-Water Exchange ± The limiting step for mass transfer from one bulk phase to the other bulk phase is the movement through the two layers ± Several models exist to describe this “rate-limiting” step. We will discuss the stagnant two-film model. 10 © Arturo A. Kel er Air-Water Exchange ± Stagnant Two-Film Model ± Molecules move through each boundary layer mostly by diffusion ± Diffusion is the random movement of molecules (Brownian motion) due to their interactions ± At the interface, we have equilibrium conditions 11 © Arturo A. Kel er Stagnant Two-Film Model Source: Schwarzenbach et al., 1993 12 © Arturo A. Kel er Stagnant Two-Film Model ± Movement of mass from one phase to another is measured as a flux ± mass moving per unit area per unit time ± Flux through the water phase is: F w = -D w (C w/a -C w ) z w D w = diffusivity in water, z w = thickness of film
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13 © Arturo A. Kel er Stagnant Two-Film Model ± Similarly, the flux of pollutant through the air phase is: F a = -D a (C a -C a/w ) z a ±
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esm222_13_14 - ESM 222 Rate-Limited Mass Transfer...

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