Experiments in Fluids

, Volume 46, Issue 2, pp 243–253

Visualizing near-surface concentration fluctuations using laser-induced fluorescence

Authors

    • Applied Physics LaboratoryUniversity of Washington
  • Trina M. Litchendorf
    • Applied Physics LaboratoryUniversity of Washington
Research Article

DOI: 10.1007/s00348-008-0554-9

Cite this article as:
Asher, W.E. & Litchendorf, T.M. Exp Fluids (2009) 46: 243. doi:10.1007/s00348-008-0554-9

Abstract

A method for observing near-surface fluctuations in pH caused by a water–air flux of carbon dioxide under conditions of ambient atmospheric carbon dioxide levels is developed and tested. Peaks in fluorescence intensity measured as a function of pH and turbulence are shown to be consistent with predictions from a chemical kinetics model of CO2 exchange. The square root of the frequency of the pH fluctuations scale linearly with independently measured bulk air–water gas transfer velocities in agreement with surface divergence models for air–water gas transfer. These data indicate that the method proposed here is tracking changes in near-surface CO2 concentrations. This laser-induced fluorescence method can be used to study the air–water exchange of CO2 in wind-wave tunnels without the need for elevated CO2 concentrations in the gas phase.

1 Introduction

Time constants of near-surface concentration fluctuations at gas–liquid interfaces are important in understanding the hydrodynamics associated with air–water gas exchange (Atmane et al. 2004). However, because the Schmidt number (i.e., the ratio of the kinematic viscosity to molecular diffusivity) of most gases in water is on the order of 103, concentration fluctuations must be measured at depths of at most several hundred micrometers to have direct relevance to air–water gas transfer. Measuring concentrations this close to a free surface, where wave amplitudes can be several orders of magnitude larger, is challenging and proven to be difficult. As a result, the correct conceptual model for air–water gas transfer, let alone a definitive mathematical relationship between the transfer velocity and parameters associated with the aqueous-phase turbulence in the near the air–water interface, is still uncertain.

Previous measurements of near-surface concentration fluctuations have been made using profiling oxygen microprobes (Chu and Jirka 1992; Lee and Luk 1982), methods based on observing laser-induced fluorescence (LIF) from dyes whose fluorescent yields are pH- or oxygen-sensitive (Asher and Pankow 1989; Herlina and Jirka 2004, 2008; Münsterer and Jähne 1998; Takehara and Etoh 2002; Tsumori and Sugihara 2007; Wolff and Hanratty 1994; Woodrow and Duke 2001), or using heat combined with infrared imagery as a proxy tracer for gas transfer (Garbe et al. 2004; Jähne et al. 1989; Schimpf et al. 2004).

The advantage in using microprobes or heat as a proxy tracer is that unlike fluorescence techniques, fluorescent dyes do not need to be added to the water. Air–water gas transfer is sensitive to the presence of adventitious surface films, and organic dye molecules (or contaminants therein) even though they are soluble might have enough surface activity to affect gas transfer. However, it is generally assumed that modification of surface chemistry by the fluorescent dyes is negligible and the ability of LIF techniques to provide two-dimensional maps of gas concentration without generating flow disturbances, which are especially useful for observing the correlation between flow maps and concentration fluctuations, is a considerable benefit to their use.

The main drawback to microprobes is that they are invasive and their presence could disrupt the fluid motions that are responsible for the concentration fluctuations. Techniques that rely on imaging molecular fluorescence are limited by difficulty in identifying the location of the free surface, where the errors can be as large as 400 μm even using an independent method to locate the free surface (Mukto et al. 2007). Additionally, in the case of the techniques using pH-sensitive dyes, the pH gradient required for driving the change in fluorescence must be relatively large, and has been generated with hydrogen chloride or ammonia, which are not liquid-phase rate controlled, or using relatively high air–water partial pressure differences of carbon dioxide (CO2). Using these gases or conditions lead to the necessity of using a hermetically sealed system, which makes the LIF technique impractical in open wind-wave tunnels. Methods that image the fluorescence from the side, looking obliquely up at the air–water interface through a significant distance of water, are also complicated by the need to account for re-absorbance of the fluorescence by the water and fluorescent dye in calculating the absolute fluorescence intensity (Münsterer and Jähne 1998). Finally, because of the mismatch in the diffusive length scales between heat and gas, it has been shown that heat may not be a useful proxy tracer for gas in many gas–liquid transfer systems (Atmane et al. 2004).

Here, the experimental details are provided for a LIF-based method for observing concentration fluctuations of CO2 in the aqueous surface microlayer without using elevated air-phase CO2 concentrations. Therefore, this method can be used in wind-wave tunnels that are not hermetically sealed, greatly simplifying the design and implementation of experiments designed to study the details of air–water gas transfer. The measurements here are made using the two-dye approach of Asher and Pankow (1989), which is somewhat simpler to implement optically, involves less data processing, and provides more accurate knowledge of the sampling depth than side-looking imaging methods.

2 Background

Asher and Pankow (1989) developed a method for observing depth-dependent CO2 concentration fluctuations based on the pH-dependent fluorescence emissions from the dye 2′,7′-dichlorofluorescein (DCFS). By measuring the pH-dependent fluorescence intensity of DCFS, pH in the range of 3.5–6.5 can be determined remotely. This permits measurement of CO2 concentrations because CO2 hydrates in water to form carbonic acid, H2CO3, causing a decrease in pH and fluorescence intensity of the DCFS (Hiby 1968). By observing the change in intensity, changes in pH are tracked and the local concentration of CO2 can be calculated from pH using standard acid–base chemical relations (DOE 1994; Stumm and Morgan 1981).

Asher and Pankow (1989) showed that by adding a non-fluorescent dye to the water that strongly absorbed the excitation light, fluorescence emissions from the bulk could be suppressed, allowing measurement of surface CO2 concentration fluctuations. This method provides a depth-integrated measurement of concentration, where the integration limits are from the surface to a depth that can be selected by adjusting the concentration of a non-fluorescent dye. One benefit of this approach is that the measurement depth is determined chemically through the absorbance of the second dye rather than optically in imaging, and therefore, unaffected by the presence of surface motions. A second benefit is that the emitted fluorescence is observed without significant transmittance through the bulk aqueous phase, making corrections for re-absorbance as done by Münsterer and Jähne (1998) unnecessary. However, the method required a gas-phase composition of pure CO2, making it impractical for use in systems where the headspace cannot be isolated from the atmosphere.

Development of a CO2-based LIF-DCFS method suitable for use in wind-wave tunnels with pass-through design relies on the fact that aqueous solutions containing only CO2 with pH values in the range of 4–7 are very poorly buffered (Stumm and Morgan 1981). Over this pH range, a very small change in the concentration of CO2 will result in relatively large change in pH. If the contribution to pH from the autodissociation of water is neglected for pH values less than 5.6, the change in pH with respect to the change in the total concentration of CO2 in solution, CT [i.e., the sum of the concentrations of unhydrated aqueous-phase CO2, CO2(aq), H2CO3, bicarbonate ion, HCO3, and carbonate ion, CO32−], is given by (Stumm and Morgan 1981)
$$ \frac{\text{dpH}}{{{\text{d}}C_{\text{T}} }} = - \frac{{0.5K_{1}^{*} \left( {C_{\text{T}} K_{1}^{*} } \right)^{ - 1/2} }}{{[{\text{H}}^{ + } ]}} $$
(1)
where \( K_{1}^{*} \) is the first acid–base dissociation constant of H2CO3* (Stumm and Morgan 1981) and [H+] is the concentration of hydrogen ion. In this pH range, the change in CT in the very near surface due to the air–water flux of CO2 is equal to
$$ \frac{{{\text{d}}C_{\text{T}} }}{{{\text{d}}t}} = \frac{{k_{\text{L}} ({\text{CO}}_{2} )}}{\delta }\left( {C_{\text{S}} - C_{\text{T}} } \right) $$
(2)
where kL(CO2) is the air–water gas transfer velocity of CO2, CS is the saturation concentration of CO2 in water relative to its ambient atmospheric partial pressure, δ is the scale depth for the concentration fluctuations, and the reaction of OH– with CO2 to produce HCO3, requiring a correction of only 0.12% at pH 6 (Ho and Sturtevant 1963), has been assumed to be negligible. For pH values less than 5.3, kL(CO2) = 100 μm s−1, and δ = 25 μm [the particular values chosen for kL(CO2) and δ will be discussed below], when the differential change of pH with respect to CT is multiplied by the expected rate of change in CT, it is found that pH decreases of 0.2 U over a time interval of 0.2 s could be expected by the evasion of CO2. A decrease of 0.2 pH units would be easily detected by a LIF-DCFS method and this sensitivity of pH to decreases in CT can be exploited for studying air–water gas transfer provided the system pH was kept at 5.3 and lower. The lower pH limit for the method is determined by the buffer intensity of the system, which increases with decreasing pH (Stumm and Morgan 1981). Consideration of buffer intensity shows that for best effect, the minimum pH value for these measurements would be 4.5.

In addition to the pH requirement listed above, there is also a kinetic requirement that must be met in order for LIF-DCFS to track CO2 concentration fluctuations. Overall, the increase in pH with evasion of CO2 is a three-step process involving the evasion of CO2(aq) to the gas phase, followed by a dehydration of H2CO3 to CO2(aq), and finally, as H2CO3 dehydrates to CO2(aq), the concentration of bicarbonate ion, [HCO3], and [H+] will decrease to maintain the acid–base equilibria (Stumm and Morgan 1981). Although the acid–base equilibrium is essentially instantaneous, the dehydration rate of H2CO3 is relatively slow (Gibbons and Edsall 1963) and it is not obvious that H2CO3 will decrease rapidly enough for pH to track changes in CT. Therefore, modeling of the chemical kinetics was performed to understand the temporal response of the proposed method.

Following the standard kinetic scheme for the hydration/dehydration of the carbonate system (Gibbons and Edsall 1963; Ho and Sturtevant 1963; Pocker and Bjorkquist 1977), for pH values less than 7 the differential equations describing the evolution of pH in the near-surface layer is given by
$$ \begin{aligned} \frac{{{\text{d}}[\text{CO}_{2} (\text{aq} )]}}{{{\text{d}}t}} & = \frac{{F_{{\text{CO}_{2} }} }}{\delta } + k_{\text{dehyd}} [\text{H}_{2} \text{CO}_{3} ] - k_{\text{hyd}} [\text{CO}_{2} (\text{aq} )] \\ \frac{{{\text{d}}[\text{H}_{2} \text{CO}_{3} ]}}{{{\text{d}}t}} & = k_{\text{hyd}} [\text{CO}_{2} (\text{aq} )] - k_{\text{dehyd}} [\text{H}_{2} \text{CO}_{3} ] \end{aligned} $$
(3)
where [CO2(aq)] and [H2CO3] are the concentrations of CO2(aq) and H2CO3, respectively, \( F_{{{\text{CO}}_{2} }} \) is the air–water flux of CO2(aq), kdehyd is the dehydration rate of H2CO3 (and is equal to 18 s−1, Pocker and Bjorkquist 1977), and khyd is the hydration rate of CO2(aq) (and is equal to 0.037 s−1, Pocker and Bjorkquist 1977). \( F_{{{\text{CO}}_{2} }} \) can be written in terms of the air–water concentration difference of CO2 and the air–water gas transfer velocity of CO2, kL(CO2), as
$$ F_{{{\text{CO}}_{2} }} = k_{\text{L}} ({\text{CO}}_{2} )(C_{\text{S}} - [{\text{CO}}_{2} ({\text{aq}})]) $$
(4)
where CS is the saturation concentration of CO2 in water relative to its ambient atmosphere pressure. By assuming that the system attains local equilibrium with respect to the pH instantaneously and accounting for the effect of DCFS on the acid–base chemistry, [H+] for a given value of [H2CO3] is found by solving
$$ [\text{H}^{ + } ] - \frac{{K_{\text{W} } }}{{[\text{H}^{ + } ]}} - \frac{{K_{1} [\text{H}_{2} \text{CO}_{3} ]}}{{[\text{H}^{ + } ]}} - 2\frac{{K_{1} K_{2} [\text{H}_{2} \text{CO}_{3} ]}}{{[\text{H}^{ + } ]^{2} }} + C_{\text{D} } \left( {2 - \frac{{K_{{\text{D} 1}} [\text{H}^{ + } ] + 2K_{{\text{D} 1}} K_{{\text{D} 2}} }}{{[\text{H}^{ + } ]^{2} + K_{{\text{D} 1}} [\text{H}^{ + } ] + K_{{\text{D} 1}} K_{{\text{D} 2}} }}} \right) = 0 $$
(5)
where K1 is the acid–base dissociation constant for H2CO3 (i.e., not K1 for H2CO3*), K2 is the acid–base dissociation constant for HCO3, CD is the total concentration of DCFS in solution, and KD1 and KD2 are the first and second acid–base dissociation constants for DCFS, respectively, and are equal to 3.2 × 10−4 and 1.0 × 10−5 mL−1, respectively (Leonhardt et al. 1971).
Figure 1 shows a time series of pH calculated by integration of the set of differential equations in Eq. 3 with kL(CO2) equal to 100 μm s−1, δ equal to 25 μm, [DCFS]0 equal to 4.0 × 10−7 mL−1. Numerical integration was done using the Runge–Kutta–Merson method (Hall and Watt 1976). The values for kL(CO2) and δ were selected to represent conditions with the most intense turbulence, where turbulence timescales would be fastest and CO2 would have the least amount of time for hydration. Correspondingly, kL(CO2) was the maximum value of kL measured for helium (scaled to the diffusivity of CO2) in the experimental apparatus described below. δ was calculated as a diffusive length scale of CO2 [i.e., δ = (Dtd)1/2 where D is the molecular diffusivity of CO2 and td is a diffusive time constant] where td was estimated from the average timescale of temperature fluctuations measured by an infrared imager in the experimental apparatus under the same conditions that gave kL(CO2) = 100 μm s−1 (i.e., 0.4 s). During the integration, pH was calculated using Eq. 5 at time steps of 2 ms. The lag between the evasion of CO2 from the surface layer and the increase in pH due to the loss of carbonic acid is seen as the slight flattening of the pH curve for very small times. Also shown in the figure is the fluorescence intensity, Φ(t), expected from the above solution in units of volts of signal as calculated using a pH-to-Φ calibration curve (see below). Assuming the minimum detectable change in Φ(t) is 0.05 V, the modeling shows that for a starting pH value of 5.0, there is a measurable pH change at timescales as short as 0.2 s.
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Fig. 1

Time series of the pH change and concomitant rise in fluorescence intensity, Φ(t), predicted by the CO2 hydration kinetics, gas exchange, and acid–base chemistry defined by Eqs. 3, 4, and 5, respectively

The timescales of the concentration fluctuations observed by Asher and Pankow (1989), the turbulence bursts measured by Komori et al. (1989), and the near-surface coherent structures identified by Siddiqui et al. (2004) are all in the range of 0.2 s. Therefore, by making measurements with pH values of 5.1 or less, the proposed technique should be able to track changes in CT at the water surface. Fortuitously, this range is consonant with the constraint imposed by the acid–base chemistry of working at pH values of 5.3 or less.

3 Experimental

The LIF-DCFS method was tested in a synthetic jet array tank (SJAT) embedded in a wind tunnel at the Harris Hydraulics Laboratory, University of Washington. The wind tunnel was a once-through design tuned to operate at low wind velocities (Flotek 5760, GDJ Inc., Mentor, OH) with a test section that is 0.5 m wide by 0.5 m high by 1 m long. The SJAT was mounted in the wind tunnel so that the upper edge of the tank was flush with the floor of the wind tunnel. The SJAT was a rectangular prism made from 1.3 cm thick acrylic sheet with inside dimensions of 0.50 m wide by 0.50 m long by 1.0 m deep giving a total volume of 0.25 m3. A schematic diagram of the wind-tunnel test section with embedded SJAT is shown in Fig. 2.
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Fig. 2

Schematic diagram of the synthetic jet array tank and wind tunnel showing dimensions and optical configuration of the laser-induced fluorescence method

Aqueous-phase turbulence in the SJAT was generated using an array of 16 DC-drive pumps similar to that described by Variano et al. (2004). The pumps were arranged in a square grid with 10-cm spacing and created horizontally isotropic turbulence at the water surface. The turbulence intensity at the surface could be varied by adjusting the drive voltage, PV, for each pump. The bulk turbulence intensity, Q (cm s−1), was measured using an acoustic Doppler velocimeter (SonTek Instruments, San Diego, CA) at a depth of 10 cm. Table 1 lists Q for the range of PV used in these experiments.
Table 1

Turbulence data, timescale data for pH fluctuations, and gas transfer measurement results from the synthetic jet-array tank, U = 3.2 m s−1

PV

Q (cm s−1)

ΛMAX

τMAX (s)

τAVG (s)

Np

Ts

s (s−1)

(Ds)1/2 (cm/h)

kL(600) (cm/h)

10

4.1

21

0.39

0.71

194

900

0.22

6.2

13.1

14

7.8

45

0.39

0.53

325

900

0.36

8.0

18.0

16

9.0

61

0.32

0.50

405

900

0.45

9.0

19.5

18

11.3

66

0.32

0.47

460

900

0.51

9.5

24.3

20

12.4

96

0.24

0.46

600

900

0.67

11.1

26.7

Water temperature in the tank was regulated by circulating constant temperature water through approximately 5 m of 10-mm OD coiled copper tubing placed in the bottom of the tank. The tubing was installed so that the coils were at least 3 cm below the output of the pump jets. Water temperature in the coil was regulated to ±0.2 K using a circulating bath (NESLAB RTE-17, Thermo Scientific, Waltham, MA) and the tank itself was stable within ±0.5 K.

For the LIF-DCFS experiments, the tank was filled with distilled water. Dissolved gases other than helium were removed from the water by sparging with helium using a porous polyethylene diffuser mounted in a through-port in the bottom of the tank. The DCFS and the non-fluorescing dye, Orange-G, were obtained as 90% pure crystals and 97% pure crystals, respectively (Sigma-Aldrich Chemical Company, Milwaukee, WI) and used without further purification. CD (the concentration of DCFS) was 4 × 10−7 M and the concentration of Orange-G was 1.9 × 10−3 M, resulting in 90% of the fluorescence being generated in the top 300 μm of the water surface [see Asher and Pankow (1991) for details on how the fluorescence depth is calculated]. Tank water was changed at approximately 2-week intervals and the tank walls rinsed and washed to prevent contamination of the water by biological activity.

Bulk pH was measured by 10 mL aliquot sampling of the tank with analysis using a pH-meter (Orion 3-Star model, Thermo Scientific, Waltham, MA) with a Ross pH electrode (Orion 8102BNUWP, Thermo Scientific, Waltham, MA). The pH meter and electrode were calibrated with standard buffers (VWR Inc., Batavia, IL) at pH values of 4 and 7.

After addition of the Orange-G and DCFS, the tank water was prepared by first lowering the pH to 4 using 4 M hydrochloric acid. This converted any bicarbonate present to carbonic acid and dissolved CO2, which was then removed by sparging for several hours with helium. After sparging, the tank pH was then raised to approximately 7 by adding 4 M sodium hydroxide solution. At this point, the flow of helium was turned off and gaseous CO2 added to the tank through the polyethylene frit, decreasing the pH as CO2 acidified the water. Once the pH of the tank had decreased to approximately 5, the flow of CO2 was stopped and the tank allowed to equilibrate for at least 15 min. The pumps were then turned off for 15 min to let the water settle. The pumps were turned back on and the tank water agitated for at least 15 min before measurements were conducted.

Water surfaces in small tanks are known to be prone to contamination from adventitious films. Because it is known that surface concentration fluctuations are sensitive to the presence of films (Asher and Pankow 1989), these accumulated films were removed from the water surface by continually vacuuming the surface with two pipettes connected to a dual-drive peristaltic-pump located each downwind tank corner. The height of each pipette was adjusted so that each continually removed water from the surface layer, with that water pumped through a filter before being returned to the tank. Figure 3 shows infrared images of the water surface with and without the pipette system in operation at a wind speed of 3.2 m s−1. The presence of a Reynold’s ridge of surfactant is clearly shown in the image without vacuuming by the pipettes. The presence of the ridge is greatly reduced by the pipettes, showing the pipette system was very effective at removing adventitious films at the downwind edge of the SJAT.
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Fig. 3

Two infrared images from the synthetic jet array tank showing the effect of the surface vacuuming system on adventitious surface films. The image on the left shows the tank surface with the vacuuming system turned off. The surface film is shown as the darker gray region covering approximately 1/4 of the tank on the downwind side with the Reynold’s ridge visible as the curved line extending from top to bottom. The image on the right shows the tank surface with the vacuum on, showing no visible Reynold’s ridge. The conditions for both images are wind speed, U = 3.2 m s−1, pump intensity, PV = 14 V

The excitation light for the fluorescence was provided by the 488-nm line from a 100 mW multi-line air-cooled argon-ion laser (Model 35-LAS-010-120, Melles-Griot Inc., Laser Group, Carlsbad, CA). The laser beam passed through narrow-band interference filter to separate the 488-nm laser emissions from the other bands. A rotating optical chopper (Model 300C, Scitec Instruments Ltd., Redruth, Cornwall, UK) provided a laser pulse frequency of 280 Hz. Laser power was monitored by sampling 9% of the total beam energy using a plate beam sampler and a photodiode module (Model 57-623, Edmund Optics, Barrington, NJ) with an upper frequency response of 500 Hz. Stray light was minimized by placing a narrow-bandpass interference filter with a center wavelength of 488 nm in front of the laser power photodiode. The main beam was then directed vertically downwards onto the water surface so that a small spot of fluorescence on the water surface approximately 4 mm in diameter was visible. The fluorescence spot was imaged onto a second photodiode module (model 57-623) using a BK-7 plano-convex lens with a focal length of 100 mm. The lens resulted in a minification of the fluorescence spot size to a diameter of approximately 1.5 mm. A bandpass interference filter centered on the fluorescence maximum of DCFS at 520 nm was placed in front of the fluorescence photodiode to minimize the effect of reflected laser light on the signal. The optical geometry is shown in Fig. 2.

The outputs from both the fluorescence photodiode and the laser power photodiode were passed to separate dual-phase lock-in amplifiers (Model 420, Scitec Instruments Ltd., Redruth, Cornwall, UK) with reference signals provided by the mechanical chopping wheel. The output from each lock-in amplifier was digitized at a rate of 100 Hz using a personal computer equipped with a single-ended 16-channel 16-bit data acquisition module (Model DT321, Data Translation, Inc., Marlboro, MA) and custom software.

Experiments were conducted with a water temperature of 295.15 K, an air temperature of 293.15 K, and a constant wind speed, U, of 3.2 m s−1. Fluorescence data were collected at pH values of 5.1, 5.4, and 5.8 to study the effect of system pH on the fluorescence fluctuations. The effect of turbulence on the fluorescence fluctuations was studied at PV = 10, 14, 16, 18, and 20 V at pH 5.0. Fluorescence measurements were also made for the conditions described above and procedures described above, but with 1 ppm (part-per-million) by weight of the soluble surfactant Triton X-100 added to the water.

Bulk phase gas transfer velocities were measured for evasion of helium at PV = 10, 14, 16, 18, and 20 V using procedures described in detail by Asher et al. (1996). These were converted to an equivalent gas transfer velocity for CO2 in freshwater at TW = 20 °C, kL(600), assuming that kL is proportional to D1/2. Table 1 lists kL(600) measured in the SJAT during the experiments using water containing no Triton X-100.

4 Data analysis and results

Time series of fluorescence intensities, Φ(t), and laser output power, Π(t) (measured here as volts of signal from the power monitoring photodiode) were collected for at least 400 s. The time series for Φ(t) were low-pass filtered using a sixth-order Chebyshev filter with an upper frequency of 10 Hz (routines: cheby2, filtfilt; Matlab Version 7.5.0.342, Natick, MA). Time series for Π(t) were low-pass filtered with an upper frequency of 0.067 Hz to provide a highly smoothed laser power record containing only long-timescale fluctuations. The smoothed series for Π(t) was used to normalize the low-pass filtered times series for Φ(t) to a common laser output power for subsequent use of a fluorescence to pH calibration curve.

Once Φ(t) was power normalized, it was converted to pH using a linear calibration such as shown in Fig. 4, where the calibration used was specific to the tank water for that run. In general, a Φ-to-pH calibration curve were generated by recording a 10-s long time series of Φ(t) when a bulk water sample was taken from the tank and analyzed for pH. Because the pH was a bulk value and Φ(t) contains data points when the surface pH was higher than the bulk pH due to the air–water flux of CO2, a filtering procedure was used to determine the Φ corresponding to the bulk pH. First, the 1,000 values of Φ(t) from the time series were sorted in order of increasing intensity and the second through sixth deciles of the sorted values of Φ (500 points total) were averaged to give the average value of Φ. Restricting the averaging to these deciles excluded both spurious low values and the high values in Φ(t) due to fluorescence peaks caused by air–water exchange of CO2. The resulting average was assumed to be the Φ that would have been measured for a surface with pH constant and equal to the bulk pH.
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Fig. 4

Calibration curve relating fluorescence intensity, Φ, to bulk pH. Solid circles are experimental data. Solid line is least-squares linear regression: Φ = −4.91 + 1.26(pH), coefficient of determination = 0.97 (4.7 < pH < 5.6)

Although pH is nonlinearly related to Φ for DCFS over pH ranges spanning 1.5 U and larger (Asher and Pankow 1986; Münsterer and Jähne 1998), over the smaller range used here a linear fit provides sufficient accuracy. For the data in Fig. 4, a least-squares linear regression found that Φ = −4.91 + 1.26(pH), with a coefficient of determination of 0.97 and a standard error of the fit of 0.04 pH units. Figure 5 shows a 30 s time series of surface pH fluctuations derived from the fluorescence measurements for three different bulk pH values in the grid flume (with U = 3.2 m s−1 and PV = 9 V). Figure 6 shows the effect of PV on temporal fluctuations in surface pH as derived from Φ(t).
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Fig. 5

Time series of pH fluctuations caused by evasion of CO2 from the water surface at three bulk pH values for a pump intensity of 9 V and a wind speed of 3.2 m s−1. Each time series was processed using the procedure described in the text

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Fig. 6

Time series of pH fluctuations caused by evasion of CO2 from the water surface measured at three pump intensities, PV and a wind speed of 3.2 m s−1. Each time series was processed using the procedure described in the text

Quantitative information concerning the timescales of the fluctuations in pH as a function of PV was extracted from time series of pH such as shown in Fig. 6 by calculating the distribution of peak widths, τ, of the fluctuations. For each peak, τ was determined using a peak detection algorithm based on that used in gas chromatographic integrators (Asher and Pankow 1989; Karohl 1967). This algorithm proceeds by first calculating the slope, b(t), of 0.06 s of data around each point in the time series for pH and calculating an average slope, bavg. It then locates the peak starts by detecting when b(t) exceeds bavg for seven time steps and the increase in pH above the baseline exceeds a value of 0.2 pH units. Peak endings are determined when −b(t) exceeds bavg for seven time steps and pH had fallen to with 20% of the baseline value. This final criterion minimized splitting of large events into several smaller fluctuations. For example, in Fig. 7 for PV = 10 V and the peak starting at 78.2 s, the algorithm of Asher and Pankow (1989), which did not use the 20%-baseline value criterion, would report six separate events. However, the various maxima and minima from t = 78.2 s to 79.1 s more likely represent fluctuations in Φ(t) from a single event. Under the criteria described above, the peak in question is detected as a single event with τ = 1.9 s.
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Fig. 7

Details of the peak detection algorithm for PV = 10 V

Representative details of the peak detection algorithm operating on the pH data for PV = 10 V from Fig. 6 are shown in Fig. 7. Figure 8 shows frequency distributions of τ, Λ(τ), measured using the full time series for Φ(t) at the three values of PV shown in Fig. 6. The average peak width, τAVG, for each Λ(τ) is shown on the x-axis of the figure. Table 1 lists τAVG, the maximum value of Λ(τ), ΛMAX, the value of τ at ΛMAX, τMAX, the total number of peaks in Λ(τ), Np, and the sampling time, Ts, for all five PV used here.
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Fig. 8

Peak width distributions, Λ(τ), for the data in Fig. 6. The average peak widths for each Λ(τ), τAVG, are shown on the x-axis and are listed in Table 1

5 Discussion

The amplitudes of the fluctuations in pH seen in Fig. 5 provide evidence that the peaks are due to CO2 concentration fluctuations. As the bulk pH increases, the peaks decrease in magnitude until at a bulk pH of 5.8 there are no significant peaks in pH. At this pH, the partial pressure of CO2 in solution is calculated to be slightly below its atmospheric partial pressure (i.e., the net CO2 flux is extremely small and into the water) so there would be essentially no air–water gas flux and no concentration fluctuations to drive a change in pH. However, fluctuations in pH are clearly seen at the two lower bulk pH values of 5.1 and 5.4, where the thermodynamic model in Eq. 1 and kinetic model in Eq. 3 both indicate there should be observable changes in pH due to the air–water gas flux. Furthermore, the average amplitude of the pH fluctuations decreases from 0.37 at a bulk pH of 5.1 to 0.24 at a bulk pH of 5.4, which also agrees with the kinetic modeling results that showed a decrease in fluorescence response as pH increased. The three time series for pH shown in Fig. 5 therefore provide evidence that the DCFS-LIF method is able to track pH changes in the aqueous surface caused by air–water gas exchange of CO2. In turn, this suggests that the timescales of the pH fluctuations contain information concerning fluctuations in the near-surface concentration of CO2.

Figure 5 also demonstrates that the fluctuations in pH were not caused by fluctuations in Φ(t) due to water surface motions causing the fluorescence spot to move briefly off of the photodiode. Aside from the fact that motion of the fluorescence spot off of the photodiode would cause decreases in Φ(t), the fact that the peaks in Φ(t) decrease as bulk pH increases as turbulence and wind speed remain constant shows they peaks are correlated with the chemistry. If the changes in Φ(t) were due to water surface motions, they be expected to remain constant with pH. Therefore, it can be concluded that water surface motions are not a large source of error in the present measurements.

Asher and Pankow (1989) observed that the timescale of near-surface CO2 concentration fluctuations decreased and the frequency at which they occurred increased as Q increased. The data for τAVG, τMAX, and ΛMAX in Table 1 shows that τAVG and τMAX decrease and ΛMAX increases with increasing PV. Because Q increases with PV, this provides further evidence that the fluctuations in pH seen in Fig. 6 are caused by fluctuation in the near-surface concentration of CO2.

The pH data in Fig. 6 are somewhat counterintuitive since the peaks heights for pH increase as PV, or Q, decrease. Quantitatively, this effect is seen by calculating the difference between the average pH value and the average of the top 5% of the distribution of pH values at each PV. For PV = 10 V, the average pH difference was 0.34 pH units, for PV = 14 V, the average pH difference was 0.32 pH units, and PV = 18 V, the average pH difference was 0.25 pH units. Similarly, the maxima in pH of approximately 5.5 also agree with maximum pH values predicted from the kinetic modeling results for water with an initial pH of 5.0. In contrast, Asher and Pankow (1989) observed that the fluorescence peak heights increased as Q increased. This seeming contradiction is explained by observing that previous measurements of surface concentration fluctuations have been made for systems where the net gas flux is from the gas phase to the water. In these cases, the minima represent times when the water surface is quiescent and saturated with CO2, and the maxima represent times when the near-surface water is being renewed or has been very recently replaced by bulk fluid. Peak heights increase with increasing Q because as velocity increases, more of the water in the near-surface layer is replaced with high-pH water from below. In contrast, during the measurements in the SJAT, the net flux of CO2 was from the water to the air. In this case, the maximum values in pH are times when the water in the near surface layer was quiescent and very nearly in equilibrium with the gas-phase CO2. The decreases in pH represent time periods when the surface pH was low as water with high CT was near the surface. In this case, peak heights decrease as Q increases since there is less time for water at the surface to come to equilibrium (at the higher pH) with the air phase.

Further evidence that the LIF-DCFS method is tracking surface CO2 concentration is provided by comparing the times series of pH taken with water containing 1-ppm by weight of Triton X-100 with pH records for a cleaned water surface. Asher and Pankow (1989) found that the presence of a surfactant suppressed concentration fluctuations near the water surface. For the SJAT, suppression of concentration fluctuations would mean the interface would equilibrate at the higher pH with maximum Φ. The result would be that as a function of time, pH would have a constant maximum value with downward-going events when lower pH bulk water was brought to the near-surface. Figure 9 shows a time series for pH for both a Triton X-100 run and a nominally clean water run, both with PV = 18 V. In agreement with the previous analysis, pH for the Triton X-100 run shows a nearly constant maximum value with downward fluctuations. The average pH of 5.8 for the Triton X-100 data is most likely due to there being a small excess of mineral base in the tank water for those experiments.
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Fig. 9

Time series of pH at a pump intensity, PV, of 18 V for nominally clean water and water containing 1 ppm by weight of Triton X-100. Each time series was processed using the procedure described in the text

Csanady (1990), Brumley and Jirka (1988), and McKenna and McGillis (2004)argued that surface divergence is the hydrodynamic mechanism generating the observed near-surface concentration fluctuations. In support of this, Tsumori and Sugihara (2007) and McKenna and McGillis (2004) found that kL scaled linearly with the quantity (RMS)1/2, where βRMS (Hz) is the RMS surface divergence. If surface divergences such as measured by Tsumori and Sugihara (2007) are responsible for the pH fluctuations measured using the LIF-DCFS method, the pH fluctuation rate should correlate linearly with kL measured for helium in the SJAT. Here, the pH fluctuation rate, s (Hz), is defined as the total number of pH peaks occurring in a time interval divided by the length of the interval. For example, for the Λ(τ) shown in Fig. 8, the time interval for each data set was 900 s. The total peak counts were 194, 325, and 460 for PV = 10, 14, and 18 V, respectively. Therefore, s was 0.22, 0.36, and 0.51 Hz at PV = 10, 14, and 18 V, respectively. Table 1 lists s calculated as Np/Ts for all five values of PV studied here.

Figure 10 shows kL measured for helium in the SJAT, kL(600) [i.e., kL referenced to a Schmidt number (Sc) of 600 based on a Sc−1/2 dependence], plotted versus (Ds)1/2 with D = 1.67 × 10−5 cm2 s−1 (i.e., Sc = 600 for freshwater at 293.15 K). The solid line in Fig. 10 is a least-squares linear regression of the data with a coefficient of determination of 0.99, indicating that the data are highly correlated. This correlation is similar to that observed by McKenna and McGillis (2004) where the square root of the frequency of occurrence of surface divergences was found to scale linearly with kL. In this case, demonstrating that s derived from pH fluctuations such as shown in Fig. 6 scale linearly with kL provides further evidence that the LIF-DCFS technique described here is able to measure near-surface concentration fluctuations of CO2. The non-zero intercept of the linear regression in Fig. 6 has been observed previously in mechanically agitated systems by Asher and Pankow (1986) and McKenna and McGillis (2004) and is thought to result from the scaling (RMS)1/2 becoming inapplicable at low turbulence intensities.
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Fig. 10

Plot of (Ds)1/2, calculated using the pH fluctuation rates, s (Hz), listed in Table 1 and a molecular diffusivity, D, of 1.67 × 10−5 cm2 s−1 plotted versus the gas transfer velocity measured for helium normalized to a Schmidt number, Sc, of 600 assuming a Sc−1/2 dependence, kL(600)

6 Conclusions

The results and analysis presented here show that the LIF-DCFS technique can be used to study the time constants of pH fluctuations near the surface of an air–water interface caused by the air–water flux of carbon dioxide and provides a complementary method to traditional imaging fluorescence techniques. The timescales of the fluctuations measured using the LIF-DCFS technique have relevance towards understanding air–water gas transfer, and this method provides a powerful new tool for studying air–water gas transfer. Although not discussed here, it is a simple matter to adjust the concentration of Orange-G to study pH fluctuations as a function of depth (Asher and Pankow 1989). Further applications of this method include concurrent measurement of the timescales of surface temperature and pH fluctuations so as to study the use of heat as a proxy tracer for gas transfer. More detailed analysis of the relationship between the pH fluctuations measured here and both bulk air–water gas transfer velocities and concurrently measured surface temperature fluctuations is the subject of a subsequent paper.

Acknowledgments

We wish to thank the three anonymous reviewers whose constructive criticisms of this manuscript paper were appreciated. This research was supported by the National Science Foundation under grant OCE-0425305.

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© Springer-Verlag 2008