Adrian Matei edited observations.tex  about 10 years ago

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Molecular diffusion for subsurface bubbles is an important feature for gas transfer, because it actually reduces the transfer velocity of gases. If the molecular diffusion through bubble walls is higher, then the number of available bubbles at the surface, which can organize in foam patches, is smaller. If the foam patches contain gases with low solubility, they become void fractions. There is a relation between void fractions and interstitial water, which involves the transfer velocity. Interstitial water is the area, at sea surface, unaffected by the disruption of surface tension. Its characteristic si that it surrounds the bubbles, and it has an influence on the total gas transfer rate. For highly insoluble gases, the capacity of the interstitial water may be smaller than that of the bubbles even for small void fractions \cite{en_Liddicoat_Baker_et_al__2007}. This is called restriction of gas transfer in a dense isolated plume "suffocation". \par  High subsurface bubbles molecular diffusion inhibits the buoyancy of bubbles and, hence, the vertical upward velocity of bubbles. In this sense, the Wolf model (2006) shows that there is a higher gas transfer for low Schmidt number, $Sc$, therefore subsurface lower molecular diffusion, $D$, generates more gas available at the surface, hence a higher transfer rate. Schmidt number describes the capacity of molecular difussion through the bubble's wall. According to Wolf (2006), the Schmidt number is equivalent to molecular difussion $W$, and it can be found in the following mathematical relation:   \begin{equation}   {K}_{b} = {Sc}^-x{\alpha}^-y, {Sc}^{-x}{\alpha}^{-y},  \end{equation} where ${K}_{b}$ is a contribution to the transfer velocity between the main air or gas and water reservoirs and it only depends on the partial equilibrium of a bubble during its lifetime. Low Schmidt number means higher upward vertical velocity for subsurface bubbles (because of low molecular difussion), therefore more bubbles are available for surfacing. Wolf model assumes two cases for the transfer velocity: one without void fraction and the other with 20 \% void fraction. It can be noticed that the transfer velocity is reduced at low Schmidt number with 20 \% void fraction present. Correlation between observed gases with different solubilities and bubble size distribution would give an insight on what type of fluxes, from the chemical point of view, are more likely to be enhanced. The presence of void fractions assumes that gas is trapped at the surface, therefore the transfer velocity is suppressed. Considering this phenomenon, one can correlate void fraction with whitecap time decay and, therefore, with transfer velocity in low winds, because in high winds condition, this phenomenon might not be so relevant. The reason is because, during high winds regime, high wind stress fragments the bubbles, so gas transfer is enhanced. \par  \section{Parameterizations and correlations}