Environ. Sci. Technol. 2001, 35, 977-983
Leaching of Toluene-Neoprene Adhesive Wastes R . F O N T , * ,† M . C . S A B A T E R , ‡ A N D M . A . M A R T IÄ N E Z ‡ Departamento de Ingenierı´a Quı´mica, Universidad de Alicante, Apartado 99, Alicante, Spain, and Instituto Tecnolo´gico del Calzado y Conexas, INESCOP, Elda, Alicante, Spain
This work consists of the study of the extraction of solvent (toluene) from a polymeric (neoprene) substrate during a leaching process. Total organic carbon (TOC) is the main contaminant parameter in the leaching of these systems due to the solution of the toluene and the dispersion of the polymer. The toxicity of the extracts was measured with a Microtox equipment, using Photobacteria phosphoreum, deducing that the toxicity of the extracts is low due to the low solubility of toluene but that the toxicity of toluene is high. On the basis of the experimental results, the amount of toluene diffused vs time in plane sheet systems was studied. A kinetic model has been developed considering two stages: In the first stage, the toluene diffuses into the system across the neoprene chains at a constant rate, not depending on the initial toluene concentration. This fact is explained by considering that there is a constant difference of the toluene concentration between the interface with the water and the inner part of the sample. In the second stage, the dispersion of the polymer with the corresponding amount of toluene takes place. The diffusion of toluene in the leaching process is compared and analyzed considering the diffusion of toluene in a desorption process in air so that the difference of toluene concentration between the interface and the interior can be estimated. A mathematical model is also proposed for considering the leaching process in other operating conditions.
Introduction Adhesives with an organic solvent base are widely used in the shoe industry, frequently being toluene-neoprene adhesives. The adhesive is composed mainly of a polymer (neoprene) and a solvent (toluene, hexane, heptane with other polar solvents) with some amount of organic loads (some resins and antioxidants) and inorganic loads (such as silica, metal oxides, and salts). Adhesive wastes contain great or small amounts of the organic solvent depending on the losses by evaporation of the solvent. The hazard of these wastes depends on the flammable vapors evolved. Frequently adhesives wastes, inside or outside of tins, are dumped, causing an organic contamination due to the migration of the solvent to the aqueous phase, so knowledge of the leaching process is useful for the characterization of the behavior of the waste in landfills. * Corresponding author fax: 34 96 590 3826; e-mail: rafael.font@ ua.es. † Universidad de Alicante. ‡ INESCOP. 10.1021/es000134c CCC: $20.00 Published on Web 01/26/2001
2001 American Chemical Society
One of the characterization methods to ascertain if a waste should be considered toxic and dangerous and/or possibly be deposited in a controlled landfill is a leaching process: The extraction procedure in the Spanish legislation is analogous to the EPA extraction procedure toxicity. The procedure uses deionized water as extractor fluid, and the pH is modified by adding acetic acid to bring the pH down to 5 when necessary. Initially, the amount of water added is 16 times the amount of sample in order to carry out the extraction for 24 h, but finally the ratio sample:water + acetic acid solution added must be 1:20 prior to the determination of the toxicity with Photobacterium phosphoreum. The extraction temperature must be between 20 and 40 °C (1). The German method DIN-38414-S4, considered in many proposals of the European Union, considers the extraction procedure that uses a sample which contains at least 100 g on a dry basis and is carried out at 25 °C. The sample is introduced into a 2-L bottle, and 1 L or more of deionized water is added, maintaining the sample mass:waste mass ratio equal to 1:10. The bottle is closed and placed in a rotator agitator for 24 h (2). The TCLP (Toxicity Characteristic Leaching Procedure) method of the EPA uses two different procedures, depending on whether volatile compounds are involved or not, adding acid solutions of acetic acid. The sample and the extraction fluid are put into a bottle and placed in a rotator-agitator for 18 h (3). During the leaching process, the solid, paste, or very viscous liquid is put in contact with the water or liquid phase. A proportion of the solvent moves from the solid to the liquid phase. Several factors affect this process: time, stirring velocity, temperature, contact surface between both phases, and geometry of the samples. The solvent diffusion in elastomers, such as the neoprene used, is generally Fickian diffusion (4-6). No papers have been found analyzing the leaching process of an adhesive waste with an organic solvent that is very poorly miscible with water. The toxicity test with photobacteria was developed to determine quickly and viably the toxicity of the aqueous specimens. This biological trial uses a nonpathogenic luminous marine bacteria from the Photobacterium phosphoreum species. These bacteria emit light as a mechanism of energy release in the course of their normal metabolism. The intensity of the emitted light is therefore a measure of the metabolic activity of the bacteria. When these microorganisms are exposed to a toxic substance, the light emission decreases in proportion to the toxicity of the sample (7). The objective of this paper has been the study of the leaching of the toluene from a neoprene-toluene adhesive considering the internal diffusion and the very low miscibility of toluene with water and also taking into account the ecotoxicity test with Photobacterium phosphoreum.
Experimental Section Materials. For the preparation of the samples used in this work, an initial solution was made with approximately 20% (wt) of commercial neoprene (AD-10 Du-Pont) and 80% of toluene. Some amounts were taken from this initial mixture and introduced inside a bottle in a chamber, where the vaporization of the toluene took place very slowly, to obtain adhesives with less percentage of toluene and with uniform composition inside the sample. Then the content of the bottle was mixed slightly to obtain a uniform composition before taking the sample to introduce it into the holder. In this way, the samples prepared only differentiate in the initial content VOL. 35, NO. 5, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Scheme of the extraction vessel. of the solvent, but the distribution of the polymer chains are similar. The preparation of the initial solution was made by mixing and stirring of the components in a mechanical agitator OLIVER BATTLE, model DISPERMIX DL-M. The notation and composition of the adhesives prepared and used in the leaching tests were the following: N/T 87/13: 87% (wt) of neoprene + 13% (wt) of toluene and so on for the remainder of adhesives prepared. All the adhesives prepared were pastes and consequently adopted the shape of the container where they were introduced. Two experimental procedures were used for the study of the leaching process: Procedure A: Leaching with water with a sample:water ratio equal to 1:10 in accordance with the DIN 38414 method in laboratory equipment and whirling at 60 rpm. Consequently, the external area of the sample varied with time due to the deformation of the sample. The extraction of liquid samples for analysis was carried out with syringes at different times to obtain the kinetics of the extraction. Procedure B: Leaching with water also with a sample water ratio 1:10, with magnetic stirring and constant contact area between the adhesive sample and the water, as indicated in Figure 1. The sample was introduced in a flat cylindrical holder, 1 cm height and 7.8 cm diameter. The contact area was 47.8 cm2. The extraction of liquid samples for analysis was also carried out with syringes at different times to obtain the kinetics of the extraction. All the runs (procedures A and B) were carried out at 23 °C in a thermostated room. The evolution of the organic contamination was determined analyzing the total organic carbon (TOC) and the toluene by gas chromatography: The determination of TOC was done using the combustion and infrared method with a TOC Shimadzu Analyzer, TOC-5050 model. The determination of toluene in the extracts was carried out using a Hewlett-Packard model 5890 with a Chompack chromato978
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graphic column with FID detector and 1-butanol as internal standard. The luminescence inhibition tests can be carried out with the EP extracts in accordance with the French method AFNOR T90-320 (7). This method establishes that the pH of the liquid to be studied has to be adjusted to a value between 5.5 and 8.5, and if a precipitation is produced, then only the clear liquid must be used. The bacteria were supplied by Microtox in frozen vials, dried, and kept at a temperature less than -20 °C. To carry out this experiment, the bacteria vial was reconstructed by adding reconstruction liquid, supplied by Microtox. In each frosted container there was the same amount of solution with different concentration and pH, an identical quantity of reactant (liquid formed by the bacteria + reconstruction liquid), and a small quantity of saline solution to adjust the osmotic pressure of the solution. The measurements of the luminescence (intensity of the light emission) of the solutions with the bacterial reactive at time zero (Io) and at time t (It) were carried out to calculate the light loss percentage. Because the bacteria may have undergone changes during this time, the same measurements were taken for a control (bacteria reactant with dilution agent) providing a correction factor that was applied to the results. All the studies in this section were done at t ) 15 min, which is the time considered in the AFNOR method. The EC50 is the concentration at which the function Γ (percentage of light loss) is 50%. A desorption run in air was also carried out in an apparatus shown in Figure 2. The sample was introduced in a 0.7 cm high and 7.9 cm diameter cylindrical holder. This holder was introduced above a balance as indicated in Figure 2. Air propelled by a fan flowed parallel to the holder with 2.5 m/s mean velocity at 23 °C. It was tested that this velocity was high enough to consider that external mass transfer was negligible. Weight vs time was registered by a computer, in this way controlling the thermogravimetric run.
Results and Discussion Procedure A (without Constant Contact Area). First, five runs were carried out at different compositions of the adhesives. Considering that some leaching tests last for a period of 24 h, the concentration of the organic contamination (COT and toluene) was determined at 24 h. Figure 3 shows the variation of the concentration of toluene and TOC vs initial toluene percentage of the sample. The theoretical values of TOC corresponding to the toluene are also plotted in Figure 3. These values are logically close to the toluene concentration (because there are 84 g of carbon in each 92 g of toluene). The solutions have a small turbidness that increases with the toluene percentage of the sample, and this fact together with the experimental determination that the TOC values are greater than those corresponding to the toluene indicate that there is a small dispersion of the polymer in the suspension. This fact, probably unexpected due to the crosslinking of the polymer, cannot be ignored. In accordance with Figure 3, when the toluene percentage is equal to or greater than 34%, the ratio of total TOC/toluene TOC is around 1.54. For the run with initial toluene percentage of 13%, the TOC value is close to the equivalent TOC of toluene, indicating that the dispersion did not take place or was negligible at low initial toluene concentrations of the sample. The toxicity of the extracts was also measured with the Microtox test. Table 1 shows the experimental values of EC50 for the extracts obtained at 24 h. The EC50 of the zinc sulfate is 6.7 ppm or 6.7 × 10-4 wt % (with 90% confidence interval equal to 6-7.4 ppm), which is inside the interval proposed for Photobacterium phosphoreum with mean metabolic
FIGURE 2. Desorption apparatus: 1, fan; 2, electric resistance (chamber where air is heated); 3, autotransformer for power control; 4, drying chamber where temperature is measured; 5, digital balance; 6, computer.
FIGURE 3. Toluene concentration and TOC vs initial toluene percentage in the sample (procedure A).
TABLE 1. Values of EC50, CTol, and EC50 × TOC for the Runs by Procedure A at 24 h sample
EC50 (wt %)
CTol (mg of toluene/L)
EC50 × CTol (wt fraction × mg/L)
N/T 17/83 N/T 31/69 N/T 41/59 N/T 67/33 N/T 87/13
6.05 12.8 23.3 38.5 >45
670 339 185 117 86
40.5 43.4 43.1 45.0 >38
activity. It can be observed that the EC50 values are high in comparison with the limit of 3000 mg/L (or 0.003 wt %) proposed as a limit for considering a waste as toxic in accordance with the Spanish Regulation (1); therefore, these wastes would not considered as toxic by the Spanish Regulation by this method. Table 1 also shows the product EC50 (mass fraction) by the toluene concentration (mg/L), obtaining values of 40-45 mg of toluene/L, which is very low values indicating a relative high toxicity of the toluene (for organics with low toxicity, for example, acetone, the product of the EC50 by the organic concentration) is around 104, and for the extracts obtained from municipal solid wastes without toxic chemicals, the product EC50 × TOC is around 106-107). The similarity of the values of the EC50 × CTol shows that the
experimental procedure is correct. In a real adhesive waste, although there may be other substances that can contribute to the toxicity, the solvent is mainly responsible. Another run by procedure A was carried out using the N/T 31/69 adhesive but extracting samples of extracts at different times to evaluate the leaching rate of TOC from the beginning of the test to 2.7 × 105 s (75 h). Figure 4 shows the variation of the TOC vs time. The experimental solubility of toluene in water is around 500 ppm at 23 °C (9). The values higher than this solubility obtained in the leaching process corroborate the fact that a small dispersion of the polymer adsorbing toluene took place. In accordance with the evolution of the TOC vs time, two tendencies can be observed: a first phase, where the TOC increases from zero to a value around 440 mg/L, and a second phase, where the TOC increases slowly but constantly. It can be convenient to remember that, by this leaching procedure, the transfer area of the toluene from the adhesive to the aqueous medium is not constant due to the deformation of the sample of adhesive taken. Similar results are obtained with other runs. To clarify the diffusion rate of the toluene, some runs were planned to be carried out by procedure B, as presented in the following section. Procedure B. Three runs were carried out by this procedure at different compositions of toluene in the sample. VOL. 35, NO. 5, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Variation of the TOC/TOC∞ vs time (procedure A).
TABLE 2. Values of k2, Correlation Coefficient, XAo - XAi, XAo, and XAi sample
mass of sample
k2 (kg of A/s-1/2)
r2
XAo - XAi (kg of A/kg of B)
XAo (kg of A/kg of B)
XAi (kg of A/kg of B)
N/T 87/13 N/T 42/58 N/T 31/69
0.0893 0.0737 0.0692
7.00 × 10-7 7.04 × 10-7 7.05 × 10-7
0.979 0.989 0.999
0.0205 0.0206 0.0206
0.149 1.381 2.226
0.129 1.360 2.205
FIGURE 5. Variation of the toluene mass extracted vs the square of time (procedure B). Table 2 shows the total mass introduced into the holder and the amount of toluene inside the mass introduced. The transfer area was constant (A ) 47.8 cm2), and the volume of the sample was approximately the same for the three runs and coincided with the volume of the holder (V ) 373 cm3). The external diffusion resistance can be considered negligible because the stirring of the solution by procedure B was sufficient enough to cause the very slow internal diffusion to be the controlling step of the process. Figure 5 shows the variation of the mass of toluene extracted vs the square of time. It can be observed that there is an initial lineal variation, which curiously is approximately the same for the three adhesives, and then another variation begins with slow toluene extraction rate from different amounts of toluene extracted. On the other hand, the 980
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turbidness of the extracts increases with time as a consequence of the dispersion of the polymer. The initial lineal variation indicates that the transfer rate of toluene can be controlled by an internal diffusion of the toluene through the polymer chains and that a Fickian diffusion of the solvent can be assumed. It was not easy to find an explanation for the coincidence of the initial lineal variation, indicating that the mass of toluene extracted is the same for the adhesive with high toluene content as for the adhesive with low toluene content. No reasons were found in the literature. To find an explanation for the diffusion of toluene during the leaching process, it was considered that some useful information could be obtained from a desorption run in air, done as explained previously. Figure 6 shows the variation of the ratio between
written that
M∞ - Mt
8
)
M∞
π
2
∞
1
∑ (2n + 1)
n)0
2
exp[-(2n + 1)2k1t]
(3)
where
k1 )
π2 De 4V2Bt
(4)
The mass M∞ can be calculated as
M∞ ) (XAo - XAi)SVBtFBp
FIGURE 6. Variation of the desorpted toluene mass/maximum desorpted toluene mass vs time (desorption run). the toluene vaporized and the maximum one vs time in a N/T 20/80 sample. During the desorption process, the sample reduced its volume due to the elimination of the toluene. Curiously, the reduction process can be adjusted to the non-steady-state equations proposed in the literature for slabs of constant thickness. Considering the space variables presented in some references (5, 8), the second law of Fick can be written as
( ) ∂XA ∂t
VB
)
( )
∂XA ∂ De ∂VB ∂VB
(1)
t
where XA is the ratio between toluene mass and neoprene mass, De is the effective diffusivity, that equals
De ) DAB 2B
(2)
where DAB is the diffusion coefficient corresponding to the normal expression of Fick’s law, B is the volume fraction of neoprene, and VB is the volume of neoprene between a layer at a distance and the bottom per unit of cross section (similar expressions can be considered assuming that XA is the ratio between the volume of toluene and the volume of neoprene). The effective diffusivity can logically be considered approximately constant when the variation of DAB and the volume fraction of polymer are not very high. It is possible that the diffusivity DAB decreases when B increases, and in these cases the effective diffusivity De (that equals DAB 2B) is also approximately constant. Waggoner et al. (10) studied the variation of the diffusivity in a polystyrene system with different solvents, including toluene. It can be deduced that the product DAB 2B is approximately constant for a volume fraction of polymer greater than 0.2. When the effective diffusivity De is approximately constant, eq 1 can be integrated. Considering that initially (t ) 0), the slab is uniform and consequently
(XA ) XAo) for 0 e VB e VBt where VBt is the total volume of neoprene per unit of cross section and that during the run, the composition of toluene inside the sample at the water-sample interface is constant:
XA ) XAi for VB ) VBt Considering the extracted toluene mass Mt at any time and the corresponding value M∞ at time infinity, it can be
(5)
where S is the surface of the water-sample interface and FBp is the density of the pure neoprene (without toluene). For the first period of time or considering a semi-infinite slab, it can be deduced that
( )
M∞ De Mt ) 2 VBt π
1/2
( )
t1/2 ) 2SFBp(XAo - XAi)
De π
1/2
t1/2 ) k2t1/2 (6)
By correlation of the experimental data presented in Figure 6, the best value of k2 was deduced, minimizing the sum of the squares of the differences between the experimental values of Mt and those calculated by eq 3. Figure 6 also shows the calculated values, thus observing a good correlation. The value optimized of k1 is 4.65 × 10-5 s-1. Considering that VBt equals 0.00135 m3 polymer/m2, the value of the effective diffusivity De (that equals DAB2B) was 2.57 × 10-11 m2/s. Considering that the diffusion of the toluene inside the sample in the leaching run takes place by eq 6, applicable when the toluene concentration of the inner layers has not decreased, a plausible explanation of the coincidence of the Mt - t1/2 variation for the samples with different initial toluene concentration would be that the difference XAo - XAi is constant for the three runs. At the neoprene-water-toluene interface, XAi is less than XAo due to the sorption of water at several active points on the neoprene. The difference XAo XAi represents the ratio of water mass adsorbed and the mass of neoprene, and consequently does not depend on the initial toluene concentration of the sample and can be considered as an adsorption characteristic of the neoprene. Taking into account only the first points of Figure 5 for each run, the corresponding value of the constant k2 of eq 6 were obtained. These values and the lineal correlation parameters are presented in Table 2. From these values of k2 and considering the value of the effective diffusivity, the values of XAo and XAi are also obtained and presented in Table 2. It can be observed that the difference XAo - XAi is very small, indicating a small sorption of water on the neoprene. The leaching process continues to reach the equilibrium phase between neoprene, water, and toluene. The higher the amount of neoprene, the lesser the amount of toluene solved in water. This fact is a consequence of the greater affinity of toluene with the neoprene than with the water. The strong decrease of the extraction process takes place when reaching equilibrium; therefore, with the sample N/T 87/13 with low neoprene percentage, the equilibrium toluene mass will be less than with the sample N/T 31/69. It has been commented previously that the second phase in the toluene extraction, coinciding with an increase in the turbidness of the extracts, is due to the loosening of some layers of polymer. To obtain some relationships and considering the last points in the Mt - t plot shown in Figure VOL. 35, NO. 5, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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The correlation obtained from Figure 8 is
TABLE 3. Values of Mte and m
Ce ) 0.133 exp(0.478XAo)
sample
Mte (kg of A)
m (kg of A/s)
r2
N/T 87/13 N/T 42/58 N/T 31/69
1.28 × 10-4 1.88 × 10-4 2.68 × 10-4
1.53 × 10-11 1.23 × 10-10 1.69 × 10-10
0.964 0.972 0.942
FIGURE 7. Variation of the estimated extracted toluene mass by diffusion (calculated as Mt - mt) vs the square of time (procedure B).
FIGURE 8. Equilibrium toluene concentration vs toluene:neoprene ratio in the sample. 5, the corresponding lineal variations in accordance with
Mt ) Mte + mt
(7)
were carried out. The parameters Mte and m are also presented in Table 3. The parameter m is the extraction rate corresponding to the second stage, and Mte is the mass of toluene corresponding to the equilibrium reached after the first stage (assuming that the extraction process takes place from the beginning of the run). It can be deduced that the values of the extraction rate m are low in the range of 1010-10-11 kg/s and logically increase with the percentage of toluene in the sample because the chains of polymer + toluene are easily separated from the sample at high toluene concentration. It seems logical to assume that the rate m is directly proportional to the surface of the water-sample interface. - mt vs t12 for the three
Figure 7 shows the variation of Mt runs. It can be observed that the values of Mt - mt remain constant and equal the toluene mass Mte when reaching equilibrium. The values of equilibrium concentration Ce (kg of toluene/m3), obtained as Mte/(volume of extract) have been plotted vs the initial toluene:neoprene ratio XAo, as shown in Figure 8. 982
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(7)
where Ce is expressed as kg of toluene/m3 and XAo is kg of toluene/kg of neoprene. Note that this equation is valid when the ratio of sample:water is 1:10 and when the contact surface/ water volume has the value of the runs presented. Considering however that the mass of toluene extracted is very small, this equilibrium relationship would be approximately the same for another sample:water and contact surface/water volume ratios, as occurs in the adsorption equilibrium. Note that eq 7 can be useful for interpolation of data. For small values of XAo, the extrapolation of eq 7 leads to values around 0.133, whereas for high values of XAo it must be considered that the maximum value of toluene concentration is 0.5 kg/m3. The density of the polymer FBp equals 1250 kg/m3, so the volume fraction of polymer B varies between 0.23 (for N/T 31/69) and 0.82 (for N/T 87/13), and the corresponding values of DAB vary between 4.6 × 10-10 and 3.8 × 10-11 m2/s (obtained from the value of DAB2B that equals 2.57 × 10-11 m2/s). The effect of the water diffusion inside the toluene + polymer has not been considered in the mathematical model. The solubility of water in toluene is 500 ppm at 25 °C (9), but the presence of the polymer can change this value. The diffusion coefficient of water in toluene is 6.19 × 10-9 m2/s (9), so the diffusion of water cannot be ignored, although the diffusion rate of water depends also on the low solubility of water in the toluene + polymer phase. These basic aspects need to be clarified by further study, but their consideration has not been the purpose of this paper. To understand all the types of diffusion and interaction between the toluene, the water and the polymer, further basic studies in this field are probably required. This paper has presented an interesting phenomena and proposed some reasons for interpreting the experimental results that can be tested with other similar materials. Extrapolation to Other Conditions. In view of the assumptions considered previously, it would be possible to deduce the extraction process of a waste with different thickness and similar concentration to those shown in this paper (10-70% toluene) when the concentration of toluene in the extracts is low and the external diffusion is fast: In the first stage, the kinetic constant k1 is directly proportional to the surface S and does not depend on the thickness, as indicated by eq 6. Consequently, it can be written that
S(m2) Mt (kg) ) 7.92 × 10-7 t(s)1/2 47.8 × 10-4
(8)
The final time of this stage corresponds when the concentration of toluene in the extracts reaches the value corresponding to
Mte ) Ce ) 0.133 exp(0.478XA) V
(9)
where Mte is the mass of toluene extracted. For the second stage, the following expression can be used:
S(m2) Mt (kg) ) Mt + m 47.8 × 10-4
(10)
where the rate m can be obtained from Table 3 or by interpolation, taking into account the great variation of the rate m. If the surface S is not constant and/or the geometry of the waste is not a slab and/or there is a considerable increase
of toluene in the extracts, the numerical integration using the basic parameters cited in this paper should be used for obtaining the solution. If long periods of time are considered, note that the toluene concentration in the sample decreases. If a uniform toluene concentration cannot be assumed, the effective diffusivity of toluene inside the toluene + neoprene system must be considered.
Acknowledgments The authors are grateful for the financial support of the Consellerı´a de Medio Ambiente of the Generalitat Valenciana (Spain).
Notation
V
volume of extract (m3)
VB
volume of B between the distance x and the bottom per unit of cross section (mB3/m2)
VBt
total volume total of polymer per unit of cross section (mB3/m2)
XA
mass ratio (kg of A/kg of B)
XAi
mass ratio at the interface with air (kg of A/kg of B)
XAo
initial mass ratio (kg of A/kg of B)
Literature Cited
A
solvent
B
polymer
Ce
equilibrium concentration (kg of A/m3)
DAB
diffusivity (m2 s-1)
De
effective diffusivity (m2 s-1)
k1
kinetic diffusion constant for a semi-infinite medium (s-1)
k2
kinetic diffusion constant for an infinite plane sheet (kg of A/s-1/2)
Mt
mass of solvent at time t (kg of A)
Mte
mass of solvent extracted at equilibrium (kg of A)
M∞
total mass of solvent that can diffuse (kg of A)
Mo
initial mass of the sample optimized (kg of A)
m
extraction rate (kg of A/s)
Received for review June 19, 2000. Revised manuscript received November 6, 2000. Accepted December 1, 2000.
S
surface of the water-sample interface (m2)
ES000134C
(1) Ministerial Order of 13 October 1989 on the Characterization of Hazardous and Toxic Wastes. Official Bulletin of Spain (B.O.E.), November 10, 1989. (2) DIN 38414-S4 Standard Method. Sludge and Sediments (groups S). Determination of Leachability by Water (S4). (3) Toxicity Characteristic Leaching Procedure, Code of Federal Regulation 40, Part 260, Protection of Environment, USA. (4) Vrentas J. S.; Duda J. L. AIChE J. 1979, 25, 1. (5) Fu, T. Z.; Durning, C. J. AIChE J. 1993, 39, 1030. (6) Edwards, D. A.; Cohen, D. S. AIChE J. 1995, 41, 2345. (7) AFNOR T90-320. French Normative on Characterization of Wastes. (8) Crank, J. The Mathematics of Diffusion; Oxford University Press: London, 1975. (9) Reid, R. C.; Prausnitz,, J. M.; Sherwood, T. K. The Properties of Gases & Liquids, 3th ed.; McGraw-Hill: New York, 1977; pp 373, 570. (10) Waggoner, R. A.; Blum, F. D.; MacElroy, J. M. D. Macromolecules 1993, 16, 6841.
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