The leaching kinetics of acetone in an acetone-polyurethane adhesive waste

The Leaching Kinetics of Acetone in an Acetone-Polyurethane Adhesive Waste

R. FONT,2 M. C. SABATER,1 M. A. MARTINEZ1

1 Instituto Tecnologico del Calzado y Conexas, INESCOP, Elda, Alicante, Spain

2 Departamento de Ingenieria Quimica, Universidad de Alicante, Apartado 99, Alicante, Spain

Received 14 March 2001; accepted 6 November 2001Published online 11 June 2002 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/app.10745

ABSTRACT: This work consists of the study of the extraction of solvent (acetone) from apolymeric (polyurethane) substrate during a leaching process. Total organic carbon(T.O.C.) is the main contaminant parameter in the leaching of these systems due to thesolution of the acetone which is practically totally extracted from the polymeric system.During the leaching process, the water (polar) diffuses across the holes formed betweenthe chains of polyurethane reacting at the same time with the isocyanate groups at theend of the chains, causing the reticulation or crosslinking of the polymer. On the basisof the experimental results, the amount of acetone diffused versus time in plane sheetsystems was studied. A diffusion model based on the Fickian law was developedconsidering two stages. In the first stage, the water diffuses into the system across thepolyurethane chains causing the reticulation of the polymer and dissolving the acetone.In the second stage, the diffusion of acetone in water, which occupies the holes or spacesbetween the reticulated polymer, takes place. The diffusion kinetics in these kinds ofsystems are similar to the diffusion kinetics in a rigid solid, considering an effectivediffusivity of the acetone through the system. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci85: 1945–1955, 2002

Key words: adhesives; waste; polyurethanes; acetone; leaching

INTRODUCTION

Adhesives with an organic solvent base are widelyused in the shoe industry, being very frequentlypolyurethane-acetone adhesives. The adhesive iscomposed mainly by a polymer (polyurethane)and a solvent (acetone or other solvent), withsome amounts of organic load (some additives)and inorganic loads (silica, metal oxides, etc.).

Adhesive wastes contain high or smallamounts of the organic solvent depending on thelosses by evaporation of the solvent. The hazard of

these wastes depends on the inflammable vaporsevolved.

The solvent diffusion in elastomers, such as thepolyurethane used, is generally Fickian diffu-sion.1–3 Some references concerning diffusion co-efficients can be found in literature: Hung andAutian4 for aliphatic alcohols in polyurethane,Storey et al.5 for various dialkyl-phthalates inpoly(vinyl chloride (PVC), Aithal et al.6 and Ha-rogopadd et al.7 for some organic solvents in poly-urethane, and Waggonner et al.8 for several sol-vents in polystyrene. On the other hand, Mencerand Gomzi9 studied the swelling kinetics of poly-(ethylene-co-vinyl acetate) in different solvents;Webb and Hall10 considered the ingress of sol-vents into vulcanized rubber by nuclear magneticresonance and observed a good diffusion behavior,

Correspondence to: R. Font ([email protected]).Contract grant sponsor: Consellerıa de Medio Ambiente of

the Generalitat Valenciana.Journal of Applied Polymer Science, Vol. 85, 1945–1955 (2002)© 2002 Wiley Periodicals, Inc.

1945

and Aminabhavi et al.11 studied the molecularmigration of organic halocarbons into thermo-plastic polymer blend membranes by using aFickian mechanism of sorption and diffusion.

Adhesives wastes are frequently dumped, in-side or outside of tins, causing an organic contam-ination due to the migration of the solvent to theaqueous phase. Knowledge of the leaching processis therefore useful for the characterization of thebehavior of the waste in landing vessels.

One of the characterization methods of a wasteis a leaching process:

The extraction procedure in the Spanish legis-lation12 is analogous to the extraction procedure(EP) of the USA legislation. The procedure usesdeionized water as extractor fluid and the pH ismodified by adding acetic acid to bring the pHdown to 5 when necessary. Initially, the amountof water added is 16 times the amount of samplefor carrying out the extraction for 24 h, but finallythe ratio of sample : water � acetic acid solutionadded must be 1 : 20 prior to the determination ofthe toxicity with Photobacterium phosphoreum.The extraction temperature must be carried outbetween 20 and 40°C.

The German method DIN-38414-S4,13 consid-ered in many proposals of the European Union,considers the extraction procedure that uses asample which contains at least 100 g in dry basisand is carried out at 25°C. The sample is intro-duced into a 2-L bottle and 1 L or more of deion-ized water is added, maintaining the sample :waste ratio equal to 1 : 10. The bottle is closedand placed in a rotator-agitator for 24 h.

The toxicity characteristic leaching procedure(TCLP)14 method of the Environmental Protec-tion Agency (EPA) uses two different procedures,depending on whether volatile compounds are in-volved or not, adding acid solutions of acetic acid.The sample and the extraction fluid are put in abottle and placed in a rotator-agitator for 18 h.

During the leaching process, the solid, paste, orvery viscous liquid is put in contact with the wa-ter or liquid phase. A proportion of the solventmoves from the solid to the liquid phase. Severalfactors affect this process: time, stirring velocity,temperature, contact surface between bothphases, internal diffusion, and chemical reac-tions.

The contamination of the extracts from thewastes of polyurethane solvent based adhesives iscaused mainly by the organic solvents, most ofthem nontoxic. Nevertheless, the main contami-nant parameter is the total organic carbon(T.O.C.).

The influence of the solvent concentration inthe sample and the contact surface are the factorsstudied in this work. The kinetics of the diffusionprocess were also studied.

At the end of the polyurethane chains, thereare isocyanate groups which react with the waterdiffused, causing the reticulation or crosslinkingof the polymer. This phenomenon must be takeninto account in the study of the extraction velocityof solvents during a leaching of acetone-polyure-thane adhesives process.15

No articles were found analyzing the leachingprocess of an adhesive waste with an organic sol-vent, in which the polymer reticulates when re-acting with the water, forming a semirigid solid.

MATERIALS

A synthetic mixture made up of 20 wt % polyure-thane (Desmocoll 540- Bayer, Leverkusen, Ger-many) and 80% acetone (MERCK KGaA, Darm-stadt, Germany) was initially prepared by mixingand stirring in an Oliver Batlle Dispermix DL-Mmodel with a speed control at 2500 rpm. Someamounts were taken from this initial mixture andintroduced inside a bottle in a chamber, where thevaporization of the acetone took place very slowly,to obtain adhesives with less percentage of ace-tone and with uniform composition inside thesample. Then the content of the bottle was mixedslightly to obtain a uniform composition beforetaking the sample to introduce it into the holder.In this way, the samples prepared only differen-tiate in the initial content of the solvent, but thedistribution of the polymer chains are similar.The three samples used were the following: PU66/a34, 66 wt % polyurethane and 34 wt % acetone;PU57/a43, 57 wt % polyurethane and 43 wt %acetone; and PU46/a54, 46 wt % polyurethaneand 54 wt % acetone.

EXPERIMENTAL

Two procedures were used to carry out the studyof the leaching process.

Procedure A

Procedure A consists of a water extraction using asample : water � 1 : 10 wt ratio, in accordancewith the DIN 38414 leaching method,13 by turn-ing the vessel at 60 rpm and with variable contactinterphase area (sample and water are intro-

1946 FONT, SABATER, AND MARTINEZ

duced into a vessel which is turned). Small quan-tities of extract were extracted with a syringe tocarry out the analysis.

Procedure B

Procedure B consists of a water extraction using asample : water � 1 : 10 ratio. During the test, thecontact surface between both stages was constantand the water was agitated with a magnetic stir-rer in a vessel. The sample holder is a cylindricalvessel with 1 cm height and 7.8 cm diameter. Thearea of the contact surface between solid sampleand liquid was 47.78 cm2.

All the experiments were carried out at 23°C.The analysis of the T.O.C. was carried out by thecombustion and infrared method using a T.O.C.Shimadzu model TOC-5050.

The solvent concentration in the extracts wasmeasured by gas chromatography in a Hewlett–Packard 5890 model gas chromatograph. A semi-capillary column Chrompack with 27.5 m lengthand 0.53 mm diameter, flame ionization detector(FID), and nitrogen as carrier gas was used foranalysis.

RESULTS AND DISCUSSION

Procedure A

Logically the amount of extracted solvent at 24 hdepends on the initial amount of solvent in thewaste due to the high solubility of acetone inwater. To deduce the extraction degree, a series ofruns with different initial acetone concentrationswere carried out following Procedure A (24-h ex-traction period, 10 : 1 water : sample ratio, water-sample contact surface variable). The values ofT.O.C. and the solvent concentration in the ex-tracts versus the initial composition (percentage)of solvent in the initial sample are shown in Fig-ure 1. The values of T.O.C. equivalent to the sol-vent quantity are also shown in Figure 1. Thesevalues are obtained by multiplying the solventconcentration in the extracts by the mass carbonproportion in the solvent molecule: T.O.C.equivalent(mg/L) � acetone concentration (mg/L) � 36/58. Itcan be observed that there is a nearly exact coin-cidence between the expected values of T.O.C.and the calculated values of T.O.C. due to theacetone analyzed, thus corroborating the experi-mental values.

Considering that the sample : water ratio was1 : 10, if the solvent extraction were total, the

ratio between the expected solvent concentration(mg/L)/solvent concentration and the initial sam-ple (wt %) is 1 : 11 � 106 : 102, which equals 909.The calculated slope for the lineal correlations ofsolvent concentration (mg/L) versus the solventconcentration (wt %) is 881, which is close to thatdeduced for total extraction, indicating nearly to-tal extraction.

Procedure B: Kinetic Model

The runs for the study of the diffusion kineticswere carried out with slabs by using Procedure Bfor maintaining the interface area constant. Inpractice, there are uncontrollable small varia-tions of the interface because of the elasticity ofthe polymers. The values obtained in the testsand their relationships with the proposed modelsare described as follows.

The variations of the ratio between the ex-tracted mass of acetone Mt and the maximummass M� versus the square of time are shown inFigure 2 for the three tests carried out with thethree samples PU66/A34, PU57/A43, and PU46/A54, with acetone weight percentages of 34, 43,and 54 wt %, respectively. It can be verified thatthe kinetics of the extraction in the three tests aresimilar.

During the leaching process, two phenomenaare produced in the polyurethane-acetone (PU/A)system: the water in the system moves into thesample through acetone by diffusion and the wa-ter also reacts with the polymeric chains of thepolyurethane, causing the reticulation or cross-linking of the polymer and forming a semirigidsolid.

Figure 1 T.O.C., acetone, and T.O.C.equivalent concen-trations in extracts obtained by procedure A at 24 hversus initial solvent concentration in samples.

LEACHING IN ACETONE-PU ADHESIVE WASTE 1947

In the present work a diffusion model was pro-posed, which explains the process considering twostages.

In the first stage, the water moves into thesample by reacting and forming a reaction frontand separating the nonreticulated polymer fromthe reticulated polymer front. The water is totallysoluble in acetone, so the movement of the reac-tion front controls the exit of the water from thepolymer.

In the second stage, the reaction front has ar-rived at the end of the slab, and the process ofdiffusion of water and acetone goes on until theconcentration inside the holes of the sampleequals the exterior concentration. The duration ofthe first stage will be from time zero to criticaltime tc and the second stage from critical time totime infinity.

The holes formed can be observed and had awide distribution size, the biggest ones with adiameter around several millimeters.

Kinetic Model in the First Stage of theDiffusion Process

The mass transfer process can be represented bythe Fick law, taking into account that the effec-tive diffusivity can be related to the ordinary dif-fusivity DAW, the internal porosity �, and the tor-

tuosity factor �, in the same way that occurs in thesolid catalysts16:

nA � � �DAW

�

�

��A

�x � �A�nA � nW� (1)

nW � � �DWA

�

�

��W

�x � �W�nA � nW� (2)

To simplify and considering that nA and nWhave opposite signs, it will be assumed that thediffusion process is the controlling process. Thetotal transport of mass is considered negligibleand a simplified law can be considered, so

nA � � DeA

��A

�x (3)

nW � � DeW

��W

�x (4)

where DeW is the effective diffusivity of water,DeW � �(DWA/�) (m2/s), similar to the diffusivitydefined in heterogeneous catalysis; and �A is theacetone concentration in the system that equals�wA (kg acetone/m3 acetone � water).

Figure 2 Relationship of Mt/M� extracted solvent versus t1/2 for the three samplesPU66/A34, PU57/A43, and PU46/A54. Leaching procedure B (surface S constant).


By mixing the polyurethane � acetone withwater, it was observed that the reaction of thewater with the isocyanate groups at the end of thechains of the polyurethane is very fast, producingthe reticulation of the polyurethane. In the modelconsidered, the front of reaction separates thenonreticulated solid with the reticulated solid andthe water diffuses from the interface slab-solutionthrough the holes of the reticulated polymer tothe boundary between the reticulated solid andthe nonreticulated solid where the water reactswith the isocyanate groups, as occurs in the non-reacted core model. On the other hand, the ace-tone diffuses in the opposite direction. Figure 3shows a scheme of the diffusion process in thisstage.

Considering an element of thickness volume�x, the mass balance of water can be deduced as:

��W

�t ��nW

�x � 0 (5)

and taking into account the velocity law, the re-sult is

��W

�t � DeW

�2�W

�x2 � 0 (6)

Considering that in the previous equations �Wrepresents the concentration of water in thespaces or holes between the chains of reticulatedpolymer (kg of water/m3 fluid) and nW is the fluxdensity through the total area, the general equa-tion of the second Fick law is obtained:

��W

�t �DeW

�

�2�W

�x2 (7)

The process of the reaction of water with thepolyurethane molecule (in the presence of ace-tone) is equivalent to the following reactionscheme:15

2R-NCO � H2Of RNHCONHR � CO2 or

Water � b PU (nonreticulated) � d acetone

f (1 � b)PU (reticulated) � d free acetone

where b and d are the yield factors: b is the massof polyurethane/mass of water reacted and d isthe mass of free acetone between the polymericchains/mass of water reacted.

The reacted mass water by volume of reticu-lated polymeric phase is equal to ((1 � �)/(1� b))�PU (mass of reacted water/volume reticu-lated polymeric phase), where �PU is the reticu-lated polyurethane density (reticulated polyure-thane mass/reticulated polyurethane volume); (1� �) is the volumetric fraction of reticulated poly-urethane in the reticulated polymeric phase; and(1 � b) is the mass unit of the reticulated poly-urethane by reacted mass unit of water.

The profile of solvent concentration during thediffusion process in the first stage is also shown inFigure 3 at t � 0 (at beginning of the run), at anintermediate time t, and at t � tc (critical time)when the reaction front or interface arrives at theend of the slab.

It was observed that a small contraction andcontact surface deformation in the solid phase is

Figure 3 Concentration profile during the diffusion process in the first stage.


produced during the process, but this fact has notbeen considered in the model.

Taking into account the concentration profile,the boundary conditions are

At the outside extreme (x � 0)

wA � 0 (8)

wW � 1 (9)

�W � �W0 (10)

At the reaction front (x � xL)

wA � 1 (11)

wW � 0 (12)

�W � 0 (13)

nA�x�L � � nWd (14)

nW�x�L � � DeW

��W

�x �x�L

�considering diffusion)

(15)

nW�x�L �1 � �

1 � b �PU

�xL

�t �considering reaction)

(16)

So, the solution of eq. (7) is

�W � A � B erfxL

2�DeW

�t

(17)

Applying the boundary conditions to the gen-eral solution eq. (17), the following equations areobtained:

At the outside extreme (x � 0)

�W � A � �W0 (18)

At the reaction front (x � xL)

0 � A � B erfxL

2�DeW

�t

(19)

B � ��W0

erfxL

2�DeW

�t

(20)

From eqs. (17), (18), and (20):

�W � �W0�1 � erfx

2�DeW

�t�erf

xL

2�DeW

�t� (21)

The length xL of the reaction front can be relatedwith the time t considering a constant :

�xL

2�DeW

�t

(22)

and

�xL

�t � �DeW

� 1/2

t��1/2� (23)

On the other hand, from eq. (21)

��W

�x �x�L

� �

�W0

2

�e� xL� 2�DeW

�t� 2�1�2�DeW

�t�

� erf�xL�2�DeW

�t�

(24)

��W

�x �x�L

� �

�W0

2

�e�2�1�2�DeW

�t�

erf (25)

The water flux density across the reactionfront, considering eq. (23), is described by theequation:

nW � � DeW

��W

�x �x�L

� ��W0�

�e2erf �DeW

� �1/2

t��1/2�

�1 � �

1 � b �PU

�xL

�t �1 � �

1 � b �PU �DeW

� �1/2

t��1/2� (26)

Considering g() � erf e2

in the aboveequation, the expression obtained is


g�� 1 � b1 � �

�W0

�PU� (27)

On the other hand,

nW�x�0 � � DeW

��W

�x �x�0

� �

DeW�W0

2

�e�0�1�2�DeW

�t�

erf �xL�2�DeW

�t�

��W0�

�erf��DeW

� �1/2

t�1/2 (28)

The equation that can be deduced with respectto the acetone is

nA�x�L � � dnW�x�L � � d��W0

g�� DeW

� �1/2

t��1/2� (29)

The equation deduced by applying a mass bal-ance to the reticulated polymer is

nW�x�L � nA�x�L � nW�x�0 � nA�x�0 � ��dxL

dt � 0 (30)

where � is the average density that can be con-sidered as not very different to �W0. So,

� nA�x�0 � ��W0

g�� DeW

� �1/2

t��1/2��1 � d�

��WA�

�erf��DeW

� �1/2

t�1/2 � ��W0�DeW

� �1/2

t��1/2�

� ��W0�DeW

� �1/2

t��1/2�� 1 � dg��

�1

�erf��

� C��W0�DeW

� �1/2

t��1/2� (31)

where, considering also eq. (27), the following ex-pression can be obtained:

C �1

�erf��

1 � dg��

�d � 1g��

�d � 11 � b

1 � �

�

�PU

�W0(32)

In the previous equation, it has been consideredthat for high values of d, as occurs in the reticu-lation process considered, the approximation car-ried out can be done (this was tested consideringdifferent values of b, d, densities of reticulatedpolymer, and porosity).

The amount of acetone extracted from t � 0,considering also eq. (32) is

Mt � 0

t

� � nA�x�0S dt � 2SC��W0�DeW

� �1/2

t1/2

� 2Sd � 11 � b �1 � ��PU�DeW

� �1/2

t1/2 (33)

Equation (33) can be simplified as follows: Theterm (1 � �)�PU represents the kg reticulatedpolyurethane per unit of total volume in the slabthat equals the product between the ratio (1� b)/d (reticulated polymer/acetone) and the ace-tone concentration (M�/Sh). So, introducing thisequality in eq. (33), it is deduced that

Mt � 2Sd � 11 � b

1 � bd

M�

Sh �DeW

� �1/2

t1/2

� 2d � 1

dM�

h �DeW

� �1/2

t1/2 (34)

and

Mt

M��

2h

d � 1d �DeW

� �1/2

t1/2 �2h �DeW

� �1/2

t1/2 (35)

In this system, the extraction of acetone kinet-ics follows Fick’s law so that Mt � k1t1/2, where k1is a constant which depends on several parame-ters: water diffusivity (DWA) in the system, poros-ity of the system �, tortuosity factor �, and theefficiency of the reticulating reaction. In the pre-vious equations, the parameter (DeW/�) equals(DAB/�), and consequently, it is possible that thevariation of Mt/M� versus t1/2 for samples with thesame value of h and with different initial acetonepercentages was similar. Figure 2 shows the evo-lution of the ratio Mt/M� versus t1/2 for the threesamples tested with different initial acetone con-centrations. The evolution of the rate, at smalltime values, is similar for the three systems to acritical time tc, in accordance with the reasonsexplained previously. The slopes obtained areshown in Table I.


The slopes k1 were calculated by using the dataobtained as follows: from t � 0 s to tc � 1.08 � 105

s for the system PU66/A34; from t � 0 s to tc� 8.64 � 104 s for the system PU57/A43; and fromt � 0 s to tc � 2.70 � 104 s for the system PU46/A54, in accordance with the limit of linearity ob-served.

From Table I and Figure 2, it can be observedthat the constants k1 are similar, around a meanvalue of 2.2 � 10�3 s�1/2.

Considering the reaction between the polyure-thane and the water, the estimated value of b isaround 40, so the values of (d � 1)/d are close tounity (between 0.95 and 0.98). The estimated val-ues for (DeW/�) that equals (DAB/�) is around 1.4� 10�10 m2/s, which is an acceptable value takinginto account that the acetone–water diffusion co-efficients17 are around 2–4 � 10�9 m2/s and thetortuosity factor is greater than 1 (it can begreater than 10, considering that the reticulationis not uniform and small channels connectingbags can be formed). Although values of the po-rosity are not necessary for the correlation of thedata, the estimated overall value of the porositywas 0.4. Nevertheless, it must be rememberedthat many simplifications were done and the cal-culation of the exact values of diffusion coeffi-cients would require many considerations, farfrom the objective of this work.

Kinetic Model in the Second Stage of the DiffusionProcess

The result of the polymer reticulation process bywater is a solid with great holes containing ace-tone and water through these holes. Acetone con-tinues diffusing to the water. DAW is the diffusiv-ity of acetone in the water retained in the holesthroughout the reticulated polymer and DeA is theeffective diffusivity, defined as

DeA �DAW

�� (36)

from the continuity equation and the Fick law,similar to eq. (7) but applied to the acetone, it canbe deduced that

��A

�t �DeA

�

�2�A

�x2 (37)

There is a profile of acetone concentration attime tc. At the inner part of the slab, the concen-tration of acetone is high, whereas at the layerjust next to the solution, it is practically nil. Inthis case, it can be considered that the acetoneprofile would be similar to that obtained in asystem with the same uniform initial concentra-tion as the real one, but from a theoretical time t*hinstead the critical time tc at the end of the firststage. So, relating the empirical date of total massof acetone Mtc at the time tc after the first stage(equivalent to the theoretical t*h), where a concen-tration profile is assumed, and considering thatonly the first term of the series is important, itcan be deduced that

M� � Mtc

M��

82 �

n�0

� 1�2n � 1�2

� exp� � �2n � 1�2

DeA

�2t*h

4h2 � �82

� exp� �

DeA

�2t*h

4h2 � (38)

where h is the thickness of reticulated polymer,Mtc is the theoretical mass of acetone extracted att*h, and M� is the total amount of free acetone.

The concentration profiles during the diffusionprocess in the second stage are shown, in sche-matic form, in Figure 4. During this stage, thesystem is made up of two phases: one of reticu-lated polymer with acetone and water throughtheir holes and the other aqueous phase of waterplus dissolved acetone.

The concentration of acetone in water, whichoccupies the holes between the reticulated poly-mer, is higher than the concentration of acetonein water, which is on the surface. The acetonediffuses through the holes to the aqueous phaseuntil the concentrations are equal.

On the other hand, at time t* t*h, it occursthat

Table I Slope and Lineal CorrelationParameter Values Obtained by Lineal Mt/M�

� k1t1/2 Correlation of the Experimental Datesat Short Periods of Time (until t � tc)

Sample k1 � 103 (s�1/2) r2

PU66/A34 2.25 0.995PU57/A43 2.16 0.994PU46/A54 2.20 0.998


M� � Mt

M��

82 exp� �

DeA

�2t*

4h2 � (39)

Dividing both equations,

M� � Mt

M� � Mtc

� exp�DeA

�2�t* � t*h�

4h2 �� exp�

DeA

�2�t � tc�

4h2 � (40)

in the previous equation, it was considered thatthe increment t* � t*h in the second stage equals t� tc logically. Equation (40) can be written as

ln�M� � Mt� � ln�M� � Mtc� �

DeA

�2tc

4h2 �

DeA

�2t

4h2

� ln�M� � Mtc� � k2tc � k2t (41)

The values of ln(M� � Mt) calculated from theexperimental dates are shown versus time in Fig-ure 5. The representation is lineal at higher timevalues. Also, the curves ln(M� � k1t1/2) versus tare shown, where k1 is the kinetic constant ob-tained for the kinetic study in the first stage. Thevalues of the slopes and intersections with thex-axis are shown in Table II, with the values of tcobtained from the intersection of the correspond-ing lineal correlations and the curve correlations.The tc value is different for each one of the runs,although it is around 1–1.2 � 105 s. This fact

Figure 4 Concentration profiles during the diffusion process in the second stage.

Figure 5 Relationship ln(M� � Mt) versus t for PU66/A34, PU57/A43, and PU46/A54samples.


confirms that the lineal correlation of the experi-mental data in the first stage is accepted for thedifferent ranges of time for each system.

As the lineal relation is performed from differ-ent times tc in each run, the ln(M� � Mt) � ln(M�

� Mtc) � k2t lineal correlations were obtained by

using values from t � 10.44 � 102 s to t � 34.56� 102 s for the PU66/A34 system, values from t� 17.28 � 102 s to t � 34.56 � 102 s for thePU57/A43 system and values from t � 17.28� 102 s to t � 34.56 � 102 s for the PU46/A54system.

Note also that the values of k2 are similar forthe three runs, because the ratio DeA/� is thediffusivity divided by the tortuosity factor thatcan be approximately constant and h is the thick-ness that has approximately the same value forthe three runs. Considering that the thickness is0.01 m, the estimated values of DeA/� that equalsDAB/� are around 1.8 � 10�10 m2/s, which areclose to the corresponding values obtained in thefirst stage (1.4 � 10�10 m2/s). The differencesbetween the values of DAB/� can be due to thedifferent range of concentration, the simplifica-tions assumed in each stage, and perhaps also tothe change of the tortuosity that can be differentwhen the polymer is reticulating than after aperiod of time.

Extrapolation to Other Conditions

In view of the assumptions considered previously,it would be possible to deduce the extraction pro-cess of a waste with different thickness and sim-ilar concentration to those shown in this article(30–70% acetone) when the concentration of ace-tone in the aqueous phase is low and the externaldiffusion is fast, as follows:

In the first stage, the kinetic constant k1 isdirectly proportional to the surface S and does notdepend on the thickness, as indicated by eq. (35),but as the value of M� is directly proportional tothe product of the surface and the thickness, itcan be written that

M1

M�� k1

0.01h�m�

t1/2 (42)

where k1 is around 2.25 � 10�3 s1/2.The critical time tc (at the end of the first stage)

is directly proportional to the square of the thick-ness h, in accordance with eq. (22), so it can bededuced that

tc�s� � 1.1 � 10�5h�m�2

�0.01�2 (43)

the mass Mtcat the critical time tc can be calcu-

lated by using eq. (42) with the value of tc calcu-lated from eq. (45).

For the second stage, the following expressioncan be used:

M� � Mt

M� � Mtc

� exp� �k2�0.01�2�t � tc�

h�m�2 � (44)

where k2 equals 4.4 � 10�6 s�1.If the surface S is not constant and/or the ge-

ometry of the waste is not a slab and/or there is aconsiderable increase of acetone in the extracts,the numerical integration using the basic param-eters cited in this article should be used for ob-taining the solution.

CONCLUSION

The main contaminant in the extracts of solvent-based adhesive wastes is the organic mater, ana-lyzed by the parameter T.O.C., due to the solventextraction. The main comments on the process ofleaching of the systems made up of acetone andpolyurethane are as follows: The acetone is prac-tically completely extracted by the water. Duringthe leaching process, the water (polar) passesthrough the polyurethane chains reacting, at thesame time, with the isocyanate groups at the ends

Table II Slope, Intersections with x-Axis and Lineal Correlation Parameter Obtained by LinealCorrelation of the Experimental Data at High Time Values and tc Estimated Value by Intersection ofthe Corresponding Lines Plotted in Figure 5

Sample r2Slope k2 � DeA2/�4h2

(s�1) � 106Axe Intersection

ln(M� � Mtc) � k2th tc � 10�5 (s)

PU66/A34 0.999 4.39 �1.76 1.17PU57/A43 0.998 4.41 �2.34 1.20PU46/A54 0.993 4.41 �2.69 1.00


of the chains producing the reticulation orcrosslinking of the polymer chains.

The experimental leaching data can be satis-factorily correlated by a diffusion model consider-ing two stages:

1. During the first stage, the water penetratesinto the system producing the reticulation ofthe polymer chains and mixing with the ac-etone. The acetone extraction kinetics canbe represented by a equation where the ex-tracted acetone mass is directly propor-tional to the square of the time.

2. During the second stage, the acetone dif-fuses through the water, which is occupyingthe holes between the reticulated polymer.The diffusion kinetics are similar to the dif-fusion in a rigid porous solid, but using aneffective diffusivity of the acetone throughthe retained water in the holes.

In any case, the diffusion rate is directly pro-portioned to the surface exposed to the extractionsolution.

The authors are grateful for the financial support of theConsellerıa de Medio Ambiente of the Generalitat Va-lenciana (Spain).

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The leaching kinetics of acetone in an acetone-polyurethane adhesive waste