## Mass Flux and Transfer Velocity KL

The mass flux j (mass per time and interfacial area) of any gas between the atmosphere and a water body is generally defined by the following equation:

where C is the average gas concentration in the water body, Cs the saturated gas concentration, and KL the overall transfer velocity. Cs is defined by Henry's law which states that at thermodynamic equilibrium in a two-phase system, the saturated concentration Cs of a dissolved gas in the liquid phase is proportional to the partial pressure p of the gas in the gas phase, Cs = p/Hc, where Hc denotes Henry's constant.

The overall transfer velocity KL is controlled by a complex interaction between molecular and turbulent processes on either side of an air-water interface. Generally, the turbulent motions greatly enhance the transport rate. At the water surface, however, any turbulent transport has to vanish as turbulent structures cannot penetrate the air-water boundary. Consequently, in the region adjacent to the boundary, gases must diffuse molecularly leading to a strong transport resistance.

For gas-transfer processes across the air-water interface, it is crucial whether additive surfactants are present at the surface on the liquid side. For clean surfaces, the overall transfer velocity KL is typically related to the individual gas-transfer coefficients (kL and kg for the liquid and gas phase, respectively), in a resistance-in-series model

c kg

Equation [2] shows that the ratio kL/Hckg controls which one of the two components dominates the overall transfer velocity. For small values of kL/Hckg the resistance on the liquid side controls the transfer process, whereas resistance on the air side controls the transfer when the ratio is large. If the ratio has a value near 1 then processes on both liquid and gas side are important. Oxygen as well as other environmentally important gases such as N2, CO2, or CO have a low solubility. Such gases have a high Henry constant Hc and thus the transfer across an air-water interface is controlled by the hydrodynamic conditions on the liquid side as depicted in Figure 1. The figure illustrates how the dissolved gas concentration in the deeper bulk region is fully mixed by the turbulent motions and the gas transfer is governed by an extremely thin aqueous boundary layer, which is typically only tens to hundreds of microns thick.

Bulk region

Depth z (unsealed)

Figure 1 Diagram depicting the gas transfer problem. The gas transfer is controlled by a complex interaction between molecular diffusion and near-surface turbulence. Note that for low-soluble gases the gas concentration boundary layer (CBL) on the liquid side controls the process and is only tens to hundreds of microns thick.

Bulk region

Depth z (unsealed)

Figure 1 Diagram depicting the gas transfer problem. The gas transfer is controlled by a complex interaction between molecular diffusion and near-surface turbulence. Note that for low-soluble gases the gas concentration boundary layer (CBL) on the liquid side controls the process and is only tens to hundreds of microns thick.

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