Stirring Effect on Kaolinite Dissolution Rate

Geochimica et Cosmochimica 65(20), 3475-3490.

Metz, Volker^* and Ganor, Jiwchar

Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev,

P. O. Box 653, Beer-Sheva 84105, Israel.

E-mail ganor@bgumail.bgu.ac.il

WEB http://www.bgu.ac.il/geol/ganor/

* present address: Institut für Nukleare Entsorgung,

Forschungszentrum Karlsruhe (FZK-INE),

P.O. Box 3640, Karlsruhe 76021, Germany

E-mail volker@ine.fzk.de

ABSTRACT

Experiments were carried out measuring kaolinite dissolution rates using stirred and non-stirred flow-through reactors at pH 2 to 4 and temperatures of 25°, 50° and 70°C. The results show an increase of kaolinite dissolution rate with increasing stirring speed. The stirring effect is reversible, i.e., as the stirring slows down the dissolution rate decreases. The effect of stirring speed on kaolinite dissolution rate is higher at 25°C than at 50° and 70°C and at pH 4 than at pH 2 and 3.

It is suggested that fine kaolinite particles are formed as a result of stirring-induced spalling-of or abrasion of kaolinite. These very fine particles have an increased ratio of reactive surface area to specific surface area, which results in enhancement of kaolinite dissolution rate. A balance between production and dissolution of the fine particles explains both the reversibility and the temperature and pH dependence of the stirring effect.

Since the stirring effect on kaolinite dissolution rate varies with temperature and pH, measurement of kinetic parameters such as activation energy maybe influenced by stirring. Therefore, standard use of non-agitated reaction vessels for kinetic experiments of mineral dissolution and precipitation is recommended, at least for slow reactions that are surface-controlled.

1 INTRODUCTION

Interpretation and modeling of natural geochemical processes on the earth's surface and in the crust, as well as of many anthropogenic environmental effects strongly depend on our understanding of the factors that control the rate of dissolution and precipitation of minerals. The rate of these dissolution and precipitation reactions depend on the intrinsic and surface properties of the mineral, as well as on environmental factors such as temperature and chemical composition of the aqueous solution. An important difference between mineral weathering in the field and dissolution in laboratory experiments is that natural systems are usually non-agitated whereas it is common practice in many experimental systems to stir or agitate the reacting mineral. It is widely accepted that under low-temperature conditions dissolution reactions of most silicates are limited by surface-controlled processes, rather than by the transport rate of products and reactants to and from the reacting surface sites (Berner, 1978; Aagaard and Helgeson, 1982; Murphy et al., 1989). Therefore, it is assumed that the method and rate of stirring do not influence the dissolution rate of most silicate minerals (Berner, 1978). However, several recent studies showed that agitation does affect dissolution rates of silicates (Amrhein and Suarez, 1992; van Grinsven and van Riemsdijk, 1992; Furrer et al., 1993; Komadel et al., 1998; Ferrow et al., 1999).

In this paper we examine the effect of stirring on kaolinite dissolution rate at 25°, 50° and 70°C, and pH 2 to 4. We present new experimental data demonstrating that kaolinite dissolution rate increases with increasing stirring effectiveness. This effect of stirring on dissolution rate is reversible and depends on temperature and pH. The possible reasons for this stirring effect are examined in detail as well as the implications of the effect on rate data and kinetic parameters obtained using stirred reactors.

2 MATERIALS AND EXPERIMENTAL METHODS

2.1 Characterization and Pretreatment of the Solid.

Two kaolinite samples are used in this study: (1) KGa-2 is an international standard sample of the Clay Mineral Society Source Clay Repository obtained from the Yale Peabody Museum; (2) kaolinite sample KGDB is from Dry Branch, Georgia, and was supplied by the Georgia Kaolin Company, Inc. Both kaolinite samples were pretreated in 0.001 M HClO₄ at 80°C for few months, using the procedure described by Ganor et al. (1995).

The specific surface area of the samples was estimated by the Brunauer-Emmett-Teller (BET) method (Brunauer et al., 1938), using 5-points of N₂ adsorption isotherms. Nitrogen adsorption isotherms were measured employing a Micromeritics Gemini II-2375 surface area analyzer. The BET-determined initial surface area of KGa-2 and KGDB are 19.4±2 and 6.4 ± 0.6 m² g^-1, respectively. The higher BET-surface area of KGa-2 compared to KGDB corresponds to the difference in crystallographic order between the disordered kaolinite KGa-2 (Hinckley index 0.37±0.05) and the well-crystallized kaolinite KGDB (Hinckley index 1.17±0.07). In most of the experiments, the final surface area was higher than the initial surface area (Table 1).

2.2 Experimental Setting

The experimental set-up is shown in Fig. 1. Dissolution experiments were carried out using flow-through reactors (ca. 35 ml in volume) fully immersed in a thermostatic water bath held at a constant temperature of 25.0°, 50.0° or 70.0 ± 0.1°C (Fig. 1a). Most of the experiments were conducted in reaction cells that were composed of two chambers (SBSB cell type in Fig. 1b and Table 1), a lower chamber of 33-mm inner diameter and an upper chamber of 26-mm inner diameter. The two chambers were separated by a fine (5 mm) nylon mesh, on which kaolinite powder was placed. A submersed stir-plate controlled two small (12.7-mm length, 3-mm diameter) Teflon-coated stir bars. The first was mounted on the bottom of the cell and the second stir bar was placed on the fine mesh to improve the stirring of the upper chamber. A similar experimental set-up, without stir bars is denoted as set-up NB in Table 1.

Few experiments were conducted without the fine mesh, so that the sample was placed together with a stir bar on the bottom of the cell. In two of these experiments the same type of small stir-bar was used (SB cell type, Fig. 1c and Table 1), whereas in another experiment a larger stir-bar (30-mm length, 8-mm diameter) was used (BB cell type, Fig. 1d and Table 1).

Flow rates (Table 1) were controlled by a peristaltic pump and ranged from 0.0070±0.0001 to 0.054±0.001 ml min^-l. In any one run, experimental conditions were held constant for sufficient time so that steady-state conditions were achieved. After steady-state conditions were reached, dissolution rates were evaluated and the stirring speed and/or the flow rate were changed to achieve a different steady state. After the end of the last stage the cell was dismantled and the final specific surface area was measured. The experimental conditions of each stage are described in Table 1.

The effect of stirring on kaolinite surface area was studied in six parallel experiments that were conducted at low temperature (25°C) in double-deionized water. Pretreated samples of kaolinite KGDB and KGa-2 were kept for 10 days in standard flow-through reaction cells (cell type SBSB; Fig. 1b) without pumping the fluid. In one set of experiments samples were stirred at 1100 rpm over the full period, whereas in the second set the samples were not stirred (Table 2).

2.3 Solutions and Analyses

Input solutions (10^-4 to 10^-2 M HClO₄) were prepared by diluting reagent grade concentrated perchloric acid with distilled, deionized water. Total Al and Si were analyzed colorimetrically with a UV-visible spectrophotometer, using the Catechol violet method (Dougan and Wilson, 1974) and the Molybdate blue method (Koroleff, 1976), respectively. The uncertainty in measured Al and Si was better than ± 5% for concentrations above 4 mM. The precision dropped to ±15% and 33% for measurements at low concentrations of 2 and 0.5 mM, respectively. The pH was measured at experimental temperature on an unstirred aliquot of solution using a semi-micro 83-01 Orion Ross combination electrode. The reported accuracy is ±0.02 pH units (±4.5% in H⁺ activities).

3 CALCULATIONS

3.1 Dissolution Rates

The overall dissolution reaction of kaolinite under acidic conditions is best expressed as

(1)

The dissolution rate in steady state was based on the release of Al and Si according to the expression:

(2)

where Rate is the dissolution rate (mole m^-2 s^-1), C_j,inp and C_j,out are the concentration of species j (Al or Si) in the input and the output solutions respectively (mole m^-3), n_j is the stoichiometric coefficient of j in the dissolution reaction, s_r is the total reactive surface area of the mineral (m²) and q is the fluid volume flux through the system (m³ s^-1). The input solutions in most experiments contained no Al and no Si and therefore equation (2) becomes

(3)

The error in the calculated rate (DRate) was estimated using the Gaussian error propagation method (Barrante, 1974) from the equation:

(4)

For most of the experiments, the errors in the calculated rates range from ±10% to ±13% (Table 1). This error includes the uncertainty of the flux (Dq=±1%), the output concentration (DC_j,out=±5%), and is dominated by the uncertainty of the BET surface area measurement (Ds_r=±10%). For experiments in which the output concentration is <3 mM, the error in the obtained dissolution rate is dominated by the uncertainty of the output concentration and may become as high as ±24%.

4 RESULTS

The variations of the output concentrations of Al and Si in three representative flow-through experiments as a function of time are shown in Fig. 2. Each experiment was composed of 1 to 4 stages, where each new stage was initiated by a change in experimental conditions. The vertical lines in the figures delineate the different stages. Average pH and Al and Si concentrations for each steady state at 25°, 50° and 70°C are compiled in Table 1. Al and Si analysis used to calculate these average steady states are denoted by open symbols in Fig. 2. Dissolution rates (Table 1) were calculated using the measured final surface area, the flow rate and the average Al and Si concentration at steady state (equation (2)).

4.1 Effect of Stirring on Kaolinite Surface Area in Flow-through Dissolution Experiments

Final surface area of samples recovered from non-stirred experiments was on average the same as the initial values. The maximum observed change in surface area of non-stirred experiments was 15%. Data of stirred experiments show a wide range of final surface areas, from values equal to the initial surface area to relatively high values. In experiments that were stirred at least in one experimental stage, the average increase in surface areas was 23% and the maximum change was 71%. Surface area data of experiments that were stopped at the maximum stirring speed do not differ from data of multi-stage experiments that were stopped at lower stirring speeds than the maximum, or under non-stirred conditions.

The effect of stirring on kaolinite surface area was also studied in experiments that were conducted under conditions that minimized the possibility of dissolution and washing out of fine particles (25°C, double-deionized water and no flow, see method). BET-surface areas of the samples recovered from experiments stirred at 1100 rpm and non-stirred experiments are the same (within error) and do not differ significantly from the respective initial BET-surface area (Table 2).

4.2 Effect of Stirring Speed on Kaolinite Dissolution Rate

Flow-through experiments carried out at 25°, 50° and 70°C and pH 2 to 4 show an enhancement of dissolution rate with increasing stirring speed (Table 1 and Fig. 3). The stirring effect is reversible, i.e., as the stirring speed decreases the dissolution rate slows down. Fig. 2c illustrates the reversibility of the stirring effect. During the first stage of this experiment (stage A) the sample was not stirred, afterwards (stage B) stirring speed was set to 650 rpm, and at the end of the experiment (stage C) stirring was stopped again. The aluminum and silicon concentration increased as a result of stirring and decreased back as stirring was stopped. Accordingly, the dissolution rate increased from 1.0^·10^‑12 mol m^‑2 s^‑1 (stage A) to 2.2^·10^-12 mol m^-2 s^-1 (stage B) and decreased back to 9.4^·10^-13 mol m^‑2 s^‑1 (stage C), which is within error the same dissolution rate as that of stage A. The reversibility of the stirring effect implies that the dissolution rate is independent of previous stirring history. Fig. 4 shows another example of this stirring history independence. The figure shows kaolinite dissolution rate of four experiments that were conducted under non-stirred conditions at 50°C and pH 3. In one of these experiments (KGDB-50-16A) the kaolinite was not exposed to stirring prior to steady state, while in the other three experiments (KGDB-50-3C, KGDB-50-15B and KGDB-50-17B) the samples were stirred during earlier experimental stages. The dissolution rates of all these experiments are the same within error and are independent of previous stirring history (Fig. 4).

The effect of stirring speed on dissolution rate of kaolinite depends on temperature (Fig. 3) and pH. In order to compare the stirring effect on reaction rate under different experimental conditions, the stirring enhancement factor, SEF, is defined as the relative difference between dissolution rate under stirred conditions and dissolution rate under non-stirred conditions:

(5)

For dissolution experiments conducted at pH=3 using the standard SBSB cell type, Fig. 5a shows that SEF_650rpm at 25°C is significantly larger than SEF_650rpm at 50° and 70°C. At pH 3 and 50°C the stirring enhancement factor, SEF_650rpm, in experiments using kaolinite KGa-2 is similar to that with kaolinite KGDB. In experiments with kaolinite KGa-2 at 50°C, SEF_650rpm is more than six times higher at pH 4 than at pH 3 and 2 (Fig. 5b).

4.3 Effect of Experimental Setting on Kaolinite Dissolution Rate

Three multi-stage experiments were conducted without the fine mesh, so that the sample was placed together with a stir bar on the bottom of the cell. Figs. 4 and 5c compare the results of these experiments to the results obtained using standard (SBSB) reaction cells. Under non-stirred conditions (Fig. 4) kaolinite dissolution rate was not influenced by the type of cell used. When the small stir-bar was used (SB cell type, Fig. 1c), kaolinite dissolution rate was not influenced by cell type even under rapid stirring of 1000 rpm (Fig. 5c). However, when a larger stir-bar was used (BB cell type, Fig. 1d), the dissolution rate determined at 650 rpm was much faster than that obtained using SBSB and SB cell type at 1000 rpm (Fig. 5c). The only difference between cell type SB and BB was that the stir bar in BB was larger than that in SB. As a result, the stirring in BB cell type was much more effective than that in the other cell types, and accordingly the dissolution rate was faster.

Figure 5c compares the stirring enhancement factors obtained in the present study to SEF calculated for the dissolution rate data of Ganor et al. (1995). The latter were calculated by dividing the dissolution rate of kaolinite KGDB obtained by Ganor et al. (1995) by the dissolution rate of the same kaolinite obtained in the present study using a non-stirred reactor at the same temperature and pH. SEF calculated for the dissolution rate data of Ganor et al. (1995) is significantly higher than that of SBSB cell type and is similar to that of BB cell type (Fig. 5c). Ganor et al. (1995) used a well-stirred flow-through reactor with a large Teflon-coated stir-bar, similar to the one used in BB cell type. Though in the study of Ganor et al. (1995) the large stir-bar was mounted on a Lexan pin to avoid grinding of the kaolinite, the stirring enhancement factor was similar to that in cell type BB, where the stir-bar was placed in direct contact with the kaolinite.

One of the non-stirred experiments (KGDB-50-3B) was shaken rigorously twice a day, in the same manner as some batch dissolution experiments (e.g., Tole et al., 1986; Bauer and Berger, 1998). The measured dissolution rate of this experiment is within the range of other non-stirred (and non-shaken) experiments (Fig. 4).

5 DISCUSSION

5.1 Variation of BET Surface Area in Flow-through Dissolution Experiments

Changes in measured surface area are commonly observed in batch and flow-through dissolution experiments (Nagy et al., 1991; Amrhein and Suarez, 1992; Nagy and Lasaga, 1992; Ganor et al., 1995; Stillings and Brantley, 1995; Kalinowski and Schweda, 1996; Malmstrom and Banwart, 1997; Ganor et al., 1999; Cama et al., 2000). It is important to note that the change in surface area in studies that used suspended stir-bars (e.g., Nagy et al., 1991; Nagy and Lasaga, 1992; Ganor et al., 1995; Ganor et al., 1999; Cama et al., 2000) was similar to the change that was observed in the present study, in which the stir-bar was in direct contact with the powder. On the other hand, in column-type experiments on gibbsite and kaolinite dissolution, where the sample powder is packed in a confined space instead of being suspended in the fluid, no significant variation between the final and initial BET-surface area is observed (Ganor et al., 1999; Mogollon et al., 2000). The observed difference between stirred experiments and column experiments supports the concept that changes in BET-surface area are caused to some extent by suspending the solid sample in the fluid. The lack of change of surface area in experiments conducted under conditions that minimized the possibility of dissolution (Table 2) and the observed change in surface area in the dissolution experiment, seem to indicate that the increase in final BET-surface area of kaolinite does not result solely from stirring. It is probably a combined effect of stirring and dissolution.

5.2 Variation of the Stirring Effect on Dissolution Rate With Temperature and its Consequences on Calculation of Apparent Activation Energy and on Reaction Mechanism

Dissolution at low temperature of phyllosilicates in general and kaolinite in particular is considered to be surface-reaction controlled (Carroll-Webb and Walther, 1988; Wieland and Stumm, 1992; Xie and Walther, 1992; Furrer et al., 1993; Ganor et al., 1995; Nagy, 1995). Since the effect of stirring on dissolution rate is observed generally in diffusion limited reactions, one may argue that the observed stirring effect is a consequence of a transport-controlled reaction mechanism. Based on two lines of evidence, we propose that the observed effect of agitation on kaolinite dissolution rate is not a transport phenomenon.

The temperature dependence of reaction rates generally follows the Arrhenius law:

(6)

where A is the pre-exponential factor, E_a is the activation energy, R is the gas constant and T is the absolute temperature. If two sequential mechanisms (e.g., surface reaction and transport process) affect the dissolution rate, the overall rate will be dominated by the slower mechanism. The rates of the two mechanisms are equal at the crossover temperature (Lasaga, 1998):

(7)

Below this temperature the dominant (i.e., the slower) mechanism is the one with the higher activation energy and also the higher pre-exponential factor.

Apparent activation energies for non-stirred experiments and for experiments stirred at 650 rpm were calculated using the Arrhenius equation (6) from a least squares estimate of the slope of ln(Rate) versus T^-1 (Fig. 6). The apparent activation energies are 12±1 kcal mol^-1 for non-stirred experiments and 8.5 ±0.4 kcal mol^-1 for experiments stirred at 650 rpm. Ganor et al. (1995) calculated apparent activation energies, using well-stirred flow-through experiments of 7.5 ±1.1 kcal mol^-1. For elementary reactions we tend to view activation energy as representing a molecular energy barrier. The energy of activation of an overall reaction is really the composite of several activation energies from the elementary reactions composing the overall reaction mechanism (Lasaga, 1998). One can argue that the change in activation energy as a function of stirring represents a change from a transport (diffusion-) controlled reaction mechanism under non-stirred conditions to a surface-controlled reaction mechanism at high stirring rate. Diffusion-controlled reactions in solution have rather low activation energies (E_a < 5 kcal mol^-1), while surface-controlled reactions have activation energies usually in the range of 10 to 20 kcal mol^-1 (Lasaga, 1984; Lasaga, 1995). Fig. 7 is a theoretical plot describing the effect of temperature on dissolution rate of a surface-controlled reaction mechanism with activation energy of 15 kcal mol^‑1 and a transport-controlled mechanism with activation energy of 5 kcal mol^‑1. Pre-exponential factors were set arbitrarily so the crossing temperature would be 15°C. Fig. 7a shows the Arrhenius plots of the two mechanisms, and Fig. 7b shows the change of dissolution rate as a function of temperature. If the experiments stirred at 650 rpm are surface-controlled and the non-stirred experiments are diffusion-controlled then the stirring enhancement factor (SEF) is the relative difference

(8)

that is shown in Fig. 7c. Fig. 7c demonstrates that in such a case, SEF increases with temperature. For nepheline (Tole et al., 1986), dissolution rate increases as a function of stirring speed at 60° and 80°C but not at 25°C, as is predicted in Fig. 7c. For kaolinite, however, SEF decreases with temperature (Fig. 5a). Moreover, a transition from a transport-controlled reaction mechanism to a surface-controlled reaction mechanism involves an increase in activation energy from less than 5 kcal mol^-1 to the range of 10 to 20 kcal mol^-1 (Lasaga, 1984). However, the activation energy obtained from the non-stirred experiments (12±1 kcal mol^‑1) is higher than those obtained from stirred experiments (8.5 ±0.4 kcal mol^‑1 and 7.5 ±1.1 kcal mol^‑1, see Fig. 6).

Kaolinite dissolution rate under non-stirred conditions is also very slow, much slower than most silicates. Thus, it is not reasonable to assume that kaolinite dissolution rate is controlled by diffusion in solution, while dissolution reactions of other, faster dissolving minerals are surface-controlled. For example, the surface-controlled nepheline dissolution rate at 25°C and pH 3 is 5·10^-7 mol m^‑2 s^-1 (Tole et al., 1986), 7 orders of magnitude faster than kaolinite dissolution rate under non-stirred conditions at the same temperature and pH. Therefore, we rule out the possibility that the stirring effect reflects a change from a transport (diffusion)-controlled reaction mechanism under non-stirred conditions to surface-controlled reaction mechanism at high stirring rate.

An alternative explanation for the observed change in apparent activation energy between stirred and non-stirred conditions is that the calculations of the apparent activation energies are erroneous. A critical assumption in calculating activation energies using the Arrhenius equation (equation (6)) is that the pre-exponential factor, A, is the same in all experiments. This pre-exponential factor includes mineral intrinsic parameters such as the surface reactivity. If, as will be suggested below, the surface reactivity varies as a function of stirring, the pre-exponential factor in equation (6) is not constant, and therefore, the calculated apparent activation energies become meaningless.

5.3 Effect of Kaolinite Abrasion and Spalling-off on its Dissolution Rate

Any possible explanation of the stirring effect on mineral dissolution rate should describe the reversibility of the effect as well as the variation of the effect with temperature and pH. Several studies proposed that increase in dissolution rate due to agitation is a consequence of abrasion of mineral particles (Amrhein and Suarez, 1992; van Grinsven and van Riemsdijk, 1992; Stillings and Brantley, 1995; Kalinowski and Schweda, 1996; Ferrow et al., 1999).

In the present study and in previous studies on mineral dissolution kinetics the BET-surface area of samples recovered from agitated dissolution experiments is in general higher than the initial BET-surface area (Amrhein and Suarez, 1992; Nagy and Lasaga, 1992; Ganor et al., 1995; Stillings and Brantley, 1995; Ganor et al., 1999). However, in many cases, the observed increase in final surface area is not proportional to the enhancement in dissolution rate. In the current study the observed increase in final surface area of experiments stirred at ≥650 rpm is much smaller (≤ 71%) than the enhancement of reaction rate due to stirring (up to 900%).

In studies on feldspar dissolution kinetics it was observed that the abrasion process leads to a much higher density of reactive sites on the surface of ultra-fine particles than on that of the relatively large grains (Helgeson et al., 1984). As the surface area of each of the ultra-fine particle is similar to the average size of the etch pits that are observed on feldspar grains, it was suggested that the entire surface area of the ultra-fine particles is composed of active sites (Helgeson et al., 1984). Since a surface-controlled reaction rate is a function of the number of reactive sites at the surface, the dissolution rate of ultra-fine particles normalized to surface area (in units of mol m^‑2 s^-1) is higher than the rate (mol m^‑2 s^-1) of the bulk material (Holdren and Speyer, 1985; Talman and Nesbitt, 1988). Similarly to agitation, vigorous ultrasonic treatment of kaolinite suspensions results in cleaving-off of fine particles along the {001} plane of the kaolinite crystals, and to a lesser extent, spalling-off of fines in the a-b dimensions of the crystals (Blum, 1994). Scanning-force microscopy imaging revealed that single unit cell kaolinite crystals (0.7 nm thick) were produced by ultrasonification (Alex E. Blum, personal communication).

Following the studies of Amrhein and Suarez (1992), van Grinsven and van Riemsdijk (1992) and Stillings and Brantley (1995) it is proposed that ultra-fine kaolinite particles (grain size <<100 nm) are formed as a consequence of spalling-off or abrasion of kaolinite particles, resulting in an enhanced kaolinite dissolution rate. The ratio of the reactive surface area to total surface area of these ultra-fine grains greatly exceeds that ratio of the bulk sample. Therefore, the production of ultra-fine grains results in significant increase in the number of reactive sites, which is not proportional to the increase in total surface area. In other words, the reactive surface area increases due to stirring without significant increase in the total BET-surface area.

At first glance, it seems that a change in reaction rate as a result of spalling-off or abrasion of kaolinite is neither reversible nor temperature dependent, and therefore it is not a viable explanation for the observed stirring effect. The following examination will show that competition between formation of ultra-fine particles by physical breakup and their extinction by chemical dissolution is reversible, depends on temperature and pH and is in agreement with the experimental observations.

The total surface area (m²) of the coarse particles, s_b, is the product of their mass (g), m_b, and their specific surface area (m² g^-1), s_b. Likewise s_f, the surface area of ultra-fine particles of a certain equivalent diameter d, is the product of the mass of ultra-fine particles, m_f, and their specific surface area, s_f. The change in surface area of these ultra-fine particles with time is controlled by the balance between their production and dissolution:

(9)

where t is time (s), P is the production rate of the ultra-fine particles (mole s^-1), MW is the molecular weight (g mol^-1) and Rate_f(d) (mol m^-2 s^-1) is their dissolution rate, which is a function of the particle size d. Solving equation (9) for initial conditions in which at t=0, s_f=0 gives:

(10)

In steady state the reactive surface area is constant with time (the left hand side of equation (9) equals 0) and the formation of ultra-fine particles is balanced by their dissolution, i.e.,

(11)

The surface area of ultra-fine particles of a certain size d in steady-state (s_fss) will therefore be:

(12)

If the fine particles are formed only as a result of stirring-induced spalling-off or abrasion of kaolinite, then under non-stirred conditions the rate of fine particle production is zero and therefore at steady-state their surface area would be zero. The total surface area at steady-state under non-stirred conditions is therefore the surface area of the large kaolinite grains (s_b), and the dissolution rate is the dissolution rate of the large kaolinite grains (Rate_b).

(13)

With stirring, the surface area of the fine particles increases until it reaches a steady-state value as described by equation (12). The total (BET) surface area at steady-state is the sum of the surface area of the ultra-fine particles and that of the large kaolinite grains, i.e., s_f+s_b. The total dissolution rate under stirred conditions is accordingly:

(14)

If the production rate of fine particles depends only on stirring intensity and the surface area of the large grains is constant with time, the dissolution rate at steady-state will depend on stirring speed but will be independent of previous stirring history. This is in agreement with the experimental observation that the stirring effect on dissolution rate is reversible and independent of previous stirring history. It follows from equation (12) that at steady-state the amount of ultra-fine grains, m_f, as well as their surface area, s_fss, is inversely proportional to the steady-state dissolution rate. Therefore, at high temperature and low pH the amount of ultra-fine grains (and their total surface area) will be smaller than at low temperature and at pH close to neutral, under the same stirring conditions. As a result, the amount and surface area of the ultra-fine particles depends on temperature and pH, albeit their production is independent of temperature and pH.

Subtracting equation (13) from equation (14) gives:

(15)

As was shown above, the BET final surface area is not correlated with the stirring speed during the experiments. These observations show that the contribution of the surface area of the ultra-fine particles to the BET surface area is negligible. An alternative explanation may be that the ultra-fine particles were dissolved or washed out before the measurement of final BET surface area. The lack in change of surface area in experiments that were conducted under conditions that minimized the possibility of dissolution and washing out of fine particles (25°C, double-deionized water and no flow) (Table 2) indicates that the contribution of the surface area of the ultra-fine particles to the BET surface area is negligible, i.e.,

(16)

A quantitative estimate of the surface area of the ultra-fine particles is presented in the end of this section. Substituting equation (16) into equation (15) gives

(17)

Rearranging equation (17) and substituting into equation (11) gives

(18)

The production rate of the ultra-fine particles for experiments stirred at 650 rpm using cell type SBSB were calculated using equation (18) and are plotted vs. the dissolution rate under non-stirred conditions at the same pH and temperature in Fig. 8. The production rates range between 7.2^·10^‑13 to 5.4^·10^‑12 mole s^-1, and are independent of pH, temperature and the dissolution rate under non-stirred conditions (Fig. 8).

Rearranging equation (18) and substituting it and equations (13) into equation (5) yields the stirring enhancement factor:

(19)

Equation (19) shows that the stirring enhancement factor decreases as the dissolution rate of the large kaolinite grains increases. Therefore, as the production rate of the fine particles is independent of temperature and pH (Fig. 8), equation (19) predicts that the stirring enhancement factor decreases with increasing kaolinite dissolution rate. This prediction is in agreement with the experimental observations that the stirring enhancement factor is faster at 25°C than at 50° and 70°C, and faster at pH 4 than at pH 3 and 2. (Fig. 5a and b).

Based on the experimental results of Holdren and Berner (1979), Helgeson et al. (1984) estimated that the dissolution rate of ultra-fine albite grains is two orders of magnitude higher than that for the coarse grains. Assuming that the dissolution rate of the ultra-fine kaolinite grains, rate_f, is similarly 100 times faster than that of the bulk kaolinite, the dissolution rate of the ultra-fine particles may be estimated for each experiment. The total surface area of the ultra-fine particles, s_f, may be calculated by substituting these values and the calculated production rates into equation (12). The obtained total surface area of the ultra-fine particles ranged from 0.0007 to 0.65 m² (Table 1). These calculations show that the estimated surface area contribution from the ultra-fines (s_f(%)=s_f/(s_f+s_b)) is only 0.02% to 7% of the total final surface area of the kaolinite, and therefore cannot be recognized with BET-surface area measurements (Table 1).

The mass of the ultra-fine particles was estimated from multi-stage experiments with a steady state at stirring speed ≥ 650 rpm, directly followed by a non-stirred stage (KGDB-50-15A/15B, KGDB-70-1B/1C and KGA2-50-5A/5B). In the examined experiments output solutions were sampled every day and the experimental conditions, i.e., temperature, pH, flow rate, composition of input solution and stirring speed (0 rpm), were constant from the end of the stirred steady state until the end of the consecutive non-stirred steady state. It was assumed, that during the transition period between the two steady states, the release of Al and Si depends (a) on constant dissolution of the bulk kaolinite at the rate that was calculated based on the non-stirred steady state data (Rate_b) and (b) on dissolution of the ultra-fine grains produced in the previous stirred steady state. Based on the calculations, the amount of ultra-fine particles, m_f (Table 1), in steady state (0.0005 g in KGDB and 0.0014 g in KGa-2) is 0.1 wt.% (KGDB experiments) to 0.3 wt.% (KGa-2 experiment) of the initial solid. Dividing the estimation of the total surface area, s_f, by the mass of the particles, the specific surface area of the ultra-fine kaolinite particles, s_f, is calculated to be 35, 70 and 90 m² g^-1, for experiments KGDB-50-15A/15B, KGDB-70-1B/1C and KGA2-50-5A/5B, respectively. The specific (geometric) surface area, s, of a grain is related to its equivalent diameter, d, according to (Tester et al., 1994):

(20)

where r represents the density of the solid (r(kaolinite) = 2.63 g cm^-3 (Deer et al., 1970)). According to equation (20), the equivalent diameter of kaolinite particles with a specific surface area of 35 to 90 m² g^-1 is 65 to 26 nm.

By modeling the change in concentration during the transient period from non-stirred steady state to stirred steady state and back to non-stirred steady state it is possible to evaluate the dissolution rate of the ultra-fine particles. Multi-stage experiment KGDB-70-1 (Fig. 9) shows that both the increase in concentration as the stirring is switched on and the decrease in concentration as the stirring is switched off are not instantaneous. The change of concentrations with time may be used to estimate the dissolution rate of the ultra fine particles. Assuming that the dissolution of the bulk kaolinite is constant since the first steady state, the change in concentration with time as a result of the dissolution of the fine particles may be described by:

(21)

where, C_j is the concentration of element j in solution due to the dissolution of the ultra-fine particles (mole l^-1) and V is the volume of the cell (l). Substituting equation (10) into equation (21) gives:

(22)

The solution of equation (22) for initial conditions in which at t=0 (the beginning of the stirring period), C_j=0 is:

(23)

It is important to note that C_j is the concentration related to the dissolution of the ultra-fine only. The actual concentration is the sum of C_j and the concentration due to the dissolution of the bulk which is equal to the concentration during the non-stirred steady state. For big t values as the exponential terms in equation (22) approach zero, the system approaches steady state and the concentration becomes constant with time. The steady-state concentration (C_jss) is:

(24)

As the stirring stops the production rate becomes zero and therefore the change in the surface area of the ultra-fine particles (equation (9)) becomes:

(25)

Solving equation (25) for initial conditions in which at t=0, s_f= s_fss, where s_fss is the steady-state surface area of the ultra-fine particles, gives:

(26)

Substituting equation (26) into equation (21) gives:

(27)

The solution of equation (27) for initial conditions in which at t=0 (the end of the stirring period), C_j=C_jss, where C_jss is the steady-state concentration due to the dissolution of the ultra-fine particles, is:

(28)

Substituting equations (12) and (24) into equation (28) gives,

(29)

The production rate of the ultra-fine particles that was previously calculated from the steady state (4.3^.10^-12 mole s^-1, Table 1), and the stoichiometric coefficient (2), the cell volume (0.035 l), the kaolinite molecular weight (258.16 g mole^-1) and the fluid flux (8.3^.10^-7 l s^-1) are all known. Therefore, the only unknown in equations (23) and (29) is the product of the dissolution rate of the ultra-fine particles and their specific surface area (Rate_f(d)^.s_f). By fitting equations (23) and (29) to the experimental data (solid line in Fig. 9) we calculate the product of the dissolution rate of the ultra-fine particles and their specific surface area to be Rate_f(d)^.s_f= 1.1±0.1^.10^-08 mole g^-1 s^-1 (R²=0.94). By substituting this value and the production rate of the ultra-fine particles into equation (12) it is possible to retrieve the steady-state mass of the ultra-fine particles to be 0.0004 g. To illustrate the sensitivity of the fitting to the value of the product Rate_f(d)^.s_f, we substitute different values of this product to equations (23) and (29). The dotted and the dashed lines in Fig. 9 represent the expected change in concentration for Rate_f(d)^.s_f=1.1^.10^-7 and 6^.10^-9 mole g^-1 s^-1, respectively. It can be seen that the steepness of the change in concentration during the transient from non-stirred to stirred steady-state and back to non-stirred steady-state, strongly depends on the dissolution rate of the ultra-fine particles and therefore can be used to estimate this rate. The estimated rate, 1.1±0.1^.10^-8 mole g^-1 s^-1, is three orders of magnitude faster than the dissolution rate (normalized to mass) of the bulk kaolinite at the same temperature and pH (3^.10^-12 mole g^-1 s^-1). As the geometric specific surface area of ultra-fine particles is one to two orders of magnitude larger than that of the bulk kaolinite (equation (20)), this estimated rate normalized to geometric surface area is one to two orders of magnitude faster than the rate of the bulk. This conclusion is in agreement with the estimation of Helgeson et al. (1984) that the dissolution rate of ultra-fine albite grains is two orders of magnitude larger than that for the coarse grains.

The proposed model for the stirring effect on kaolinite dissolution rate corresponds to the experimental data of the present study. Unfortunately, direct evidence for the presence of ultra-fine grains was not obtained. The resolution of the scanning-electron microscope used is insufficient to measure a variation in quantity of these grains. In a future study we plan to directly measure the ultra-fine particles, which is beyond the scope of the present paper.

5.4 Implication of the Stirring Effect on Kinetic Parameters Obtained Using Stirred Reactors

5.4.1 Laboratory and Field Estimations of Mineral Dissolution Rate

The reproducibility of dissolution rates is a major concern in interpreting kinetics data and in comparison of results obtained in different laboratories. For example, the reproducibility of feldspar rate determinations by the same laboratory are almost always within a factor of two, while the agreement between rates obtained under similar conditions by different laboratories is generally within a factor of 5 (Blum and Stillings, 1995).

Fig. 10 compares the results of kaolinite dissolution rates at 25°C and pH 3 as obtained in the present study, with those of Carroll-Webb and Walther (1988), Wieland and Stumm (1992) and Ganor et al. (1995). The dissolution rates obtained by Ganor et al. (1995) agree with those of Wieland and Stumm (1992) and are four to five times faster than the rates obtained by Carroll-Webb and Walther (1988). Ganor et al. (1995) listed all the experimental differences between the above-mentioned studies and their possible consequences on dissolution rate but did not point out the reason for the observed differences in dissolution rate. Walther (1996) argued that the results of Carroll-Webb and Walther (1988) are more accurate than those of Wieland and Stumm (1992) and Ganor et al. (1995) because 1000 hours were used to approach steady-state while reaction times in the other studies were considerably lower. Walther (1996) explained that faster dissolution rates were observed in the latter studies because the reaction did not reach steady-state stoichiometric dissolution. The assertions of Walther (1996) are rejected for two major reasons: Firstly, the kaolinite dissolution rates shown in Fig. 10 were obtained by Ganor et al. (1995) at steady-state after 1080 and 1460 hours (see Fig. 1b of Ganor et al., 1995). Secondly, Fig. 11 compares log stoichiometric ratio of kaolinite dissolution at 25°C and pH range of 3.1 to 4.2 obtained by Carroll-Webb and Walther (1988) to that obtained by Ganor et al. (1995). It seems to be that the results of Carroll-Webb and Walther (1988) are not more stoichiometric than those of Ganor et al. (1995).

We suggest that the differences in kaolinite dissolution rates observed by the different studies are a result of differences in stirring efficiency. The experimental setting used in the present study is similar to that used in the study of Ganor et al. (1995). However, the design of the reaction vessel in the current study is different from that in the study of Ganor et al. (1995). They used a well-stirred flow-through reactor with a large Teflon-coated stir-bar, similar to the one used in BB cell type. The stir-bar was mounted on a Lexan pin to avoid grinding the kaolinite. Figure 5 shows that for the same temperature, SEF calculated for the dissolution rate data of Ganor et al. (1995) is significantly higher than that of SBSB cell type and is similar to that of BB cell type. It seems therefore that the fast dissolution rate observed by Ganor et al. (1995) reflects the stirring efficiency of their reactor. Wieland and Stumm (1992) used a well-stirred batch reaction vessel and obtained a kaolinite dissolution rate similar to that obtained by the well-stirred flow-through reactor of Ganor et al. (1995). The Carroll-Webb and Walther (1988) experiments were constantly shaken (Susan Carroll, personal communication). In the present study it is found that the kaolinite dissolution rate was not influenced by rigorous shaking of the reactor twice a day (Fig. 4). Amrhein and Suarez (1992) observed similar anorthite dissolution rates in experiments that were agitated by hand once a day and experiments that were conducted using a gentle wrist-action shaker. The dissolution rate in these experiments was half than those in experiments conducted using a reciprocating shaker. Fig. 10 shows that the rates obtained by Carroll-Webb and Walther (1988) are intermediate between those obtained using a non-stirred reactor, and those obtained using SBSB cell type at 650 rpm. In the current study it is suggested that the observed stirring effect is a result of spalling-off or abrasion of kaolinite particles and formation of very fine particles that have a very fast dissolution rate. Based on this suggestion it is predicted that stirring effect will be less effective when using gentle agitation. Furthermore it is suggested that at least some of the scatter in dissolution rates obtained in different laboratories can be explained by differences in agitating efficiency.

It is usually assumed that all the fine particles are dissolved during the non-linear initial stage of a batch experiment (Holdren and Berner, 1979; Helgeson et al., 1984; Holdren and Speyer, 1985) and the non-steady state stage of a flow-through experiment, and therefore there are no fine particles during the linear stage and steady-state stage in batch and flow-through experiments respectively. The results of the present study indicate that this assumption might be wrong, and that during these last stages a constant amount of fine particles exist. The constant dissolution rate at these stages reflects a steady state between the production by stirring and dissolution of the fine particles. Re-examining the results of Ganor, et al. (1995) indicates that the production of such fine particles is not eliminated by the usage of a suspended stir-bar.

Weathering rates of silicates observed in the laboratory are in general up to three orders of magnitude higher than those inferred from field studies (Stumm, 1992; van Grinsven and van Riemsdijk, 1992; Anbeek, 1993; Casey et al., 1993; Blum and Stillings, 1995). In nature, weathering is conducted under non-stirred conditions and therefore, stirring effects similar to those described in the present study may partly explain the discrepancy between laboratory and field studies. The last conclusion is in accordance with those of Amrhein and Suarez (1992) and van Grinsven and van Riemsdijk (1992). It is important to note that the stirring effect is too small to explain all the differences found between weathering rates of silicates observed in the laboratory and in the field.

5.4.2 Estimations of Apparent Activation Energies

Using well-stirred flow-through experiments and the Arrhenius equation, Ganor et al. (1995) calculated apparent activation energies for the kaolinite dissolution reaction under acidic conditions of 7.5 ±1.1 kcal mol^-1 (Fig. 6c). This value is lower than that reported for most other silicate minerals (average of around 15 kcal mol-1, see Lasaga et al., 1994). The present study shows that under non-stirred conditions, apparent activation energy of the kaolinite dissolution reaction is 12±1 kcal mol^-1. It was demonstrated that competition between formation of fine particles by physical breakup and their extinction by chemical dissolution is a viable explanation for the observed stirring effect. The change in reactive surface area with time is described by the balance between spalling-off or abrasion of kaolinite particles and dissolution of the ultra-fine particles, which is temperature dependent. If the production rate of the ultra-fine particles is independent of temperature, the proposed model predicts that the stirring effect will decrease with increasing temperature (equation (19)). Such a stirring effect on mineral dissolution rate is hidden in the pre-exponential factor, A, in the Arrhenius equation (6). As a result of the temperature dependence of the stirring effect, the pre-exponential factor is higher under low temperature than high temperature conditions and the slope of the Arrhenius plot decreases. Therefore, the slope of the Arrhenius plot is steeper for non-stirred experiments than for well-stirred experiments. Under non-stirred conditions the pre-exponential factor is not influenced by the formation of ultra-fine particles and therefore, is temperature independent. It is suggested that the apparent activation energy that is retrieved under non-stirred conditions is a better approximation for the activation energy of mineral dissolution. For kaolinite, this apparent activation energy (12±1 kcal mol^-1) is closer to apparent activation energy for dissolution of other silicates, than that obtained by Ganor et al. (1995) for kaolinite using a well-stirred reactor (7.5 ±1.1kcal mol^-1).

5.4.3 Estimation of Other Kinetic Parameters

A consequence of the proposed explanation for the stirring effect and its dependence on temperature and pH is that the stirring effect will depend on any kinetic variable that influences the dissolution rate. As is shown in equation (19), the stirring enhancement factor decreases as the dissolution rate of the kaolinite increases. Therefore, the stirring effect becomes stronger under conditions of slower dissolution rate. As a result, experiments under non-stirred conditions will yield, for example, stronger effects of catalysts on reaction rate than well-stirred dissolution experiments.

6 Conclusions

Dissolution rate of kaolinite was examined in flow-through experiments at pH 2 to 4, different stirring speeds and temperatures of 25°, 50° and 70°C. Although kaolinite dissolution is surface-controlled and not diffusion-controlled at this low-temperature range, calculated dissolution rate is enhanced by stirring. The stirring effect is reversible and its intensity increases with the size of the stir bar used. At 25°C the stirring effect is stronger than at 50° or at 70°C, and at pH 4 stronger than at pH 2 and 3.

We propose that very fine kaolinite particles are formed as a result of spalling-off or abrasion of the kaolinite. These very fine particles have a very high ratio of reactive surface area to specific surface area and therefore, the dissolution rate increased with stirring. The production of such fine particles is not eliminated by the usage of a suspended stir-bar as was used in many studies (e.g., Nagy et al., 1991; Nagy and Lasaga, 1992; Ganor et al., 1995; Ganor et al., 1999; Cama et al., 2000).

Balance between the formation and dissolution of the fine kaolinite particles controls the change in reactive surface area with time. The dissolution rate is temperature- and pH-dependent and therefore the stirring effect decreases with temperature. Under non-stirred conditions the pre-exponential factor of the Arrhenius equation is not influenced by the formation of fine particles and therefore, the apparent activation energy that is retrieved under non-stirred conditions is a better approximation for the activation energy of mineral dissolution. The stirring enhancement factor decreases as kaolinite dissolution rate increases. As a result, kinetic factors obtained under stirred conditions will be smaller than those obtained under non-stirred conditions. As for apparent activation energy, the latter is a better approximation for the real kinetic factors.

We recommend the standard use of non-stirred reaction vessels for kinetic experiments of mineral dissolution and precipitation, at least for slow reactions that are surface-controlled.

Acknowledgments. This research was supported by grant # ES-66-96 from the Ministry of Energy and Infrastructure and by the Belfer Foundation for Energy and Environmental Research. Volker Metz would like to thank the Minerva Science Foundation for a graduate fellowship. We wish to express our gratitude to A. C. Lasaga, A. Banin, J. Cama and S. Nir for fruitful discussions and to E. Shani, A. Avital, R. Holzmann, N. Leshem, E. Roueff, G. Ronen and Y. Shalmi for their technical assistance.

7 references

Aagaard P. and Helgeson H. C. (1982) Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. I. Theoretical considerations. Amer. J. Sci. 282, 237-285.

Amrhein C. and Suarez D. L. (1992) Some factors affecting the dissolution kinetics of anorthite at 25 °C. Geochim. Cosmochim. Acta 56, 1815-1826.

Anbeek C. (1993) The effect of natural weathering on dissolution rates. Geochim. Cosmochim. Acta 57, 4963-4975.

Barrante J. R. (1974) Applied Mathematics for Physical Chemistry. Prentice-Hall, INC.

Bauer A. and Berger G. (1998) Kaolinite and smectite dissolution rate in high molar KOH solutions at 35° and 80°C. Appl. Geochem. 13, 905-916.

Berner R. A. (1978) Rate control of mineral dissolution under earth surface conditions. Amer. J. Sci. 278, 1235-1252.

Blum A. and Stillings L. L. (1995) Feldspar dissolution kinetics. In Chemical Weathering Rates of Silicate Minerals, Vol. 31 (eds. A. F. White and S. L. Brantley), pp. 291-351. Mineralogical Society of America.

Blum A. E. (1994) Determination of illite/smectite particle morphology using scanning force microscopy. In Scanning Probe Microscopy of Clay Minerals (eds. K. L. Nagy and A. E. Blum), pp. 172-203. Clay Minerals Society.

Brunauer S., Emmett P. H., and Teller E. (1938) Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309-319.

Cama J., Ganor J., Ayora C., and Lasaga C. A. (2000) Smectite dissolution kinetics at 80°C and pH 8.8. Geochim. Cosmochim. Acta 64, 2701-2717.

Carroll-Webb S. A. and Walther J. V. (1988) A surface complex reaction model for the pH-dependence of corundum and kaolinite dissolution rates. Geochim. Cosmochim. Acta 52, 2609-2623.

Casey W. H., Banfield J. F., Westrich H. R., and McLaughlin L. (1993) What do dissolution experiments tell us about natural weathering? Chem. Geol. 105, 1-15.

Deer W. A., Howie R. A., and Zussman J. (1970) An Introduction to the Rock-forming Minerals. Longman Scientific & Technical, Harlow.

Dougan W. K. and Wilson A. L. (1974) The absorptiometric determination of aluminum in water. A comparison of some chromogenic reagents and the development of an improved method. Analyst 99, 413-430.

Ferrow E. A., Kalinowski B. E., Veblen D. R., and Schweda P. (1999) Alteration products of experimentally weathered biotite studied by high-resolution TEM and Mossbauer spectroscopy. Eur. J. Minral. 11, 999-1010.

Furrer G., Zysset M., and Schindler P. W. (1993) Weathering kinetics of montmorillonite: Investigations in batch and mixed-flow reactors. In Geochemistry of clay-pore fluid interaction, Vol. 4 (eds. D. A. C. Manning, P. L. Hall, and C. R. Hughes), pp. 243-262. Chapman & Hall.

Ganor J., Mogollon J. L., and Lasaga A. C. (1995) The effect of pH on kaolinite dissolution rates and on activation energy. Geochim. Cosmochim. Acta 59, 1037-1052.

Ganor J., Mogollon J. L., and Lasaga A. C. (1999) Kinetics of gibbsite dissolution under low ionic strength conditions. Geochim. Cosmochim. Acta 63, 1635-1651.

Helgeson H. C., Murphy W. M., and Aagaard P. (1984) Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. II. Rate constants, effective surface area, and the hydrolysis of feldspar. Geochim. Cosmochim. Acta 48, 2405-2432.

Holdren G. R. and Berner R. (1979) Mechanism of feldspar weathering. I. Experimental studies. Geochim. Cosmochim. Acta 43, 1161-1171.

Holdren G. R. and Speyer P. M. (1985) Reaction rate-surface area relationships during the early stages of weathering I. Initial observations. Geochim. Cosmochim. Acta 49, 675-681.

Kalinowski B. E. and Schweda P. (1996) Kinetics of muscovite, phlogopite and biotite dissolution and alteration at pH 1-4, room temperature. Geochim. Cosmochim. Acta 60, 367-385.

Komadel P., Madejova J., and Stucki J. W. (1998) Variables affecting the dissolution of smectites in inorganic acids. 35th Annual Meeting of the Clay Minerals Society, 111.

Koroleff F. (1976) Determination of silicon. In Methods of Seawater Analysis. (eds. K. Grasshoff), pp. 149-158. Verlag Chemie.

Lasaga A. C. (1984) Chemical kinetics of water-rock interactions. J. Geophys. Res. 89, 4009-4025.

Lasaga A. C. (1995) Fundamental approaches in describing mineral dissolution and precipitation rate. In Chemical Weathering Rates of Silicate Minerals, Vol. 31 (eds. A. F. White and S. L. Brantley), pp. 23-86. Mineralogical Society of America.

Lasaga A. C. (1998) Kinetic Theory in the Earth Sciences. Princeton University Press.

Lasaga A. C., Soler J. M., Ganor J., Burch T. E., and Nagy K. L. (1994) Chemical weathering rate laws and global geochemical cycles. Geochim. Cosmochim. Acta 58, 2361-2386.

Malmstrom M. and Banwart S. (1997) Biotite dissolution at 25°C: The pH dependence of dissolution rate and stoichiometry. Geochim. Cosmochim. Acta 61, 2779-2799.

Mogollon J. L., Perez-Diaz A., and Lo Monaco S. (2000) The effects of ion identity and ionic strength on the dissolution rate of a gibbsitic bauxite. Geochim. Cosmochim. Acta 64, 781-795.

Murphy W. M., Oelkers E. H., and Lichtner P. C. (1989) Surface reaction versus diffusion control of mineral dissolution and growth rates in geochemical processes. Chem. Geol. 78, 357-380.

Nagy K. L. (1995) Dissolution and precipitation kinetics of sheet silicates. In Chemical Weathering Rates of Silicate Minerals, Vol. 31 (eds. A. F. White and S. L. Brantley), pp. 173-233. Mineralogical Society of America.

Nagy K. L., Blum A. E., and Lasaga A. C. (1991) Dissolution and precipitation kinetics of kaolinite at 80°C and pH 3: The dependence on solution saturation state. Amer. J. Sci. 291, 649-686.

Nagy K. L. and Lasaga A. C. (1992) Dissolution and precipitation kinetics of gibbsite at 80°C and pH 3: The dependence on solution saturation state. Geochim. Cosmochim. Acta 56, 3093-3111.

Stillings L. L. and Brantley S. L. (1995) Feldspar dissolution at 25⁰ C and pH 3: Reaction stoichiometry and the effect of cations. Geochim. Cosmochim. Acta 59, 1483-1496.

Stumm W. (1992) Chemistry of the Solid-Water Interface: Processes at the Mineral-Water and Particle-Water Interface in Natural Systems. John Wiley & Sons, Inc.

Talman S. J. and Nesbitt H. W. (1988) Dissolution of populations of ulfrafine grains with applications to feldspars. Geochim. Cosmochim. Acta 52, 1467-1471.

Tester J. W., Worley W. G., Robinson B. A., Grigsby C. O., and Feerer J. L. (1994) Correlating quartz dissolution kinetics in pure water from 25° to 625°C. Geochim. Cosmochim. Acta 58, 2407-2420.

Tole M. P., Lasaga A. C., Pantano C., and White W. B. (1986) The kinetics of dissolution of nepheline (NaAlSiO₄). Geochim. Cosmochim. Acta 50, 379-392.

van Grinsven H. J. M. and van Riemsdijk W. H. (1992) Evaluation of batch and column techniques to measure weathering rates in soils. Geoderma 52, 41-57.

Walther J. V. (1996) Relation between rates of aluminosilicate mineral dissolution, pH, temperature, and surface charge. Amer. J. Sci. 296, 693-728.

Wieland E. and Stumm W. (1992) Dissolution kinetics of kaolinite in acidic aqueous solutions at 25^°C. Geochim. Cosmochim. Acta 56, 3339-3355.

Xie Z. and Walther J. V. (1992) Incongruent dissolution and surface area of kaolinite. Geochim. Cosmochim. Acta 56, 3357-3363.

1 Table 1: Experimental conditions and results

2 Table 2: Initial and final BET-surface areas of kaolinite samples in stirring experiments

experiment	stirring speed	final BET-surface	initial BET-surface
	(rpm)	area (m^2 g^-1)	area (m^2 g^-1)
KGDB-25-S1	1100	6.2 ±0.6
KGDB-25-S2	1100	5.7 ±0.6	6.4 ±0.6
KGDB-25-U1	0	5.9 ±0.6
KGA2-25-S1	1100	18.1 ±1.8
KGA2-25-S2	1100	18.4 ±1.8	19.4 ±2
KGA2-25-U1	0	18.4 ±1.8

FIGURE CAPTIONS

1 Fig. 1: General experimental set-up and detailed view of the reaction cells used in the present study; a) Schematic illustration of the flow-through system; b) SBSB cell type; c) SB cell type; d) BB cell type.

2 Fig. 2: Variation in the output concentration of Al and Si as a function of time in three representative experiments. The vertical lines represent changes in experimental conditions between the different stages. Al and Si values used to calculate average steady state are denoted by open symbols.

3 Fig. 3: Effect of stirring speed on kaolinite dissolution rate at pH=3 using SBSB cell type. a) KGDB, 25°C; b) KGa-2, 50°C; c) KGDB, 50°C; d) KGDB, 70°C

4 Fig. 4: Comparison of dissolution rates of kaolinite under non-stirred conditions at 50°C. Some of the samples were stirred during earlier experimental stages, while the others were not exposed to stirring prior to the experimental stage. The results show independence of kaolinite dissolution rate on previous stirring history.

5 Fig. 5: The effect of temperature, pH and cell type on stirring enhancement factor, SEF. a) temperature effect at constant stirring speed (650 rpm) and pH (3) using the standard SBSB cell type; b) pH effect at constant stirring speed (650 rpm) and temperature (50°C) using the standard SBSB cell type. c) effect of cell type at constant temperature (50°C) and pH (3).

6 Fig. 6: Arrhenius plots of kaolinite dissolution. a) non-stirred experiments; b) experiments stirred at 650 rpm using SBSB cell type; c) well-stirred flow-through experiments using reactor with a large Teflon-coated suspending stir-bar, after Ganor et al. (1995).

7 Fig. 7: Theoretical Arrhenius plots describing the effect of temperature on dissolution rate of a surface-controlled reaction mechanism and a transport-controlled mechanism. a) Arrhenius plots of the two mechanisms; b) change of dissolution rate as a function of temperature; c) relative difference between the dissolution rate of the surface-controlled and the transport-controlled reaction mechanisms.

8 Fig. 8: Calculated production rate of the ultra-fine particles for experiments stirred at 650 rpm (equation (18)) plotted vs. the dissolution rate under non-stirred conditions at the same pH and temperature. The production rate is independent of pH, temperature and the dissolution rate under non-stirred conditions

9 Fig. 9: The change in Si concentration with time in multi-stage experiment KGDB-70-1. The solid line is a fitting of equations (23) and (29) to the experimental data of stage B (stirred) and C (non-stirred), respectively. The regression coefficient of the fitting, R² is 0.94. The dotted and the dashed lines illustrate the sensitivity of the fitting to the value of the product of the dissolution rate of the ultra-fine particles and their specific surface area (see text).

10 Fig. 10 Comparison of kaolinite dissolution rates at 25°C and pH=3 obtained in the present and in previous studies. CW88 = Carroll-Webb and Walther (1988); WS92 = Wieland and Stumm (1992) and GML95 = Ganor et al. (1995).

11 Fig. 11 Comparison of the stoichiometric ratio obtained by Carroll-Webb and Walther (1988) to that obtained by Ganor et al. (1995). Values in shaded area (log stoichiometric ratio = 0±0.12) represent stoichiometric dissolution.

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Last update: June. 19, 2001