Bubble Gas Transfer
- Unbroken Surface
- Bubbles
- Dynamic Equilibrium
Unbroken Surface
When disequilibrium conditions (determined by Henry's Law) exist for a gas between its gaseous phase and aqueous concentration, gas transfer occurs. The concentration gradient drives a gas flux according to the equation:
with the gas invading if P>C/H and evading for the opposite conditions. Clearly the system will tend towards equilibrium as determined by Henry's Law for each gas. Thus one gas can be invading while a second gas is evading. Probably the best introductory discussion on the thin film model, of which all other models of gas transfer (except surface renewal) are based is provided in Liss, 1973.
Bubbles
Due to the La Place pressure (a result of surface tension on a curved surface), and hydrostatic pressure (from the weight of the water), the bubble's internal pressure is greater than atmospheric. As a result, bubbles in a system in Henry's Law equilibrium will invade gas. Thus in the presence of bubbles, equilibrium occurs at a slight supersaturation.The effect of surface tension on residence time is only important for bubbles smaller than 100 micrometers.
The time evolution of a bubble is described by a series of coupled differential equations that describing the time variation of bubble pressure, radius, depth, and molar content as the bubble rises. From this, the flux (or gas transfer) of the bubble can be calculated at any time. The equation describing the mass transfer is
The other equations are in Leifer and Patro (2002) and the system of equations can be solved numerically. An example of model output is shown in the following figure.
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| Time evolution of molar content, radius and depth of a 500 micrometer clean bubble from 22 m. |
As CH4 outflows the bubble shrinks, increasing the La Place pressure; however, as the bubble rises the hydrostatic pressure decreases. The situation is complicated further by the presence of oxygen (O2) and (N2) in the water which inflow simultaneously. The 500 micrometer bubble shown dissolved and thus after ~25 seconds, the air that had just inflowed the bubble was forced to outflow by the more rapidly outflowing methane. When a bubble dissolves, the total gas transfered becomes purely dependant upon the initial gas composition and the solubility coefficient. Diffusivity only affects how long it takes the bubble to dissolve. In this case, that happeded after ~200 s and after rising only ~5 m.
Another effect of the finite bubble volume (other than the possibility of dissolution) is that the flux tends towards zero as the bubble equilibrates; however, since the hydrostatic pressure continues to decrease as the bubble rises, a gas that initially outflowed may inflow at shallower depths.
Let us first consider gases with an atmospheric source.
Dynamic Equilibrium
Because of the overpressure, gases outflow the bubble even under conditions where the net flux through the air-water interface is zero. As a result, the concentration of the gases in the bubble build towards a supersaturation equilibrium concentration. This concentration is determined by the effects of bubble "pumping" or invasion of the water due to bubble gas outflow and evasion (loss) through the air-water interface due to non-bubble gas exchange. Thus the system approaches a "dynamic" equilibrium where invasion and evasion balance. There are many complexities in the bubble contribution. At dynamic equilibrium, large bubbles outflow gas (gas invasion) while small bubbles inflow gas (gas evasion). The transition size between inflowing large bubbles and outflowing small bubbles depends upon all the many factors that affect the fate of a bubble including the bubble depth-size distribution, as well as factors that affect the bubble parameterizations like surfactants and temperature. Since the bubble gas exchange rate varies between gases (i.e., diffusivity) a bubble may have a net inflow of one gas and outflow of another. In other words, the transition radius between inflowing and outflowing bubbles is gas dependant.
If the air-water exchange rate was infinitely fast, dynamic equilibrium would be the same as the normal equilibrium determined by Henry's Law (solubility). Instead, the gas concentration builds up to a supersaturation where the gas flux from the bubbles into the water is equivalent to loss through the interface. The concept of dynamic equilibrium is important for several reasons:
- The asymmetery in the gas exchange rate for invasion and evasion in the presence of bubbles arises because the gas transfer rate is referenced to Henry's Law equilibrium rather than the dynamic equilibrium.
- Many processes require a net flux of gas into (or out of) the water. Aeration of water in a sewage treatment plant or fish pond, are two examples. By considering the mechanisms responsible for creating dynamic equilibrium, greater efficiency can be achieved.
- In the ocean (or any large body of water), not only is there loss at the air-water interface, but there is also loss (diffusion) to the bulk ocean. For bubble plumes from breaking waves, the source is dispersed, thus loss is primarily due to vertical diffusion (up into the air and down within the mixed layer.
The discussion of dynamic equilibrium naturally leads into another complexity of bubble gas transfer, local saturation.
Local saturation
Not only does bubble-mediated gas transfer lead to local supersaturation (Dynamic equilibrium), but the local saturation causes a feedback effect, decreasing the gas transfer rate. This is simply because by increasing the concentration, C, in the bubble plume, the driving force decreases.
Hydrocarbon seeps represent a line source of gases that due to the hydrostatic pressure are significantly above saturation (as determined by the atmospheric composition). As a result, there is a continuous flux of gas into the ocean. This gas then primarily diffuses laterally, i.e., similar to the previous discussion. And as above, the water concentration becomes locally elevated relative to the bulk ocean, which decreases gas outflow. This has the effect of allowing the bubble to retain more of its methane to a shallower depth. In a sense, one can consider the hydrocarbon gases in the bubble the same as the air gases for the purposes of this discussion.
Let us now consider gases with an oceanic source. These include many trace gases, and for the case of hydrocarbon seep bubbles, air.
Oceanic source gases
For gases with an oceanic source, e.g., dimethyl sulfide, or in some regions, carbon dioxide, the dynamic equilibrium is below saturation. As mentioned above, not only do the bubbles outflow air due to the overpressure, but bubbles inflow gases that are below the concentration in the bubble. Thus dynamic equilibrium involves a subsaturation rather than a supersaturation. In this case, bubbles remove gas from the water (stripping) which at dynamic equilibrium is balanced by bubble injection of the gas and diffusion across the interface.
For hydrocarbon seeps, this means the removal of air gases from the water. The inflow of air into the rising seep bubbles from the plume water is replaced by diffusion from the surrounding bulk water.
