The Rate of Air-Sea CO2 Exchange: Chemical Enhancement and Catalysis by Marine Microalgae.

Chapter 4: Design and Principles of Steady-State-Tank

4.1 A holistic experiment achieved by a steady-state method?

From the early investigations reported in the previous chapter, it was concluded that an all-in-one "holistic" experiment was required, in which CO2 air-water exchange is measured directly in seawater containing a bloom of actively photosynthesising marine algae. This is necessary, because direct measurements of carbonic anhydrase taken from algal cultures seawater samples, would not in themselves tell us how much enzyme would be present at the top of the sea-surface microlayer, and how much it would catalyse air-sea CO2 exchange.

However, such an experiment had never been done before because it is difficult to measure the air-water CO2 flux whilst CO2 is simultaneously being taken up or released by algae. If I tried to estimate the CO2 flux (and hence the transfer velocity) based on measurements of changing water pCO2, the signal to noise ratio would be small due to chemical buffering by the alkaline seawater, and it would probably not be possible to determine the small variations in transfer velocity which might be caused by chemical enhancement and biological catalysis.

Therefore it would be better to measure changes in the air pCO2 in a closed headspace. The simplest way to do this would be to perturb the air pCO2 and then observe its rate of return to "equilibrium" with the water. However, the water pCO2 would also be changing during this reequilibration, both due to gas exchange and due to photosynthesis and respiration, so many measurements would still be needed from each phase. Moreover, if the water pCO2 is a major factor influencing the gas exchange rate (as predicted by theory and borne out by the results of this work), this would add a further complication to analysis of the results.

An alternative approach is to construct a tank with several separate gas-tight headspaces, all exchanging gases with the same body of water such that there is a net flux of CO2 into the water from one headspace and out of it from another. Thus it should be possible to balance the air-water fluxes and the biology (on a short timescale) such that the change in pCO2 of the water is negligible during the course of the transfer velocity measurement. A third "equilibrium" headspace could be used to measure the pCO2 of the water, and thus no water-phase pCO2 measurements would be needed.

A plan view of such a steady-state tank with four headspaces is shown in figure 4-1 . All the headspaces are in contact with the same body of water, which must be well mixed. The pCO2 in one headspace is greater than that of the water, while the pCO2 in another headspace is less than that of the water, such that the two air-water fluxes roughly balance.

To measure the gas exchange, you need to know only the flow rate of air entering each headspace, the pCO2 of air entering and leaving each headspace in steady state, and the pCO2 of the water. The latter should not change significantly during the timescale of achieving the steady state, so it can be measured from another "equilibrium" headspace.

4.2 Advantages and disadvantages of the steady -state method.

Listed below are some useful features of the steady-state design, which led to the decision to develop this idea further and construct such a tank.

The chief drawback of the steady-state method is that it is more complicated to design and construct such a tank with multiple headspaces. The lid had to be removable to allow access, but a gas-tight seal had to be made with all of the walls dividing the headspaces. Each headspace also had to be stirred independently. Therefore it took a long time (about five months) to have the tank designed and built by the workshop. It also took several more months to develop the temperature control, appropriate air and water stirring systems ( Section 4.7 ), and a reliable supply of continuously flowing air with a constant but adjustable pCO2 ( Section 5.7 ). However, at the early design stage we did not know how long it would take to get the whole system going! Another problem is that the steady state method is not appropriate for low- solubility inert trace gases, as will be demonstrated below ( Section 4.5 ).

In retrospect, it might have been easier to use a simpler tank with only one headspace, making gas exchange measurements by following reequilibration after perturbation of air pCO2, combined with continuous automated pCO2 measurements saved automatically onto the computer attached to the LiCOR pCO2 analyser. A sophisticated computer programme could then have been written to analyse such large datasets and compute the gas exchange compensating for various estimated biological fluxes and chemical buffering effects. However, as we did not have the LiCOR analyser until after the tank was complete, the full potential of such an automated system was not recognised at the early design stage.

4.3 Principle of steady-state CO2 gas exchange calculation

Figure 4-2 shows the basic principle of such a measurement for any one headspace.

The formula for calculating the transfer velocity is derived as follows. Firstly, symbols and units are given in the table below.




Transfer Velocity k m s-1
Water Surface Area A m2
Flux F mol s-1
CO2 concentration (water) [CO2] mol m-3

Flow rate

f m3 s-1
Atmospheric Pressure p Pa (=kg m-1 s-2 )

Partial Pressure of CO2

pCO2 parts per million (dimensionless)
Temperature T K
Gas Constant


kg m2 s-2 K-1 mol-1
dimensionless solubility


(mol l-1water / mol l-1 air)    


mol kg-1 atm-1

In Steady-State the Flux (F) into the water must be the difference between the amount of CO2 entering and leaving the headspace. Applying the gas law pV = nRT gives :

F = f * p * ( pCO2in - pCO2out ) / RT

As explained in Section 1.2.1 , the transfer velocity (k) can be defined as:

k = (F / A) / ([CO2]air - [CO2]water)

[CO2]air is the concentration of CO2 in the water at the top of the water-surface microlayer, whereas [CO2]water is the concentration in the bulk water. Both of these can be derived from the pCO2 measured in the gas-exchange and equilibrium headspaces respectively, using the solubility K0 given by Weiss (1974) (see Section 1.2.2 , Section 6.2 ).

[CO2]air = ( 1 / 103.5 ) * K0 * p * pCO2out

[CO2]water = ( 1 / 103.5 )* K0 * p * pCO2eq

(the factor 1 / 103.5) converts mol kg-1 atm-1 to mol m-3 Pa-1 assuming salinity = 35)

Altogether we have:

k = [f * p * ( pCO2in - pCO2out )] / [A* RT * ( 1 / 103.5 ) K0 p ( pCO2out - pCO2eq) ]

It can be seen that the pressure p now cancels.

K0 RT (1 / 103.5) is the dimensionless solubility "a" .

Substituting this in gives:

k = (f / a A) * ( pCO2in - pCO2out ) / ( pCO2out - pCO2eq)

which is the steady-state equation used for calculating transfer velocities.

4.4 Timescale for approach to steady state

4.4.1 Equations describing approach to steady state in the headspace for CO2

The steady-state method for measuring CO2 gas exchange is clearly only practical if the steady state in the headspace can be reached within a reasonably short timescale. The equation developed in the section above describes the situation in steady state. Before steady state is reached, "pCO2out" is not the same as its value in steady state, which I will rewrite instead as "pCO2ss".

We can now write the rate of change of pCO2 in the headspace:

d(pCO2out - pCO2ss) / dt = dpCO2out / dt = [kaA (pCO2eq -pCO2out) +f (pCO2in -pCO2out)]/ volair
where volair is the volume of the headspace (m3) and other symbols are as in the table above.

This can be rearranged to:

d(pCO2out - pCO2ss) / dt = [(kaA pCO2eq + f pCO2in)- (kaA pCO2out +f pCO2out) ]/ volair

Also, rearranging the steady state equation gives:

kaA pCO2eq + f pCO2in = kaA pCO2ss + f pCO2ss

Substituting this in and rearranging gives:

d(pCO2out - pCO2ss) / (pCO2out - pCO2ss ) = - [ (kaA + f ) / volair ] dt

Integrating is now straightforward:

(pCO2out - pCO2ss) / (pCO2initial - pCO2ss) = exp -t [ (kaA + f ) / volair ]
where pCO2intial = pCO2out at time t = 0

The quantity [ (kaA + f ) / volair ] can be thought of as the number of times the headspace is flushed per unit time. This quantity is used in Section 6.5 to calculate the error in each measurement due to the headspace not being in steady state. Generally it was very small.

Introducing some typical numbers (at the slow end of the range),

k = 3 cm hr-1, a = 1, A = 1130 cm2, f = 60 cm3 min-1 (=3600 cm3 hr-1 ), volair = 11300 cm3

gives 0.619 "flushes per hour", or an e-folding time of 1.616 hours.

The corresponding "half life" for approach to steady state is 1.12 hours, and after 8 hours the error is less than 1%. Typically, gas flows were set up in the evening and measured assuming steady-state the following morning, or vice versa, allowing sufficient time for the headspace to reach steady state.

The rate of change of pCO2eq in the water is more difficult to derive algebraically as it depends on the chemical buffering factor TCO2 / pCO2 which varies with pCO2. However, due to this chemical buffering, it is reasonable to assume for the purpose of the calculation above that pCO2eq (pCO2 of the water) is constant over the timescale that the headspace takes to approach steady-state. This is confirmed by the computer model below.

The buffering is greatest when pCO2 is low, although this also corresponded to the periods of intense algal uptake. The "Carbon Budget" plots in chapter 8 indicate the rate of change of pCO2 during the algal blooms. When there were few or no algae, and there was no reason to require a change in pCO2eq, then the air inflows were normally set up to balance such that pCO2eq should remain constant.

4.4.2 Computer model of approach to steady-state

A BASIC computer programme was also written to model gas fluxes in the tank and to give an indication of the approximate timescales required to reach steady-state. An example of the output of this model is shown in figure 4.3, which is a "snapshot" taken from the screen while the program is running. The table below it shows the key variables defining this particular run of the model.

The numbers in the figure indicate the situation in the tank headspaces and water at the moment of the "snapshot". This corresponds to the right hand end of the coloured curves, which show how each variable changes as a function of time. The left hand end of the curves corresponds to the disequilibrium state defined by the initial variables listed in the table. By changing these key variables, many different scenarios for running the tank were investigated with the computer model. The carbonate speciation, solubilities and transfer velocities were calculated from these variables using temperature dependent equilibrium constants as described in detail in

4.5 Low-solubility inert gases

4.5.1 Problem with steady-state measurement of transfer velocity

It is clear from figure 4.3 that for CO2 the steady-state assumption becomes valid where the yellow line meets the grey line, after about 7 hours in this scenario. However this is not true for SF6, for which the brown line should reach the same grey line (due to the way the vertical scale for the curves is calculated) when the headspace A is in steady state. The brown line actually crosses well below the grey line and after 23 hours the calculated transfer velocity assuming steady-state is only 68.0% of the actual transfer velocity, and the error due to measurement inaccuracy is 13 times greater than the transfer velocity itself!

The problem is caused by the low solubility of SF6 in seawater, whose dimensionless solubility a [mol l-1 (water) / mol l-1 (air)] is about 1/300 of that of CO2. Since the gas exchange rate is dominated by transfer across the water surface microlayer rather than the air boundary layer, then the rate of change of concentration in the air phase due to air-water exchange is proportional to this dimensionless solubility. Therefore the air-water fluxes for SF6 are very small compared to the fluxes of SF6 in the air flowing in and out of the headspaces, and so the difference between the SF6 concentration in the air entering and leaving the headspaces is tiny - as shown by the blue curves on the figure which almost meet the green lines at the top and the bottom (the lower green line is obscured by the blue SF6 one). Hence the difference between pSF6out and pSF6in is greater than the precision of measurement, and the error is very large.

To achieve an accurate steady-state measurement of the SF6 transfer velocity, the quantities kaA and f (from the equations above) would have to be similar in size, in order to minimise the error in the calculation of k (see also Section 6.5 ). Therefore when the dimensionless solubility "a" is very small the corresponding flow rate "f" (of air into or out of the headspace) would also have to be small. The rate of approaching steady state, determined by [ (kaA + f) / volair ] as above, would likewise be very slow, and the experiment would take far too long.

Nevertheless it is critical to compare the gas exchange for CO2 with that of inert gases, both to show the effect of chemical enhancement and to calculate the "Schmidt number dependence" of gas exchange in this tank (see introduction Section 1.2.4 ). For the former a gas whose diffusivity is close to that of CO2 (such as oxygen) is most suitable, whereas for the latter a pair of gases are needed whose diffusivities differ as much as possible (the diffusivity of SF6 is much lower than that of CO2 or O2). These inert gases would also show whether there is any physical impact of a surface organic "film" reducing the transfer velocity, as discussed in Section 1.4.5 .

By changing the Schmidt number and solubility within the program, the computer model was also used to investigate other gases (O2, N2O, CCl4) instead of SF6. Although the dimensionless solubility of O2 is about 1/30th of that of CO2 (10x greater than SF6), it was still too low for satisfactory steady-state measurement of the transfer velocity. The solubility of N2O is similar to that of CO2, but unlike CO2 it is not stabilised by chemical buffering and it might still be affected by biological activity in the water. CCl4 was ruled out because it is highly toxic.

Therefore alternative methods had to be developed for measuring the transfer velocity of inert gases for comparison with CO2.

4.5.2 Principle for measuring SF6 transfer velocity

The easiest method is to add a spike of SF6 to the water and then observe the transfer of this SF6 into the air phase in a closed headspace. The driving force for gas exchange ([SF6]water - [SF6]air) is then dominated by the water phase, although at equilibrium almost all of the SF6 is in the air phase. This is because the concentration in the water at the top of the water surface-microlayer ([SF6]air) is always close to zero due to the low solubility, whereas the disequilibrium concentration in the water is determined by the spike added. Consequently, the flux is always one-way and virtually independent of the air concentration, and thus it is possible to measure the accumulation of SF6 in one headspace, whilst continuing CO2 exchange in another. Only after a very long time (several days) would the SF6 escape via the water to the CO2 headspace.

However it is easier to follow algebraically if we assume that all headspaces are closed, and in practice this was usually the case as several headspaces could then be sampled to check consistency.

If "a" is the dimensionless solubility as above, "t" is the total amount of SF6 (in moles) added to the water, and ew , vw , ea and va are the SF6 equilibrium concentrations (mol m-3) and the volumes (m3) of the water and of all four headspaces respectively, then at equilibrium the SF6 will be partitioned such that
ew = a ea.
ew vw + ea va = t

If cw and ca are the respective concentrations before equilibrium, A the total water surface area (m2) , and k the transfer velocity (m s-1 ), then gas exchange can be represented by:

d(ea - ca) / dt = - dca / dt = - kA (cw - a ca) / va

Also mass balance requires that at all times: cw vw + ca va = t = ew vw + ea va

Substituting cw = (ew vw + ea va - ca va) / vw gives:

d(ea - ca) / dt = - kA (ew vw + ea va - ca va - a ca vw ) / va vw

Substituting for ew and rearranging gives:

d(ea - ca) / (ea - ca) = [ kA (a vw + va ) / va vw ] dt

As the part in brackets is a time constant (units s-1), integration is now straightforward.

If ia is the initial air concentration at time t=0, then:

ln [(ea - ca)/ (ea - ia)] = t kA[ (a vw + va) / va vw]

This expression can be used to estimate k from a series of measurements of ca, ia and ea, and known tank dimensions.

In practice a is very small and ia = 0 if the spike is added to the water, so the expression simplifies to:

ln [ 1 - ca / ea ] = t k / d*

Where d* = vw / A, which is the "effective depth" calculated in figure 4-5 .

Note that because the gas exchange is dominated by the water phase concentration, the solubility a disappears altogether in this approximation. Also ea should be equal to t / va, which can be checked if the amount of SF6 added is known.

4.5.3 Principle for measuring Oxygen transfer velocity

The principle here is similar to that for SF6, except that the measurements are done in the water phase and the "spike" is added to the air (using oxygen gas) or "subtracted" using nitrogen gas. Assume the water concentration starts at equilibrium with normal air, i.e. about 8 mg l-1.

The same symbols will be used as above, but this time we are interested in the change in the water phase, so:

d (ew -cw ) / dt = - d cw /dt = -kA (a ca - cw ) / vw

as before we can use the mass balance and equilibrium to give:

ca = ( ew vw + ea va - cw vw ) / va , and ea = ew / a

substituting these two and rearranging gives:

d (ew - cw) / (ew - cw) = - [ kA (a vw + va ) / va vw ] dt

which has the same time constant as above (for the air phase). Integrating gives:

ln [(ew - cw)/ (ew - iw)] = t kA[(a vw + va) / va vw]

In this case iw is not zero and a is larger than for SF6, although still small, so it is better to retain the full expression.

Details of the measurement and calculation procedures for SF6 and oxygen are given later in Section 5.11 and Section 5.12 .

4.6 Design and Construction of the Steady-State Tank

The basic design for the steady-state tank evolved from a consideration of several factors, and after much consultation with Frank Robinson of the Mechanical Workshop in the School of Environmental Sciences, who would later construct it. The final design is summarised by figure 4-4 .

4.6.1 Shape and Dimensions

It seemed sensible to make a circular tank which could be stirred evenly by a central paddle without any "corner" effects. However a revolving paddle would create a central vortex around its axis, which might suck down bubbles and thus affect the gas exchange. Therefore the central portion of the headspace was removed such that the stirring paddle shaft emerged below the water level (this is clearer in cross-section, figure 4.5). The annular headspace could then be divided into four section y dividing walls extending a few centimetres below the water level.

The overall diameter of the tank was constrained to 80cm by the size of UEA's lathe. The height of the headspace - 10cm, was constrained by the time required for it to reach steady-state, as modelled by the computer program described above. For the water depth the main consideration was the volume of seawater we could easily obtain and develop as an algal culture - a depth of 10cm corresponded to a volume of about 50 litres. All measured dimensions are shown in figure 4-5 . From these the water volume and surface areas can be calculated, the volume being corrected for immersed objects, and also checked by filling from volumetric flasks. The tank was always filled to the same depth, 10cm below the lid, marked on the inner wall. The volume/surface area ratio, termed "effective depth", is used for the oxygen and SF6 transfer velocity calculations, whereas for CO2 only the surface area is needed, the CO2 transfer calculation is independent of depth.

4.6.2 Materials

The tank walls and base are made of grey PVC, and the lid of perspex (both 11mm thick), to allow illumination for algal photosynthesis (with hindsight, we should also have used a white plastic for the base to maximise the available light). The joints are glued and sealed with silcone sealant. We were concerned at first that the plastic and sealant would adsorb non-polar trace gases such as SF6, thus creating a "memory" effect. This is often a problem for part-per trillion levels typical of environmental samples. However, for gas exchange experiments the disequilibrium is created by adding SF6 at whatever concentration we choose to measure it, so we could use part-per billion levels and there was no indication of a memory problem.

4.6.3 Gas tight headspaces

It was not easy to obtain a gas tight seal between the dividing walls and the removable lid, since perspex warps slightly with varying temperature and moisture above and below, so the lid will not remain perfectly flat. The solution was an O-ring (silicone rubber) protruding from a recess in the top of the wall, onto which the lid was pressed firmly with G-clamps around the inner and outer perimeters, as shown in Figure 4-6 . This figure also shows how two lip-seal O- rings were used to seal the rotating air-stirrer shaft entering the lid of each compartment, although the resisting torque these exerted reduced the lifetime of the air-stirring motors.

Two methods were used to check for leaks. During development, the tank was filled with CO2, which could be detected by a commercial leak-detector, which measures the thermal conductivity of air entering the probe tip. This indicated a small escape of gas around the perimeter, which was prevented by the addition of silicone sealant to widen the top of the O-ring.

A more routine method for leak testing made use of the multiple headspaces. The tank was 2/3 filled with water, and air was pumped into one headspace while the others were left open to the atmosphere. This creates an imbalance in water levels between the different headspaces, due to different air-pressures (about 8cm water or 8millibar). The stoppers were all closed and the tank left overnight. If air could leak over the top of the dividing walls, the water levels would slowly reequilibrate. By a systematic repetition of this procedure, all the section f wall could be tested and the seal improved, again with silicone sealant. This check was made every couple of months.

The seal was never perfect, for if left long enough, the water level would always adjust slightly (a few mm / day). Headspace B, which also had the water cooling pipes, and oxygen electrode and temperature probe cables entering through the wall, was less pressure-tight than the others. However, it should be noted that during normal operation, the pressure difference between the headspaces is extremely small (<1mm water) and therefore there is minimal driving force for a leak. Also, as there is a continuous flow out to the atmosphere from the steady-state headspaces, any leak should also be in that direction. As the gas exchange calculation is based upon the measured flow rate of gas entering the headspace, this would not be affected by such a leak.

4.6.4 Temperature Control

Gas diffusivities in water are very temperature dependent (See ections 1.2.2, 6.2), so variability must be minimised. For most experiments, the water temperature was maintained in the range 13-15C. To aid this, the base and sides of the tank were enclosed by an 8cm thick layer of polystyrene. However, light has to pass in through the lid and the stirring motors also radiate some heat. To compensate, the water was continuously cooled by a stainless-steel pipe (1/4" tube) around the base of the tank, through which colder water flowed. A dribble of tap water was sufficient in winter, but a cooler was installed for the summer of 1996. This circulated water from a thermostatically controlled bath, thus compensating automatically for the large diurnal temperature variation in the south-facing labs of the building. Before the cooler was available, the tap-water flow had to be adjusted manually as the weather changed, and the typical variability was about 1oC change in half a day (the same timescale as a typical gas exchange experiment).

Temperature was initially monitored with a thermistor probe immersed in the tank water, connected to a "Squirrel" logger by a cable through the tank wall. This consistently read 1oC lower than thermometers against which it was checked, so a correction was made. In later experiments only thermometers were used.

4.7 Stirring

Before completing construction of the tank stirring motors and while waiting for the LiCOR analyser to arrive, I carried out some crude experiments with the oxygen electrode to gauge the relative importance of the air stirring and water stirring on gas exchange.

4.7.1 Water Stirring

Initially we only had a fixed speed geared DC motor for stirring the water, so the paddle size was varied to achieve a range of gas exchange rates. Different paddle lengths (flat PVC blades 1-3cm high) could be bolted onto to a central stump, whose shaft passed through a watertight seal into the central well of the tank, where it was coupled to the motor. Figure 4-7 shows two measurements of the rate of oxygen invasion into the water in the tank, made using two different paddle blades rotating at the same speed. The gradient of each line indicates the transfer velocity. Increasing the length of the paddle (from radius about 10cm to radius about 30cm) increased the transfer velocity by a factor of about eight. It was possible to reach transfer velocities of up to 30 cm hr-1 , before any waves were visible on the surface of the water.

However, changing the paddles was inconvenient because to do this the lid of the tank had to be removed, and the process of attaching a paddle underwater might contaminate the water sample.

Therefore a separate variable-speed power supply was later set up for the water-stirring motor. This was used with a fixed paddle of radius 24cm and height 1cm, producing a typical transfer velocity of about 3cm/hr for oxygen at 13 revolutions per minute. However, as the air-temperature in the lab increased, the motor tended to slow slightly, and wear on the gearbox and brushes also caused minor variation. Therefore the motor speed was checked during every gas exchange measurement. The motor speed was measured simply by timing 5 (or as appropriate) full revolutions of the paddle (typically 23 seconds), and repeating at least three times until consistent to within 1%, the short-term variability. The variability was much less after June 1996, when a better motor was found.

Later, many measurements were made to investigate the effect of varying the paddle speed on the enhanced and unenhanced CO2 transfer velocity -these are reported in

4.7.2 Air Stirring

On the other hand, varying the rate of air-stirring seemed to have little effect on the transfer velocity, as shown by figure 4-8

The left hand plot shows an experiment in which pure oxygen flowed through one of the four headspaces, which was stirred by a variable-speed fan. The other headspaces were initially in equilibrium with the water and were not stirred. The circles show measurements of oxygen in the water, and the line shows the speed of the rotating fan tip. Clearly the speed of the fan has no significant effect on the rate of O2 invasion into the water. A similar experiment in which the flux of oxygen was from the water to the air (which was continuously flushed by N2) showed the same result.

The right hand plot shows another experiment, in which oxygen was initially bubbled through the water and then gradually returns to equilibrium with the air pCO2 (hence the slight curve). A large fan was positioned above all four headspaces. Again, switching the fan on and off seems to make no difference to the transfer velocity.

Since the air stirring would not dominate the gas exchange, serving merely to ensure that the headspaces are well-mixed, it did not need to be too vigorous, and a minor variation between the headspaces would not be critical to the results. Therefore, we decided to use four separate but identical DC motors, connected to simple fan blades (8x 45o angle blades 5cm radius 2cm high) by a shaft passing through the lid (as in figure 4-6 ) and turning at about 300rpm when all went well. Unfortunately these motors did not turn out to be very reliable, and occasionally one or two were not operating. Even so, these headspaces were still useful for equilibration, lagging only a little behind stirred headspaces.

4.7.3 Discussion of relative importance of air and water stirring

Thus, contrary to expectations from published literature, which often emphasises the importance of capillary waves created by friction from the air (see Section 1.2.5 ), I found that varying the air-stirring made very little difference to the gas exchange rate, over a range of transfer velocities from 2 to 30 cm hr-1, which was instead dominated by the size of the water-stirring paddle. This is partly because the headspaces are too small to create a realistic surface "wind". Moreover, the tank design is such that the walls dividing the headspaces also act as baffles in the water, preventing laminar flow and forcing it to turn over vertically. These dividing walls also prevent a circular flow of air, or a standing wave pattern due to resonance around the ring of the tank, as was observed in one larger annular gas-exchange tank in Heidelberg (Jahne et al 1979,1987a -see Section 1.2.5 ). This resonance could be responsible for the sudden onset of capillary waves at a particular windspeed in that tank, below which the gas exchange rate was very low. No such phenomenon occurred in my small tank, and capillary waves were not observed even at a transfer velocity of 30 cm hr-1.
Continue to Chapter 5:
Operation of steady-state gas exchange tank

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