ACCEPTED FOR PUBLICATION IN APPLIED GEOCHEMISTRY APRIL 2015.

MEASURING FLOW RATES AND CHARACTERIZING FLOW REGIMES IN HOT SPRINGS

B. R. Mathon1, M. A. Schoonen2,3, A. Riccardi4, M. J. Borda5 Department of Geosciences, Stony Brook University, Stony Brook NY11794-2100.

ABSTRACT Detailed studies were conducted at Big Boiler hot spring in Lassen Volcanic

National Park, CA, and Ojo Caliente hot spring in Yellowstone National Park, WY, to measure the flow rate and characterize the flow regime of hot spring drainages. These drainages represent some of the most dynamic interfaces between the hydrosphere and atmosphere with steep temperature gradients and chemical gradients. The rate of thermal disequilibrium and chemical disequilibrium dissipation depends on the flow rate and flow regime.

The drainage of each hot spring was divided into ten or more segments and water samples were collected at segment boundaries. Fluid flow velocity throughout the drainage was measured using an in situ flow probe where possible and by determining the advancement of a red food dye tracer through the flow channel. A combination of field and laboratory studies was used to adapt a method based on the transport-controlled dissolution rate of gypsum to characterize the flow regime throughout the drainages.

Laboratory experiments as a well as a deployment in an artificial drainage were

1 Current Address: Johnson State College, Department of Environmental & Health Sciences, Johnson, VT 05656 2 Corresponding author: [email protected] 3 Current Address: Environmental and Climate Sciences, Brookhaven National Laboratory, Upton NY. 4 Current Address: British Petroleum, Houston Texas. 5 Current Address: Golder Associates, 200 Century Parkway, Suite C, Mt. Laurel, New Jersey, USA 08054

1 conducted to validate the application of this method for hot spring environments. The deployment of the gypsum tablets was complemented by using digital videography to record the nature of the flow regime throughout the drainages.

In situ flow probe measurements were not possible at all locations. The data obtained with the probe showed a range of values that was in reasonable agreement with the flow rates obtained using the dye tracer. The average flow rate based on advancement of dye tracer determined at Big Boiler was 0.22 m/s in both 2000 and 2001, while in Ojo Caliente flow rate varied from 0.39 m/s in 2001 to 0.45 m/s in 2002. The results of the gypsum dissolution measurement in the field yield boundary layer thicknesses between 8 and 38 micron, with most values between 15 and 25 micron, indicating well-developed turbulent flow throughout the drainages. The results, consistent with videography, indicate that gypsum dissolution rates based on the deployment of well-characterized and pure gypsum tablets can be used in hot-spring environments. An analysis of cooling rates within the drainages illustrates the importance of turbulent flow in cooling the waters.

2 1. INTRODUCTION

Hot springs and their drainages represent some of the most dynamic interfaces between the hydrosphere and atmosphere with steep temperature gradients and chemical gradients.

As hot spring waters discharge, the thermal disequilibrium and chemical disequilibrium with the atmosphere is the driving force for heat transfer (i.e., cooling of the water), mass transfer (e.g., degassing volatile species), and chemical reactions (e.g., mineral precipitation or oxidation) (Druschel et al., 2004). These processes are coupled as mass transfer and chemical reactions are typically temperature dependent and chemical reaction rates are often dependent on mass transfer of a reactant (e.g, ingassing of molecular oxygen) (Hill, 2009; Lemoine et al., 2003; Mills, 1999; Ocampo-Torres et al.,

1994; Welty et al., 2001). The presence of microbial communities thriving on the disequilibrium conditions in the drainage adds another layer of complexity. The flow rate is an important factor as it dictates the overall mass transfer of solution through the system, while the flow regime dictates how rapidly thermal and chemical disequilibrium is dissipated in the system (Sherwood and Pigford, 1952). The flow regime, which can range from laminar to turbulent, depends on whether the flow is governed by viscous forces that tend to keep fluid parcels from moving chaotically versus inertial forces that induce chaotic movement among fluid parcels. In the laminar flow regime, the viscous forces dominate and the fluid flow can be represented by thin layers of fluid moving parallel to one another. The velocity of the fluid layer closest to the bottom is the lowest in an open channel governed by laminar flow. In turbulent flow, the layers are broken up

3 and fluid parcels move chaotically. The breakdown of laminar flow and development of turbulent flow is a gradual process and referred to as a transitional flow regime.

Understanding the processes and obtaining rates for cooling, gas transfer and chemical reactions will ultimately allow for better geochemical and thermal modeling of hot springs. An understanding of the dissipation of the thermal disequilibrium and the dissipation of the chemical disequilibrium through abiotic processes will provide microbiologist and biogeochemists with the physicochemical constraints on microbes living in hot springs and their drainage systems. This may also allow one to evaluate to what extent microbes influence the dissipation of chemical and thermal disequilibrium.

With a fundamental understanding of the physicochemistry of hot spring systems on Earth, it may be possible to constrain or characterize the physicochemical conditions of ancient hot spring systems found on Mars. It is already believed that images resembling terraced pools on Mars could have formed from discharging hydrothermal fluids (El Maarry et al., 2012; Farmer, 1996; Schulze-Makuch et al., 2007). The ability to understand how chemical disequilibrium is dissipated on Mars will provide insight as to whether life could have thrived near Martian hydrothermal systems.

In this paper we present a detailed assessment of the physical characteristics, flow rate, and flow regime of drainages of two hot springs. Each drainage was divided into segments by establishing sampling stations where flow velocity was measured and flow regime was characterized along the drainage. While measuring flow velocities is relatively straightforward, it is a challenge to characterize flow regime in the drainages.

One approach to characterize flow regime is to calculate Reynolds numbers for each segment of the drainages. Reynolds numbers, defined as the ratio of inertial forces

4 to viscous forces, provide an indication which of these forces dominates flow (Reynolds,

1883). If viscous forces dominate (low Reynolds numbers), the flow is laminar.

Conversely, if inertial forces dominate (high Reynolds numbers) the flow is turbulent.

However, calculating Reynolds numbers for hot spring drainages is fraught with uncertainty because empirical formulas have been developed for well-defined open channels and pipes, but are not available for the type of irregular drainages studied here

(Mathon, 2002). As an alternative, we evaluated the applicability of a method to characterize the flow regime based on measuring the in situ dissolution rate of gypsum plates that yields boundary layer thicknesses. The smaller the value of the boundary layer, the more turbulent the flow.

2. BACKGROUND The in situ technique used here to characterize flow regime involves determining the dissolution rate of gypsum plates with a known surface area. The underlying assumption is that the rate-limiting step is transport from the mineral surface through a stationary layer into the bulk solution (Fig.1). It is assumed that fluid at the mineral

Figure 1 Conceptual figure of the boundary layer developed on a surface of a binary mineral, CD, with C+ and D- as constituents. The arrows indicate the transition of constituent ions into the overlying fluid. The concentration profile in the solution film adjacent to the surface for either one of the constituent ions is schematically shown. Note that the boundary layer thickness will decrease with increasing flow rate parallel to surface and the onset of turbulence. 5 interface is in equilibrium with the mineral. The thickness of the stationary or boundary layer, δ, is dictated by the hydrodynamics of the system (Dreybrodt et al., 1992;

Opdyke et al., 1987; Tengberg et al., 2005). A recent exhaustive literature review by

Colombani (2012) has shown that the rate of gypsum dissolution is directly proportional to the disequilibrium between the bulk solution and the solution immediately adjacent to the mineral surface. Hence, the undersaturation of the bulk solution with respect to gypsum provides the driving force for the reaction. The difference between the calcium concentration in the bulk solution and at equilibrium with gypsum is commonly used to express the driving force (Opdyke et al., 1987; Tengberg et al., 2005). Hence, in equation 1, which describes the rate of gypsum dissolution, D is the diffusion coefficient

2+ 2 2+ 3 for Ca (aq) (cm /s), ceq is the equilibrium Ca (aq) concentration (mol/cm ), cb is the actual

2+ 3 Ca (aq) concentration in the bulk solution (mol/cm ) . The dissolution rate is determined on the basis of the mass loss of the tablet after 2.5 to 3 hours of exposure to the flowing water (equation 2).

Rdiss = k(ceq-cb)=(D/δ )*(ceq-cb) (1)

Rdiss = Δm/(A*Δt) (2)

For Equation 2, Δm is mass loss (mol gypsum), A is the surface area (cm2), and Δt is the exposure time (s).

The important assumptions underlying the use of this method in the field are (1) that the water is significantly undersaturated with respect to gypsum and (2) that the dissolution is governed by a transport-controlled mechanism as opposed to a surface- controlled mechanism. In a transport-controlled dissolution mechanism, the rate depends

2+ 2- on how quickly the constituent ions (here Ca and SO4 ) are removed from the mineral 6 surface to the bulk solution through the boundary layer. By contrast, in surface- controlled reactions, an elementary reaction step at the mineral surface is the rate-limiting step. Hence, to extract boundary layer thicknesses from the deployment of gypsum plates in an aqueous environment it is critical to validate whether the dissolution mechnism is a transport-controlled mechanism under the prevailing conditions. Results of earlier experimental studies have confirmed that the kinetics of gypsum dissolution is transport controlled for conditions in which cb< 0.9ceq (Barton and Wilde, 1971; Christoffersen and

Christoffersen, 1976; James and Lupton, 1978; Jeschke et al., 2001; Liu and Nancollas,

1971). Closer to equilibrium, 0.9ceq

The in situ gypsum method has been used in a variety of settings before. Opdyke et al. (1987) used gypsum plates to calculate the mass transfer velocity and determined that this method could be used to estimate the viscous stress in ocean floor studies. Field studies by Dreybrodt et al. (1992) and Zaihua et al. (1995) focused on measuring precipitation rates of calcite in spring-fed streams. Gypsum tablets were used to estimate

δ in order to correct their estimated rates for the diffusive resistance of the boundary layer. Values for δ range from 100 to 300 µm. 7

Table 1. Summary of selected earlier deployments of in situ gypsum method $ Investigator Site of Deployment T Velocity δ (µm) δ25 (µm) (°C) Opdyke et al., 6m x 30m flume 26 4.8·10-3 230* 230 1987 m/s Dreybrodt et al., Small spring-fed 10 0.2-0.5 100-300 74-221 1992 stream m/s Zaihua et al., Huanglong Ravine, 4 – Average 100 74 1995 spring-fed stream 15 of 1 m/s ** Nixon et al., 1980 • Naragansett Bay 0.5- Not 4 2.3 ** • Microcosm tank 28 reported 20 11.5 Santschi et al., • Benthic chamber 50-200 400-800±100 230-459 1983 mock ups mL/min • Sea floor 0 3 ± 2 cm/s 470 269 • Very high 25 14 turbulence Tengberg et al • Large chamber with 19.0 n.a. 254-322 232-293 (2005) mechanical stirrer, 10 rpm (CISE design) • Small chamber with 19.0 n.a. 484-1029 441-937 circulation pump (DUINEV design) * Estimated from mass transfer velocity data at T = 26°C (Opdyke et al., 1987) ** Estimated assuming T = 0.5°C, P = 1atm, initial mass = 7g, surface area = 4.5 cm2, -5 3 -5 3 cs = 2.73 ·10 mol/cm s, cw = 1.06·10 mol/cm s (Santschi et al., 1983) $ normalized boundary layer thickness to reference temperature of 25ºC, see text.

Gypsum dissolution has also been used in marine studies to quantify flow regime.

Nixon et al. (1980) used dissolution rates of gypsum blocks (~2.5 by 1.8 by 0.7 cm and 6 to 8 g) to compare flow regime in the natural environment (Narragansett Bay, Rhode

Island) to flow regimes in microcosms induced by a mixer. Santschi et al. (1983) developed a strategy to calibrate measurements of chemical transport across the sediment-water interface made in benthic chambers. Gypsum plates were used to measure boundary layer resistances to chemical transport both within the benthic chamber and on the sea floor itself. The method to calculate δ in their study was similar 8 to the one used here, see Equation 1. Their results ranged from 400 ± 100 µm to 800 ±

100 µm, with one experiment performed under highly turbulent flow conditions leading to a δ value of 25 µm. More recently Tengberg et al. (2005) conducted an extensive intercomparison of marine benthic flux chamber designs in which the gypsum method was used to determine flow regime in each design. Boundary layer thickness ranged from 254 to 1029 µm. Porter et al. (2000) reviewed the use of this technique in a variety of natural and engineered settings. Table 1 summarizes results from some of the earlier deployments of the in situ gypsum method.

While the in situ gypsum method has been deployed in a number of environments, it has its limitations. As pointed out by Porter et al. (2000) the method is not well suited for environments with fluctuating or pulsating flow conditions. However, these authors do support the use of the method in environments with steady flow conditions and to extract mass transfer values in such settings. The hot springs studied here represent steady flow conditions and the objective is to characterize mass transfer within these systems.

Earlier studies using the in situ gypsum dissolution method have not included hot spring environments. Hence, it is critical to evaluate if the dissolution mechanism for gypsum in non-stoichiometric solutions at temperatures greater than 25°C changes. In this study we present experimental results that validate the use of the method over a much wider temperature range and in non-stoichiometric solutions that are far from saturation with respect to gypsum. The experiments were guided by the temperature range encountered in the hot spring drainages studied (55 to 92 ºC) and the stoichiometry of the solutions. 9 3. Description of Field Sites

Field studies were conducted at Big Boiler in the Bumpass Hell hydrothermal area of Lassen Volcanic National Park (LVNP), in north central ( a location map is available in Supplemental Materials 1) and Ojo Caliente in the Lower Geyser Basin of

Yellowstone National Park (YNP), WY ( a location map is available in Supplemental

Materials 1). In addition, a trial experiment was also conducted in an artificial overflow of a fountain on the Stony Brook University campus. The fountain has a flow rate similar to the hot springs, but the water is at ambient temperature.

3.1. Big Boiler, LVNP erupted last on May 22, 1915. While Lassen Peak is one of the world’s largest domes, it is believed that Lassen Peak began as a volcanic vent on the side of an even larger named Mount Tehama (Clynne et al., 2000).

Mount Tehama last erupted approximately 600,000 years ago, leaving behind a vast . The still active hydrothermal areas include such features as Sulphur Works,

Bumpass Hell, Devil’s Kitchen, Little Hot Springs Valley, Boiling Springs Lake, and

Terminal Geyser. The activity of Bumpass Hell is visible in the numerous fumaroles and several boiling mud pots. Bumpass Hell is a steam-dominated hydrothermal system with fumaroles and water condensing in several pools that feed small drainages (Ingebritsen and Sorey, 1985). The source of the water is predominantly meteoric (Day and Allen,

1924; Ingebritsen and Sorey, 1985; Janik and Bergfield, 2010; Xu and Lowell, 1998).

The drainages contain several small cascading falls and rocks present in the drainage create eddies. Small steam vents are located in close proximity to the drainages and may contribute heat and steam to the water in the drainage. Images and a general description

10 of the area are available from the USGS (2009). Pictures and video of Big Boiler (

40°27'27.74"N 121°30'6.70"W; elevation 2500m) are available in Supplemental Material

1.

The study at Big Boiler, LVNP, was conducted in August 2000 and in July 2001.

The drainage is approximately 57 m in length. The beginning of the drainage is well

defined. After about the first 30 m, the slope decreases, the channel widens and the

drainage becomes shallower. In order to conduct a detailed study, the drainage was

divided into segments by establishing 24 stations along the drainage. At each station, pH,

temperature, and water samples were collected. A plot of temperature versus distance

shows significant cooling (Fig. 2). The source of the drainage was approximately 85°C

(about 7°C below the boiling point at 2500 m) while the end of the drainage was

approximately 55°C. The average air temperature was 22°C and humidity was 27%.

11 Figure 2. Temperature measurements in Big Boiler drainage, LVNP, versus distance.

3.2. Ojo Caliente, YNP

Yellowstone National Park has been a site for scientific studies since 1888

(Gooch and Whitfield, 1888). The first comprehensive study in YNP was conducted by

Allen and Day (Allen and Day, 1935). The park itself resides on a high (~2,500m) plateau (Smith and Braile, 1994). YNP’s volcanic history involves the formation of three at 2.1 Ma, 1.3 Ma, and 0.64 Ma ago (Smith and Siegel, 2000). The majority of the hydrothermal activity can be found within the youngest caldera (Xu et al., 1998). Ojo

Caliente is located in the Lower Geyser Basin (44°33'46.37"N 110°50'19.70"W). It consists of a source pool and a well-defined run-off drainage developed on a hard, impermeable subsurface. The drainage forks and flows into the Firehole River. The immediate surrounding area appears less complex than at Big Boiler. A large meadow with a smooth gradient and abundant flora surrounds Ojo Caliente and the ground is markedly more stable.

12 Figure 3. Temperature measurements in Ojo Caliente, YNP. Top panel shows a single set of data collected in 2001, while the bottom panel shows temperature profiles measures on three different days in 2002. Note that the three measurements in 2002 show some differences in temperature profile, particularly in the downstream portion of the drainage. At Ojo Caliente, YNP, field studies were conducted in July 2001 and July 2002.

13 The drainage is approximately 24 m long (see pictures and video in Supplemental

Material 2). The channel begins wide (121.9 cm) and well defined, but after about 4 meters the channel becomes narrower. There are several forks in the drainage (Ball et al.,

2001), however for simplicity only one fork was investigated during the 2001 and 2002 field studies. (Previous studies showed that the other forks have a similar temperature profile and chemical composition (Ball et al., 2001)). With the water split among several forks, each channel is narrower and shallower than the single channel close to the source .

The drainage was divided into 11 stations. At each station, pH and temperature were measured and water samples were collected. The source pool is about 92˚C and boiling.

At the first station closest to the pool, the temperature is 89˚C (2001) to 92˚C (2002) and at the end of the drainage the temperature has dropped to 67˚C (2001) and 63˚C (2002)

(Fig. 3). The data collected in 2002 over three consecquetive days shows that the conditions at Ojo Caliente do vary somewhat (Figure 3b). Average air temperature was

20˚C and humidity was 20%.

3.3. Stony Brook Fountain

The Stony Brook fountain is located on the main campus in Stony Brook, New

York, USA ( 40°54'53.38"N 73° 7'16.27"W). The fountain consists of a fountain basin, which is connected to a stepped, landscaped, brick-lined channel. The flow velocity and geometry of the channel is uniform over the entire length. The fountain is about 16 m in total length, 1.22 m wide and the water is generally 10 cm deep. The fountain is constructed in such a way that there are five sections each 6.5 m in length with no change

14 in slope. Hence, the flow in the fountain is uniform compared to the hot spring drainages. The sections are separated by a 90° step that is approximately 40 cm in height, and produces turbulence in the water, see overview picture and video

(Supplemental Materials 3). Unlike the hot spring drainages, the only varying condition in the fountain is the turbulence. The temperature of the water (21ºC) is consistent throughout the drainage, the velocity of the water in the two different sections is essentially constant, and the dimensions of the fountain do not change. This experiment provided a test on the in situ technique under flow conditions that were comparable, but without the complexity of elevated temperatures and the presence of appreciable amounts of calcium and sulfate in solution.

4. METHODS

4.1. Field Methods and Water Analyses

Water samples were taken at each station using a 60 mL plastic syringe. The syringe was rinsed twice with sample before filtering the water through a 0.45 µm

(LVNP 2000) or a 0.22 µm (LVNP/YNP 2001; YNP 2002) filter into a 125 or 60 mL

Nalgene bottle. Separate water samples were collected for anion and cation analysis. A small amount (1 vol%) of 6N HCl was added to the sample collected for cations. The

2+ 2+ + + + - 2- water samples were analyzed in triplicate for Mg , Ca , K , Na , NH4 , Cl , and SO4 on a Dionex Series 500 ion chromatograph equipped with a conductivity detector and an automatic sampler, upon return to the laboratory. Cations were analyzed using a 22 mN

H2SO4 eluent at a 1.0 mL/min flow rate through an IonPac CS12 column. The anions were analyzed using a 1.8 mM Na2CO3/ 1.7 mM NaHCO3 eluent at a flow rate of 2.0

15 mL/min over an IonPac AS4A-SC column. One standard deviation uncertainty in the cation measurements based on triplicate analysis was calculated to be 2.5%; whereas the one-standard-deviation uncertainty in anions was calculated to be 1.5%. Temperature and pH measurements were obtained on site using a Fisher Scientific™ Accumet AP62 pH meter equipped with a combination pH electrode and Pt thermistor. The electrode was calibrated using pH 7 buffer in combination with either pH 2 (LVNP) or pH 4

(YNP) buffer solutions.

Width and depth measurements of the channels were taken using a tape measure at each station marking. Length measurements were taken between each station marking.

The velocity of the fluid was measured by two methods. In situ measurements were made, where possible, with a FP101 model Global Water Instrumentation Incorporated flow probe. The probe consists of a small paddle wheel held in a 5.08 cm diameter PVC tube. The instrument can measure flow rates as low as 0.1 m/s and and high as 4.5 m/s.

Measurements were possible at most stations; however, some locations in the individual drainages were too shallow to immerse the probe. Some of the measured velocities were at or just below the lower range of the flow probe. A red food dye tracer method was also used to obtain an average velocity for each of the two hot spring drainages. The dye was added at the first station, time 0, and the time when the front of the dye plume passed each station was recorded. The food dye could not be used in the Stony Brook fountain overflow.

To characterize the flow regime in the field, gypsum tablets were placed in the channel at most or all stations. After a known amount of exposure time the tablets were removed from the channel, immediately blotted dry, and then allowed to dry overnight.

16 The mass loss was measured upon return to the laboratory on an analytical balance

(Mettler) and used to determine the rate of dissolution using Equation 2. For the July

2001 field studies, a Canon Elura 2 MC digital video camcorder was used to film the water flow motion to characterize the flow regime at each station. The video was edited using the software Studio DV 1.2.6.0 and rendered as a RealVideo file at a resolution of

240 x 180 pixels.

The gypsum used in this study were hand specimen samples of alabaster, purchased from Ward’s Natural Science Establishment, Inc. Rochester, New York.

Samples were cut to a measurement of ~ 1.5 x 2.5 x 0.25 inches (3.81 x 3.81 x 0.635 cm).

Next, specimens were hand polished using silicon carbide (grit # 110) and ethanol. Four coats of polyurethane were applied to the sides and bottom of the tablet to control the exposed surface area, ~14.5 cm. After a separate lab experiment, which subjected gypsum tablets with various numbers of coatings to a beaker of water at 90 ± 2°C, it was determined that four coats was sufficient to withstand the water in the hot spring environments. To determine the exposed surface area, the tablets were placed on a xerox copier producing copies on millimeter graph paper. The outline of the tablet was then cut out and weighed on a high precision analytical balance to determine the surface area that was exposed. The tablets were weighed prior to deployment using a Mettler top-loading balance (0.0001g accuracy).

4.2. Experimental Methods for determining gypsum dissolution rates

17 Two types of experiments were conducted. Flow-through experiments were used to evaluate the temperature dependence of the gypsum dissolution. Batch experiments with non-stoichiometric and stoichiometric solutions were conducted to evaluate the effect of stoichiometry on the dissolution rate.

4.2.1. Flow-through Experiments The temperature at the drainages in this study ranged from 55 to 92°C, while the in situ gypsum method has not been deployed at temperatures above 25°C in previous work. As mentioned in the introduction, the application of the in situ gypsum method rests on the assumption that the dissolution of gypsum is a transport-controlled reaction mechanism. To evaluate whether this holds for conditions encountered at LVNP and

YNP, we conducted five flow through experiments to determine the activation energy for the reaction over a temperature range from 38 to 72°C.

The flow-through experiments were conducted in a 500 mL plastic container (7.0 by 12.7 by 6.4 cm). Two holes were drilled in the container, one low to allow water to be pumped into the container and one opposite near the top of the container to allow water to fill and flow out of the container. A piece of Velcro was attached to the bottom of the container to insure exact placement of the gypsum tablet in all experiments. A plastic cover was attached to the container to prevent evaporation and subsequent heat loss. A small hole (~1mm diameter) was drilled in the cover to allow for a thermocouple to monitor the temperature of the water in the flow through container. A peristaltic pump was used to circulate water through the system at a velocity of approximately 0.09 m/s.

For the first three experiments, water was drawn from a 42.5 L reservoir that was constantly being refilled by hot tap water. The remaining two experiments, conducted in 18 a closed system, relied on water being drawn from a water bath which was heated to 58.5

± 1.0°C and 72.3 ± 0.4°C. This was circulated through the system and returned to the water bath to minimize heat loss. To maintain a high degree of undersaturation with respect to gypsum, a shallow flat dish containing a mixed anion/cation resin was used to

2+ 2- remove Ca and SO4 ions from solution.

4.2.2. Batch Experiments Three batch experiments with different initial solution composition were conducted to evalute if the dissolution mechanism changes as a function of solution stochiometry. The experimental conditions were guided by the the chemical composition of the water in the two drainages. Using water analysis data and the USGS geochemical software PHREEQC with the database phreeqc.dat, we calculated that Big Boiler has a saturation index (SI) of –1.87 (based on the 2000 field data) with respect to gypsum, and

Ojo Caliente has an SI of –3.27 (July 2001). Note that both drainages are sufficiently far from equilibrium so that the rate of gypsum dissolution is expected to be directly proportional to the undersaturation of the solution. For example, in Big Boiler, which is closer to equilibrium to gypsum than Ojo Caliente, the calcium concentration is less than

3% of the equilibrium calcium concentration, well below the 90% threshold when equation 1 no longer hold. Given that the waters at Big Boiler were the most saturated with respect to gypsum, we chose to create two solutions that mimic the saturation in this

2+ 2- water. One was a stoichiometric solution (1:1) with respect to Ca and SO4 (Solution

2+ 2- A) and the other was a non-stoichiometric solution with a Ca to SO4 ratio of 1:8

(Solution B). Both solutions were prepared using powdered CaCO3 and a stock 1N

H2SO4 solution. The pH of the 1:8 solution measured 2.5. Since, in a solution with pH of 19 - 2- approximately 2, the dominate sulfur species in solution becomes HSO4 not SO4 , the

2- pH was increased so SO4 is the dominant species. The pH was adjusted to 6.7 using a concentrated solution of NaOH. A third experiment was run using deionized water,

(EasyPure DI, 18 MΩcm-1). This was used as a comparison to experiments with Solution

A and B.

The tablets were prepared with the same method as described above. During an experiment, the tablet was mounted to the bottom of a 1 L Pyrex vessel with Velcro.

This was to ensure that the tablets used in each experiment were in the same place in the vessel and undergoing identical flow conditions. The vessel was placed in heated water.

The temperature of the solution in the vessel (approximately 750 ml) was held at ~55.5°

± 1°C. Each experiment lasted approximately two hours. In the first hour, the solution was allowed to heat to the desired temperature; after this warm up period, the gypsum plate was placed in the vessel and allowed to dissolve for 1 hour. A laboratory stirrer, set at a constant stirring rate of ~530 rpm was used to keep the solution well mixed. Every

10 minutes, 1 mL of sample was removed for analysis of Ca2+ using ion chromatography.

Temperature and pH were recorded throughout the experiment using a thermocouple and a Fisher Scientific Accumet AP62 pH meter, respectively. After the gypsum was exposed for 1 hour, the tablet was removed and allowed to dry overnight. The following day it was weighed and the rate of dissolution was calculated using Equation 2.

4.3 Determination of cooling rate of near-boiling standing water

For comparison to the cooling rate of the flowing water in the hot spring drainages, we conducted three simple experiments in which we heated up tap water to

20 near boiling temperatures (90-95°C) poured it gently into a Pyrex™ rectangular container

(17x22 cm). The temperature in the standing water was measured using a K-type thermocouple and recorded every 15 seconds. The cooling experiment was conducted with water depths of 5.9, 3.8, and 1.7 cm. The ambient temperature of the air was 17 °C.

5. RESULTS In this section, the laboratory dissolution experiments will be presented first, followed by the results from the field studies and the cooling rate measurements.

5.1. Temperature Dependence of Gypsum Dissolution Rate

The results of the laboratory flow-through experiments at five temperatures between 35 and 73°C are summarized in Table 2. The rate of dissolution is based on the mass loss and calculated using equation 2. Given that in these experiments the bulk concentration of the constituent ions, calcium and sulfate, is minimized by circulating the solution through a mixed bed ion exchanger, the concentration gradient is dictated by the equilibrium concentration, ceq. This then simplifies equation 1 to:

Rdiss = kceq (3)

Using this simplified equation we have calculated the reaction rate constant for each temperature by dividing the rate by the equilibrium concentration. Using the Arrhenius plot (Fig. 4), we obtain an activation energy of 15.4 kJ/mol or 3.68 kcal/mol.

21 Table 2. Summary results of flow-through experiments as function of T. -2 # Experiment T (°C) * Exposure Rdiss (mol·cm · k time (s) s-1) -8 T-1 35.8 ± 0.5 21360 2.86 x 10 1.78E-06 -8 T-2 41.5 ± 0.3 16020 3.36 x 10 2.08E-06 -8 T-3 57.0 ± 1.4 10860 3.83 x 10 2.40E-06 -8 T-4 58.5 ± 1.0 7260 4.22 x 10 2.66E-06 -8 T-5 72.3 ± 0.4 3840 5.33 x 10 3.53E-06

*:based on 10-12 thermocouple measurement during course of experiment. #:calculated by using equation 2 and dividing by equilibrium calcium concentration (mol cm-3).

$12.5"

$12.7"

$12.9" lnk$

$13.1" y"="$1852.1x"$"7.244" R²"="0.95601"

$13.3" 0.0028" 0.0029" 0.003" 0.0031" 0.0032" 0.0033" 1/T(K)$

Figure 4. Arrhenius plot for flow-through laboratory experiments.

22

Table 3. Summary experimental results to evaluate influence of solution stoichiometry. Solution Exposure time Surface Area Mass Loss Rdiss (seconds) (cm2) (grams) (mol/cm2s) Deionized Water 3703 14.49 0.765 8.28E-08 Solution A (1:1) 3731 14.62 0.794 8.46E-08 Solution B (1:8) 3739 13.16 0.713 8.42E-08

Solution ratios are molar Ca:SO4 ratios. Temperature for all experiments was ~ 55.5° ± 1°C.

5.2. Rates of Gypsum Dissolution in Solutions Similar to Hydrothermal Springs

Figure 5. Calcium versus time in laboratory experiments with varying stoichiometry and undersaturation levels.

The experiments with two solutions matching Big Boiler in terms of saturation

state (Solution A) and staturation state as well as stoichiometry (Solution B) are

23 summarized in Table 3, along with an experiment with deionized water as starting solution (C). Solution A has an SI of –1.95, while Solution B has an SI of –1.90. Hence, both A and B are close to the SI value of –1.87 calculated for water collected in Big

Boiler in August 2000. The rates of dissolution that were calculated based on the mass loss of gypsum showed little difference between the three solutions, see Table 3. The evolution of Ca2+ concentrations in each of the three experiments is presented in Figure 5.

All three experiments show a linear increase in calcium concentration over time, which suggest that the dissolution rate remains linear over time. This despite the fact that the saturation indices had significantly changed from their initial values over the course of the experiment. For example, the final SI of the DI experiment was –0.55 and for

Solutions A (1:1) and B (1:8), -0.47 and -0.46, respectively.

5.3. Field Flow Rates and Boundary Layer Thicknesses

Measurements of width, depth and velocity at the various stations are reported in

Table 4. The hot spring drainages are typically less than a meter wide and shallow, with water depths typically less than 5 cm. The fluid velocity taken with the flow probe reveals variations between stations with an average at Big Boiler of 0.2 ± 0.1 m/s and at

Ojo Caliente, 0.3 ± 0.2 m/s, see Table 4. The Stony Brook Fountain is larger than the natural drainages (width of 122 cm and depth of 10 cm) and does not vary with distance along the channel (i.e., is uniform). The velocity is comparable to that in the natural drainages with 0.09 m/s measured in the flat section and 0.2 m/s in the area following the step (Table 4). It should be noted, however, that these velocities are at the lower end of

24 the operational range for the in situ flow probe. The in situ flow measurements in the hot spring drainages are in reasonable agreement with the average flow rates based on the

Table 4 Drainage dimensions and flow rates.

Station Width Depth Velocity Number (cm) (cm) (m/s)# Stony Brook Fountain, July 2000 (step) 1 122 10.2 0.2 (smooth) 122 10.2 0.09 2 Big Boiler, August 2000 2 22.9 2.5 0.2 4 19.1 3.8 0.2 5 35.6 6.4 0.2 6 25.4 3.8 0.2 8 27.9 3.8 0.2 9 21.6 3.2 0.2 11 21.6 3.2 0.3 13 17.8 3.8 0.2 15 33.0 3.8 0.2 16 40.6 3.2 0.2 19 27.9 1.3 0.2 21 20.3 3.2 0.2 22 17.8 4.4 0.2 23 30.5 4.4 0.2 24 17.8 3.8 0.2 Big Boiler, July 2001 1 8.3 7.0 0.3 2 26.7 5.7 0.3 4 16.5 4.4 0.3 5 35.6 5.1 0.1 6 22.9 3.8 0.2 7 33.7 5.1 0.2 8 30.5 5.1 0.4 9 21.6 2.5 0.2 11 48.3 1.3 0.3 12 25.4 7.6 0.2 13 16.5 4.1 0.2 15 29.2 3.8 0.2 16 40.6 2.5 0.3 18 54.6 1.3 0.2 19 76.2 2.5 0.2 25 21 38.1 2.5 0.2 22 17.8 6.4 0.2 23 36.8 2.5 0.3 24 25.4 3.2 0.2

Station Width Depth Velocity Number (cm) (cm) (m/s) Ojo Caliente, July 2001 1 121.9 2.5 0.2 2 96.5 7.6 0.2 3 35.6 5.1 0.8 4 99.1 2.5 0.3 5 45.7 5.1 0.4 6 38.1 5.7 0.2 7 50.8 1.3 0.1 8 45.7 1.3 0.3 9 38.1 0.6 0.4 10 20.3 2.5 0.4 11 15.2 1.3 0.4 # in situ flow probe measurements

26 Figure 6. Flow rate measurements in drainages: left panel Big Boiler, LVNP, and right panel Ojo Caliente, YNP. Insets in both panels show collected using in situ flow probe where possible, while main figure are arrival times of most intense color of food dye at each station. The equation for each of the regression lines is in the form of y=a+bx.

27 dye tracer experiments, Fig 6. There is also good agreement between the tracer- based measurements obtained in each of the two years at Big Boiler. The 2002 measurements in Ojo Caliente indicate that the flow rate was higher (0.45 m/s) compared to the data collected the previous year (0.39 m/s)

The results of the deployment of the in situ gypsum dissolution experiments are summarized in Table 5. Table 5 also contains the results of a calculation of the thickness of the boundary layer for each station. This calculation was based on Equation 1, with the equilibrium calcium concentration calculated using PHREEQC, the observed calcium concentration from the analysis of the water collected in the field, and an estimation of the diffusion coefficient for calcium at the observed temperature. Diffusion coefficients increase with temperature and we used the temperature dependence for diffusion coefficients shown in Equation 4 (Flury and Gimmi, 2002):

DT=(T/298)*(µ298/ µT)*D298 (4), where µ is the dynamic viscosity of water. It should be noted that the dynamic viscosity of water increases by a factor of 3 when water temperature increases from 298 K (25ºC) to 353 K (80ºC). The result of the calculations indicate that the boundary layer thickness is consistently less than 35 micron in all cases. Most values are between 15 and 25 micron. The boundary layer thickness varies, however, along the drainage. In the following sections the results for each of the drainages are presented separately.

28

Table 5. Field data and calculated diffusion coefficients and boundary layer thicknesses*

2- 2+ 2+ 2 Station T pH SO4 Caw Caeq D (cm /s) Rdiss δt δ25 3 3 3 2 (˚C) (mol/cm ) (mol/cm ) (mol/cm ) (mol/cm s) (µm) (µm) Big Boiler, August 2000 2 84.5 2.15 1.42E-06 2.96E-07 1.09E-05 2.34E-05 1.04E-07 24 49 4 82 2.15 3.15E-06 2.96E-07 1.09E-05 2.26E-05 1.92E-07 13 26 5 81.1 2.17 1.56E-06 2.97E-07 1.08E-05 2.26E-05 8.80E-08 27 53 6 80 2.16 1.54E-06 3.01E-07 1.09E-05 2.20E-05 1.34E-07 17 33 8 73.9 2.19 1.80E-06 3.01E-07 1.08E-05 2.06E-05 1.09E-07 20 36 9 73.4 2.22 2.69E-06 2.98E-07 1.06E-05 2.08E-05 9.10E-08 23 42 11 72.2 2.2 2.74E-06 3.02E-07 1.07E-05 2.02E-05 1.07E-07 20 36 13 66.6 2.21 2.54E-06 3.01E-07 1.07E-05 1.87E-05 1.31E-07 15 26 15 69.2 2.22 2.61E-06 3.08E-07 1.06E-05 1.95E-05 8.62E-08 23 40 16 63.4 2.22 2.41E-06 3.03E-07 1.07E-05 1.79E-05 7.27E-08 25 42 19 62.7 2.24 2.37E-06 3.04E-07 1.05E-05 1.79E-05 8.27E-08 22 37 21 60.7 2.22 2.35E-06 3.04E-07 1.07E-05 1.72E-05 7.82E-08 23 38 22 56.2 2.17 2.36E-06 3.09E-07 1.09E-05 1.57E-05 7.39E-08 23 36 23 53.9 2.19 2.50E-06 3.07E-07 1.08E-05 1.53E-05 1.00E-07 16 25 24 50.6 2.17 2.54E-06 3.11E-07 1.09E-05 1.44E-05 5.81E-08 26 38 Big Boiler, July 2001 1 84.3 2.22 1.88E-06 3.36E-07 1.02E-05 2.50E-05 1.60E-07 15 31 2 83.5 2.26 2.04E-06 3.30E-07 9.93E-06 2.54E-05 1.01E-07 24 49 4 81.6 2.29 2.19E-06 3.25E-07 9.78E-06 2.51E-05 1.41E-07 17 34 5 80.5 2.29 2.25E-06 3.16E-07 9.79E-06 2.47E-05 7.81E-08 30 59 6 79.1 2.29 2.29E-06 3.17E-07 9.82E-06 2.42E-05 7.72E-08 30 58 7 77.1 2.29 2.39E-06 3.22E-07 9.83E-06 2.35E-05 8.47E-08 26 49 8 75.9 2.29 2.47E-06 3.19E-07 9.83E-06 2.31E-05 1.05E-07 21 39 9 74.2 2.29 2.52E-06 3.24E-07 9.86E-06 2.25E-05 8.46E-08 25 46 11 72.5 2.30 2.61E-06 3.25E-07 9.84E-06 2.21E-05 9.95E-08 21 38 12 70.5 2.28 2.63E-06 3.47E-07 9.97E-06 2.12E-05 8.11E-08 25 44 13 69.6 2.3 2.73E-06 3.26E-07 9.87E-06 2.11E-05 5.37E-08 38 67 15 67.0 2.29 2.82E-06 3.44E-07 9.94E-06 2.02E-05 2.40E-07 8 14 16 67.0 2.29 2.88E-06 3.23E-07 9.90E-06 2.03E-05 1.08E-07 18 31 18 64.9 2.27 2.86E-06 3.36E-07 1.00E-05 1.94E-05 1.30E-07 14 24 19 63.9 2.28 2.89E-06 3.16E-07 1.00E-05 1.92E-05 8.40E-08 22 37 21 61.5 2.26 2.97E-06 3.30E-07 1.01E-05 1.84E-05 6.13E-08 29 48 22 59.3 2.25 3.15E-06 3.29E-07 1.01E-05 1.78E-05 7.24E-08 24 37 23 57.2 2.22 3.14E-06 3.28E-07 1.02E-05 1.70E-05 7.06E-08 24 38 24 55.7 2.23 3.14E-06 3.27E-07 1.02E-05 1.66E-05 7.23E-08 23 36 29

Table 5 Continued

Ojo Caliente, July 2001

2- 2+ 2+ Station T pH SO4 Caw Caeq D Rdiss δt δ25 3 3 3 2 2 (˚C) (mol/cm ) (mol/cm ) (mol/cm ) (cm /s) (mol/cm s) (µm) (µm) 1 89.4 7.78 2.38E-07 5.60E-08 8.84E-06 2.73E-05 1.38E-07 17 38 2 89.7 7.78 2.41E-07 6.36E-08 8.82E-06 2.75E-05 8.15E-08 30 68 3 87.0 7.77 2.39E-07 5.71E-08 8.97E-06 2.64E-05 1.67E-07 14 30 4 86.2 7.78 2.4E-07 6.56E-08 9.03E-06 2.61E-05 1.69E-07 14 30 5 86.1 7.78 2.4E-07 5.86E-08 9.02E-06 2.61E-05 9.85E-08 24 51 6 85.5 7.78 2.41E-07 6.58E-08 9.06E-06 2.58E-05 1.28E-07 18 38 7 83.4 7.85 2.42E-07 6.75E-08 9.18E-06 2.50E-05 1.25E-07 18 37 8 76.5 8.00 2.56E-07 7.99E-08 9.52E-06 2.25E-05 1.43E-07 15 28 9 73.7 8.05 2.58E-07 7.70E-08 9.66E-06 2.15E-05 1.63E-07 13 24 10 71.2 8.11 2.64E-07 8.13E-08 9.78E-06 2.07E-05 1.27E-07 16 28 11 67.0 8.17 2.77E-07 8.89E-08 9.96E-06 1.93E-05 1.31E-07 14 24 Ojo Caliente, July 2002 1 92.0 7.30 1.92E-07 6.17E-08 9.54E-06 2.84E-05 1.32E-07 20 48 2 90.0 7.29 1.92E-07 6.35E-08 9.65E-06 2.76E-05 8.55E-08 31 71 3 88.9 7.25 1.91E-07 6.34E-08 9.74E-06 2.71E-05 1.62E-07 16 36 4 85.9 7.36 1.92E-07 6.47E-08 9.87E-06 2.60E-05 1.25E-07 20 42 5 86.0 7.42 1.92E-07 6.34E-08 9.91E-06 2.60E-05 9.81E-08 26 55 6 85.5 7.45 1.93E-07 6.37E-08 9.97E-06 2.58E-05 1.32E-07 19 40 7 81.4 7.59 1.99E-07 6.55E-08 1.01E-05 2.43E-05 1.16E-07 21 41 8 75.4 7.63 1.98E-07 6.70E-08 1.04E-05 2.21E-05 1.66E-07 14 26 9 72.0 7.84 2.02E-07 6.58E-08 1.05E-05 2.10E-05 1.46E-07 15 27 10 66.4 7.89 2.06E-07 6.67E-08 1.07E-05 1.91E-05 2.28E-07 9 15 11 63.2 7.94 2.07E-07 6.66E-08 1.08E-05 1.81E-05 1.44E-07 13 22 *Field data, as well as, calculated diffusion coefficients and boundary layer data from the Lassen Volcanic National Park field study, August 2000 and July 2001, and Ojo Caliente, July 2001 and 2+ 2+ July 2002. Caw refers to the free calcium concentrations in the water and Caeq refers to equilibrium calcium concentrations in these waters with respect to gypsum. Concentrations are calculated using PHREEQC 2.4.2. δ25 calculated from δ using equation 8, see text.

30 5.3.1 Big Boiler, LNVP The study conducted in August 2000 at Big Boiler, LVNP, shows the thinnest boundary layer at station 4 of 13 µm (Fig. 7). This corresponds to field notes that there is a cascading fall of several inches at this location. As the bottom of the drainage becomes smoother in the next section the boundary layer increases. At around station 12 the drainage forks off for about five feet before coming together again. Looking downstream, the right side of this fork is studied and there is another drastic change in slope with much more turbulent flow. This is reflected in station 13 with δ equal to 15 µm. After about

30 m (approximately between stations 15 and 16) there is a marked changed in the geometry of the drainage. The slope decreases, the drainage becomes wider and shallower. The water starts to flow smoother at that location and the boundary layer thickness increases. There is one anomaly at station 23 where a thin boundary layer of 16

µm was calculated, however, field notes did not record any significant turbulence. Data obtained during the July 2001 field study show that station 23 has a boundary layer of 24

µm, similar to the values of the other stations in the area (Fig. 7).

In the July 2001 study, we used a digital video recorder to capture the flow regime at each station. This proved helpful in ground proofing the method. We deployed more gypsum tablets than in the previous year. In general, we found that the data between the two field stations is consistent, except that stations 13 and 15 appear to be opposite in

2001 of what they were in 2000. In studying the video of July 2001, (Video BB station

13, Supplemental materials 1) we saw that at station 13, instead of the tablet being directly under the falling water, it appears to be sitting in a pool of water just downstream of the turbulent water. This explains why in August 2000 we calculated a boundary layer

31 Figure 7. Boundary layer thickness values for Big Boiler (top panel) and Ojo Caliente (bottom panel).

32 of 15 µm and in July 2001 the value was 38 µm. As for station 15, the video for

July 2001 shows the tablet directly in cascading water with a resulting boundary layer of

8 µm (Video BB station 15, supplemental material 1). In August 2000, the tablet was placed near this location but not directly in this turbulent area. Initially we tried to place it in this turbulent area but the tablet immediately flipped over as we deployed it. So we decided to move it slightly down stream. Again after about 30 m in the drainage (between stations 15 and 16), the boundary layer thickness increases as the geometry of the drainage changes and the water flows more calmly, see video BB station 23 and 24

(Supplemental Material 1).

5.3.2. Ojo Caliente, YNP The boundary layer thicknesses obtained for the two field studies at Ojo Caliente are in good agreement. Within the drainage there is a significant change in the geometry of the flow channel between station 2 and 3. From the pool to station 2, the drainage is wide and then significantly narrows at station 3 where it is visible that turbulence is produced, see Video OC station 3 (Supplemental Material 2). This change in geometry is reflected in a significant decrease in boundary layer thickness, 30-31 µm at station 2 to

14-16 µm at station 3 (Fig. 7). After station 5, the drainage undergoes a series of forks.

At each point turbulence is produced (Video OC Forks, Supplemental Material 2). The boundary layers continue to thin downstream as the water becomes more turbulent (Fig.

7).

5.3.3. Stony Brook Fountain The boundary layer thickness calculations for the fountain on SUNY Stony Brook campus yield values significantly larger (in most cases, at least twice as large) than those 33 obtained in the hot spring drainages. For the area immediately after the step in the channel, δ is equal to 44 µm and for the area of smooth flow, δ is 78 µm. It should be noted that the fountain overflow is about twice as deep as found along most segments of the hot spring drainages.

5.4. Cooling Rate of Near-boiling Standing Water

The results of the three experiments exploring the cooling rate of near-boiling standing water are presented in Figure 8. The rate of cooling in all three experiments shows non-linear drop in temperature (Fig. 8a). The highest cooling rates are observed for the experiment with the least amount of water and, therefore, shallowest water depth.

For comparison, the temperature data obtained in 2000 for Big Boiler and the data collected on 7/29/02 in Ojo Caliente are also presented in Figure 8a. It is clear that the water in the drainages cools faster than the standing water despite the fact that the thermal mass of the water in the experiment is much smaller.

34 Figure 8. Temperature change in near-boiling standing water and the hot spring drainages. For clarity all temperatures in top panel are normalized to the initial temperature. In bottom panel the data for each of the experiment is recast as Ln(Twater-Tair) versus time, see equation 10.

35

6. DISCUSSION For clarity, the experimental results will be discussed first, followed by a discussion of the field observations in each of the locations. The discussion is focused on the applicability of the gypsum dissolution measurement and a comparison of the field results intra site and among sites. The discussion concludes with an assessment of the importance of turbulence in cooling the water in the drainages.

6.1. Experimental Gypsum Dissolution Studies

The experimental results on gypsum dissolution in waters at temperatures between 35 and 73°C yield an activation energy, Ea, equal to 3.68 kcal/mol (Fig. 4) which is consistent with transport-controlled reactions, which have an Ea < 5 kcal/mol (Lasaga,

1998). Surface-controlled reactions typically have Ea values in excess of 15 kcal/mol.

This result supports the notion that the dissolution is transport-controlled from room temperature (Barton and Wilde, 1971; Christoffersen and Christoffersen, 1976; James and Lupton, 1978; Liu and Nancollas, 1971) to conditions commonly found in hot springs. Hence, this validates the use of the gypsum dissolution rate method at temperatures beyond 25 °C.

Previous studies on gypsum dissolution were conducted in either deionized water or stoichiometric salt solutions. Natural solutions, including hot spring waters, are rarely stoichiometric with respect to gypsum. For example, the water in Big Boiler has a 8 to 1 molar sulfate to calcium ratio. However, the rates of dissolution in the three experimental solutions are identical (within experimental error), this supports the notion that the non- stoichiometric composition of the water in the hot spring drainages does not affect the 36 rate of gypsum dissolution. Based on the work of Jeschke et al. (2001), there appears to be a non-linear trend in the kinetics of gypsum dissolution as saturation is approached.

The results of the experiments with different solution stochiometries (Fig. 5) show that the dissolution rate remains linear throughout the experiment despite the fact that the undersaturation in the solution decreases down to an SI value of -0.46 (Solution B).

Hence, we conclude that at these undersaturation levels the system remains far enough from equilibrium to induce non-linear kinetics. Taken together, the laboratory studies suggest that the in situ gypsum method can be used to characterize flow regimes encountered in hot springs for which the solutions are undersaturated with gypsum (SI <-

0.5). The technique is easy to employ since the material is inexpensive, simple to cut, and it does not chemically alter the water it is deployed in (i.e., it is acceptable to use in sensitive study sites such as national parks).

6.2. Field Studies

One of the challenges in interpreting the boundary layer thickness (δ) obtained by the deployment of the gypsum tablets is the temperature dependence of the boundary layer thickness. The viscosity of water increases with decreasing temperature as the internal resistance to flow increases. Hence, for a drainage with constant dimensions, roughness, and flow rate, the boundary layer will increase with decreasing temperature.

Given the temperature drop in hot spring drainages, we would expect to see an increase in

δ values on the basis of the temperature drop alone. Since our interest is in determining changes in flow regime, it is useful to develop a way to report the boundary layer thickness values for a reference temperature (arbitrarily chosen to be 25ºC). The earlier

37 work by Dreybrodt et al. (1992) provides a way to achieve this. Dreybrodt and co- workers presented a method to estimate the boundary layer thickness developed over a flat plate with length L positioned on the bottom of a stream based on the Sherwood number, NSH (equation 5).

δ = L/NSH (5)

The Sherwood number for this geometry is given by:

0.8 NSH = 0.37*(u*L/ν) (6)

In equation 6, u is the stream velocity (m/s), L the tablet length (m), and ν the kinematic viscosity of water. NSH is dependent on temperature because the kinematic viscosity of water decreases by a factor of 2.74 with a temperature increase from 25ºC to 90ºC

(Sengers and Kamgar-Parsi, 1984). The boundary layer thickness for a system at a given temperature (δt) can be related to the boundary layer thickness of the same system at

25ºC, δ25, by using equation 7:

t 25 δ25 = δt (NSH /NSH ) (7).

Given that the length scale L and flow rates are independent of temperature, equation 7 reduces to :

0.8 δ25 = δt (ν25/νt) (8).

This last equation can be used to recast a boundary layer thickness reported for a system to the reference temperature of 25ºC so that different systems can be compared without the added complication of the fluid temperature. Equation 8 was used in Table 1 to recast boundary layer thicknesses reported in earlier studies to values for that same system at 25ºC. The δ values obtained for Big Boiler and Ojo Caliente are all recast as values for 25ºC using equation 8 (Table 5). The temperature corrected boundary layer 38 Figure 9. Boundary layer thickness values at a reference temperature of 25ºC for Big Boiler (top panel) and Ojo Caliente (bottom panel) as well as values calculated using equation 8 for comparison. 39

thicknesses, δ25, for each station in both springs are presented in Figure 9 as a function of position in drainage. In addition, calculated δ25 value using equations 5 and 6 for each of these drainages on the basis of the flow rate determined by the tracer technique is shown for comparison to the values derived from the gypsum tablet method. The water in the

Stony Brook overflow was at 21ºC, the δ values for this system were 44 and 78µm, which leads to tablet-derived δ25 values of 40 and 70µm, respectively. Assuming a flow rate of 0.2 m/s, the δ25 value on the basis of equations 5 and 6 is calculated to be 73µm, this value increases to 140µm if a flow rate of 0.09 m/s is used.

To simplify the discussion we will focus on a comparison of δ25 values obtained through the deployment of the gypsum tablets and values calculated using equation 5 and the average flow rate. The inference is that a higher degree of turbulence will translate into a smaller δ25 value.

The δ25 values for Big Boiler are consistently lower than the value calculated on the basis of equation 5 and there is no obvious trend in the δ25 values with respect to the position in the drainage. The low δ25 values compared to the calculated value indicates that flow is more turbulent than the turbulence induced by placing a flat plate in an otherwise smooth flume. This is not unexpected as Big Boiler has a large number of small cascading water falls (ledges) and rocks within the drainage inducing turbulence.

On the other hand, the δ25 values based on the deployment of the gypsum plates for Ojo

Caliente fall around the values calculated using equation 5. In addition, the δ25 values for the first five stations, which represent the single channel before the split in forks, are 40 higher than for the stations in the fork. The values for the stations in the fork are consistently lower than the calculated values, indicating a higher degree of turbulence.

Compared to the results of prior studies in spring-fed streams, the overflow of the

Stony Brook fountain, as well as a flume with smooth-wall turbulent conditions (Opdyke et al., 1987) both hot spring drainages have δ25 values that are significantly smaller

(Table 1). The δ25 value reported by Santshi and co-workers for conditions described as highly turbulent equals 14 micron and each of the hot spring drainages have segments that approach this value (Santschi et al., 1983).

One indication of the importance of turbulence is illustrated by the comparison of the cooling rates of standing hot water to the rate of flowing hot water (Fig. 8a). The cooling rate of an object can be described by Newton’s law of cooling (Mills, 1999), which states that the cooling rate, dT/dt, depends on the temperature contrast between the hot object (here hot water, Twater) and the cooler surroundings (here air, Tair) (eq. 9).

(dT/dt) = h (Twater-Tair) (9)

As the water cools, the temperature contrast decreases and the cooling rate decreases.

The differential equation can be integrated to give:

Ln(Twater-Tair) = ht + lnTt=0 (10)

The rate of cooling is characterized by the parameter h, which can be extracted from the data by plotting Ln(Twater-Tair) versus time (Fig. 8b). Table 6 summarizes the h values for the two drainages and the three experiments with standing near-boiling water. The h values for Ojo Caliente and Big Boiler are a factor 2 to 8 higher than the h value for the shallowest standing water, which cools most rapidly of the three experiments. This result is consistent with results obtained for engineered systems in which the h value is

41

Table 6. Cooling time constant for near-boiling standing water and hot spring drainages*. h (sec-1) x103 R2 N (# data points) Experiments #1 (5.9 cm depth) -0.531 0.994 40 #2 (3.8 cm depth) -0.631 0.985 27 #3 (1.7 cm depth) -1.133 0.984 20 Hot Springs Ojo Cal. 2001 1-11** -6.567 0.906 13 Ojo Cal. 2001 1-5 -2.838 0.860 5 Ojo Cal. 2001 5-11 -9.067 0.948 8 Ojo Cal.7/29/02 1-11 -9.860 0.916 13 Ojo Cal. 7/29/02 1-5 -4.028 0.882 5 Ojo Cal. 7/29/02 5-11 -12.56 0.927 8 Ojo Cal.7/30/02 1-11 -8.521 0.940 13 Ojo Cal.7/30/02 1-5 -4.216 0.951 5 Ojo Cal.7/30/02 5-11 -10.57 0.941 8 Ojo Cal.7/31/02 1-11 -7.129 0.932 13 Ojo Cal.7/31/02 1-5 -4.588 0.947 5 Ojo Cal.7/31/02 5-11 -9.016 0.932 8 Big Boiler, 2000 -2.940 0.971 24 Big Boiler, 2001 -2.339 0.990 24

*:based slope of linear regression of ln(Twater-Tair) versus time, see equation 10. ** stations included in regression. Station 1 through 5 is the section of Ojo Caliente from orifice to onset of forks. Stations 5-11 are all within one fork.

measured for water cooling under no-flow conditions, laminar flow and turbulent flow

(Mills, 1999). It should be noted that Newton’s law of cooling provides no insight into the mechanism by which fluid cools. At the near-boiling conditions in the experiments and the drainages, evaporative cooling is the dominant mechanism. This is also illustrated by the fact that the experiment with the shallowest water depth has the highest cooling rate.

A detailed examination of the data collected at Ojo Caliente over the two field campaigns shows that there is a break in the temperature profile around the midpoint 42 (Fig. 10a). Prior to the midpoint the cooling rate is lower than past the midpoint as indicated by the change in the value for the cooling rate time constant h (Table 6 and inset in Fig. 10a). The midpoint is where the water from the single channel draining the pool is spread out over several forks and δ25 values on the basis of the deployment of the gypsum plates drop below the calculated values, indicating a shift to more turbulent conditions and more efficient cooling. If the drainage was uniform in dimensions, flow rate, and flow regime, Newton’s law of cooling would predict that the rate of cooling would be the highest near the orifice of the drainage and drop off as the water cools. In

Ojo Caliente, we see the opposite, indicating that the increase in surface area to volume ratio and turbulence within the drainage as it transitions from one channel into several shallower ones increases the cooling rate. By comparison, the temperature profile in Big

Boiler (Fig. 10b) suggest that the cooling within the drainage can be parameterized adequately with one h value (Table 6 and inset Fig. 10b), although there is a slight difference between the cooling rate in the two field seasons with a higher cooling rate in

2000. The interpretation of the temperature data in Big Boiler is, however, complicated

43 Figure 10. Detailed data of temperature change in hot springs. Ojo Caliente 2002 data with data replotted as Ln(Twater-Tair) versus time in inset (panel A) and Big Boiler 2001 with data replotted as Ln(Twater-Tair) versus time in inset (panel B).

44 by the fact that we observed several small fumaroles close to the drainage, which add heat.

6.3. Limitations and Uncertainty of Gypsum Tablet Method

While this study suggest that the gypsum tablet method originally developed for oceanographic studies can be used in hot spring environments, our data also suggest that the boundary layer thicknesses calculated using this method are strongly influenced by the exact location within the drainage. This is illustrated by the fact that for station 13 in

Big Boiler the calculated boundary layer varied from 15 µm in 2000 when the tablet was placed under the cascading water to 38 µm in 2001 when the tablet was placed in a pool of water just downstream. As suggested by one of the reviewers, in further studies this sensitivity to placement might be exploited to resolve the spatial heterogeneity of flow regimes within similar drainages by, for example, placing tablets across the width of a drainage or on the inside and outside of a bend in the drainage.

Finally, it is important to evaluate what the major uncertainties are in calculating the boundary layer thickness for a given deployment. The measurements of the weight of the tablets—typically more than 1.5 grams of mass loss from tablets with initial weights in excess of 20 grams—was conducted with a high-precision balance (±0.001 g) and contributes little uncertainty. The measurement of the surface area, provided that the tablets are carefully polished to an uniform smooth surface, also contributes little to the uncertainty. As shown in equation 1, the calcium concentration of the bulk water determines the driving force. Uncertainty in the calcium concentration is the largest factor. While our uncertainty in the triplicate analysis is limited to 2.5 %, we cannot

45 exclude the fact that there could be a systematic error in the calcium concentration as a result of precipitation after sample collection as suggested by a reviewer. However, for the systems studied here the concentration of dissolved calcium is about two orders of magnitude lower than the equilibrium calcium concentration. Hence, the driving force for the dissolution is dominated by the calculated equilibrium calcium concentration. To illustrate this one may consider a hypothetical case in which we multiply the measured calcium concentrations by a factor of 10 for station 11 in Ojo Caliente (this is equivalent to assuming that 90% of the dissolved calcium was lost prior to analysis). The increase in dissolved calcium has no material effect on the driving force and the calculated δ25 value changes from 13.5 micron to 12.7 micron.

7. CONCLUSION The primary interest of this research was to develop a quantitative method to characterize the flow regime in hot spring drainages as a stepping stone for the interpretation of abiotic reactions within the drainages. Laboratory experiments confirm that gypsum dissolution is transport-controlled in systems with temperatures as high as

72ºC. Furthermore, the highly non-stoichiometric composition has no effect on the dissolution rate. The dissolution rate remains linear with undersaturation levels reaching

SI values of -0.5. Therefore, the in situ gypsum dissolution method is applicable to hydrothermal systems with SI values below –0.5.

In order to compare field sites with different temperatures and flow conditions, it is useful to derive δ25 values by using an approach based on earlier work by Dreybrodt et al. (1992). On the basis of δ25 values, it is clear that both hot spring drainages are considerably more turbulent than two earlier studies in spring-fed streams which were 46 characterized as turbulent streams. As demonstrated in Ojo Caliente, deploying gypsum tablets at various locations in drainages can lead to a deeper insight into changes in flow regime within the system. The deployment of the gypsum tablets in streams, including hot spring drainages, is a relatively simple method to obtain a quantitative measure δ that can be used to characterize the flow regime. More experiments with gypsum plates in flumes under a wide range of flow condions would allow one to establish an empirial relationship between boundary layer thickness derived using this method and Reynolds number, which remains the preferred method of communicating the flow regime within a system.

Acknowledgements: This work was supported by awards by NSF-EAR to M.Schoonen.

The work benefited from the introduction to YNP and LVNP by Dr. Kirk Nordstrom,

USGS, Boulder, CO, with whom Schoonen conducted joint research for several years.

This paper benefited from two thorough reviews by anonymous reviewers.

47 LIST OF FIGURES

Figure 1. Conceptual figure of the boundary layer developed on a surface of a binary mineral, CD, with C+ and D- as constituents. The arrows indicate the transition of constituent ions into the overlying fluid. The concentration profile in the solution film adjacent to the surface for either one of the constituent ions is schematically shown. Note that the boundary layer thickness will decrease with increasing flow rate parallel to surface and the onset of turbulence.

Figure 2. Temperature measurements in Big Boiler drainage, LVNP, versus distance.

Figure 3. Temperature measurements in Ojo Caliente, YNP. Left panel shows a single set of data collected in 2001, while the left shows temperature profiles measures on three different days in 2002. Note that the three measurements in 2002 show some differences in temperature profile, particularly in the downstream portion of the drainage.

Figure 4. Arrhenius plot for flow-through laboratory experiments.

Figure 5. Calcium versus time in laboratory experiments with varying stoichiometry and undersaturation levels.

Figure 6. Flow rate measurements in drainages: left panel Big Boiler, LVNP, and right panel Ojo Caliente, YNP. Insets in both panels show collected using in situ flow probe where possible, while main figure are arrival times of most intense color of food dye at each station. The equation for each of the regression lines is in the form of y=a+bx.

Figure 7. Boundary layer thickness values for Big Boiler (top panel) and Ojo Caliente

(bottom panel).

48 Figure 8. Temperature change in near-boiling standing water and the hot spring drainages. For clarity all temperatures in panel A are normalized to the initial temperature. In panel B the data for each of the experiment is recast as Ln(Twater-Tair) versus time, see equation 10.

Figure 9. Boundary layer thickness values at a reference temperature of 25ºC for Big

Boiler (top panel) and Ojo Caliente (bottom panel) as well as values calculated using equation 8 for comparison.

Figure 10. Detailed data of temperature change in hot springs. Ojo Caliente 2002 data with data replotted as Ln(Twater-Tair) versus time in inset (panel A) and Big Boiler 2001 with data replotted as Ln(Twater-Tair) versus time in inset (panel B).

49

List of Tables

Table 1. Results from earlier deployments of the in situ gypsum technique.

Table 2. Results of laboratory flow-through experiments.

Table 3. Results of dissolution experiments with varying stochiometry and undersaturation.

Table 4. Dimensions of drainages and measured flow rates.

Table 5. Results of field deployment of gypsum tablets and calculation of boundary layer thickness.

Table 6. Cooling time constant for near-boiling standing water and hot spring drainages.

50

List of Supplemental Materials

S.1 Overview pictures and video of Big Boiler, LVNP.

S.2. Overview pictures and video of Ojo Caliente, YNP.

S.3. Overview picture and video of fountain overflow on Stony Brook campus, Stony

Brook, NY.

References Allen, E.T., Day, A.L., 1935. Hot springs of the Yellowstone National Park. Carnegie Institute of Washington Publications. Ball, J.W., Nordstrom, D.K., Cunningham, K.M., Schoonen, M.A.A., Xu, Y., DeMonge, J.M., 2001. Water-chemistry and on-site sulfur-speciation data for selected springs in Yellowstone National Park, Wyoming, 1994-1995. USGS-WR, Boulder, p. 35. Barton, A.F.M., Wilde, N.M., 1971. Dissolution rates of polycrystalline samples of gypsum and orthorhombic forms of calcium sulphate by a rotating disc method. Transactions of the Faraday Society 67, 3590-3597. Christoffersen, J., Christoffersen, M.R., 1976. The kinetics of dissolution of calcium sulphate dihydrate in water. J. Crystal Growth 35, 79-88. Clynne, M.A., Christiansen, R.L., Miller, C.D., Stauffer, P.H., Hendley II, J.W., 2000. hazards of the Lassen Volcanic National Park, California. USGS Fact Sheet 022-00. Colombani, J., 2012. Dissolution measurement free from mass transport, Pure and Applied Chemistry, p. 61. Day, A.L., Allen, E.T., 1924. The source of the heat and the source of the water in the hot springs of the Lassen National Park. Journal of Geology 32, 178-190. Dreybrodt, W., Buhmann, D., Michaelis, J., Usdowski, E., 1992. Geochemically controlled calcite precipitation by CO2 outgassing: Field measurements of precipitation rates in comparison to theoretical predictions. Chemical Geology 97, 285-294. Druschel, B.R., Borda, M.J., Schoonen, M.A.A., 2004. A gas transfer study at Ojo Caliente, Yellowstone National Park, USA, in: Wanty, R.B., Seal II., R.R. (Eds.), Water-Rock interaction 11. Taylor&Francis group, London, pp. 119-123. El Maarry, M.R., Dohm, J.M., Marzo, G.A., Fergason, R., Goetz, W., Heggy, E., Pack, A., Markiewicz, W.J., 2012. Searching for evidence of hydrothermal activity at Apollinaris Mons, Mars. Icarus 217, 297-314.

51 Farmer, J.D., 1996. Hydrothermal systems on Mars: an assessment of present evidence, in: Walter, M.R. (Ed.), Evolution of hydrothermal ecosystems on Earth (and Mars?). Wiley, Chichester, pp. 273-299. Flury, M., Gimmi, T., 2002. Solute diffusion, in: Dane, J.H., Topp, G.C. (Eds.), Methods in Soil Analysis, Part 4, Physical Methods. Soil Science Society of America, Madison, WI, pp. 1323-1351. Gooch, F.A., Whitfield, J.E., 1888. Analyses of waters of the Yellowstone National Park with an account of the methods of analysis employed. U.S. Geological Survey Bulletin 47, 84. Hill, G.A., 2009. Oxygen Mass Transfer Correlations for Pure and Salt Water in a Well- Mixed Vessel. Industrial & Engineering Chemistry Research 48, 3696-3699. Ingebritsen, S.E., Sorey, M.L., 1985. A quantitative analysis of the Lassen hydrothermal system, North Central California. Water Resouces Research 21, 853-868. James, A.N., Lupton, A.R.R., 1978. Gypsum and anhydrite in foundations of hydraulic structures. Geotechnique 28, 249-272. Janik, C.J., Bergfield, D., 2010. Analyses of gas, steam, and water samples collected in and around Lassen Volcanic National Park, California, 1975-2002 Open-File Report 2010-1036, Open-File Report 2010-1036. USGS, p. 13. Jeschke, A.A., Vosbeck, K., Dreybrodt, W., 2001. Surface controlled dissolution rates of gypsum in aqueous solutions exhibit nonlinear dissolution kinetics. Geochimica et Cosmochimica Acta 65, 27-34. Lasaga, A.C., 1998. Theory of Crysal Growth and Dissolution, in: Holland, H.D. (Ed.), Kinetic Theory in the Earth Sciences. Princeton University Press, New Jersey, pp. 581-599. Lemoine, R., Fillion, B., Behkish, A., Smith, A.E., Morsi, B.I., 2003. Prediction of the gas-liquid volumetric mass transfer coefficients in surface-aeration and gas-inducing reactors using neural networks. Chemical Engineering and Processing 42, 621-643. Liu, S., Nancollas, G.H., 1971. The kinetics of dissolution of calcium sulfate dihydrate. Journal of Inorganic Nuclear Chemistry 33, 2311-2316. Mathon, B., 2002. Dissipation of Chemical and Thermal Disequilibrium in Hot Springs, Department of Geosciences. Stony Brook University, Stony Brook. Mills, A.F., 1999. Basic heat and mass transfer, 2nd ed. Prentice Hall, Upper Saddle River, NJ. Ocampo-Torres, F.J., Donelan, M.A., Merzi, N., Jia, F., 1994. Laboratory measurements of mass transfer of carbon dioxide and water vapour for smooth and rough flow conditions. Tellus 46B, 16-32. Opdyke, B.N., Gust, G., Ledwell, J.R., 1987. Mass transfer from smooth alabaster surfaces in turbulent flow. Geophysical Research Letters 14, 1131-1134. Porter, E.T., Sanford, L.P., Suttles, S.E., 2000. Gypsum dissolution is not a universal integrator of 'water motion'. Limnology and Oceanography 45, 145-158. Reynolds, O., 1883. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philosophical Transactions of the Royal Society 174, 935-982. Santschi, P.H., Bower, P., Nuffeler, U.P., Azevedo, A., Broecker, W.S., 1983. Estimates of the resistance to chemical transport posed by the deep-sea boundary layer. Limnology and Oceanography 28, 899-912.

52 Schulze-Makuch, D., Dohm, J.M., Fan, C., Fairén, A.G., Rodriguez, J.A.P., Baker, V.R., Fink, W., 2007. Exploration of hydrothermal targets on Mars. Icarus 189, 308-324. Sengers, J.V., Kamgar-Parsi, B., 1984. Representative equations for the viscosity of water substance. J. Phys. Chem. Ref. Data 13, 185-205. Sherwood, T.K., Pigford, R.L., 1952. Absorption and extraction. McGraw-Hill, New York, pp. 51-93. Smith, R.B., Braile, L.W., 1994. The Yellowstone hotspot. Journal of Volcanology and Geothermal Research 61, 121-187. Smith, R.B., Siegel, L.J., 2000. Windows into the Earth: The Geologic Story of Yellowstone and Grand Teton National Parks. Oxford University Press, NY, NY. Tengberg, A., Hall, P.O.J., Andersson, U., Lindén, B., Styrenius, O., Boland, G., de Bovee, F., Carlsson, B., Ceradini, S., Devol, A., Duineveld, G., Friemann, J.U., Glud, R.N., Khripounoff, A., Leather, J., Linke, P., Lund-Hansen, L., Rowe, G., Santschi, P., de Wilde, P., Witte, U., 2005. Intercalibration of benthic flux chambers: II. Hydrodynamic characterization and flux comparisons of 14 different designs. Marine Chemistry 94, 147-173. US Geological Survey, 2009. “Hot Water” in Lassen Volcanic National Park— Fumaroles, Steaming Ground, and Boiling Mudpots, USGS FACT SHEET. Welty, J.R., Wicks, C.E., Wilson, R.E., Rorrer, G., 2001. Fundamentals of Mass Transfer, Fundamentals of Momentum, Heat, and Mass Transfer, 4 ed. John Wiley & Sons, Inc., New York, pp. 438-442. Xu, W., Lowell, R.P., 1998. An alternative model of the Lassen hydrothermal system, Lassen Volcanic National Park, California. Journal of Geophysical Research 103, 20,869-820,881. Xu, Y., Schoonen, M.A.A., Nordstrom, D.K., Cunningham, K.M., Ball, J.W., 1998. Sulfur geochemistry of hydrothermal waters in Yellowstone National Park: I The origin of thiosulfate in hot spring waters. Geochimica Cosmochimica Acta 62, 3729- 3743. Zaihua, L., Svensson, U., Dreybrodt, W., Daoxian, Y., Buhmann, D., 1995. Hydrodynamic control of inorganic calcite precipitation in Huanglong Ravine, China: field measurements and theoretical prediction of deposition rates. Geochimica et Cosmochimica Acta 59, 3087-3097.

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