ARTICLE pubs.acs.org/IECR
Kinetics of Dry Neutralization of Dodecyl-Benzenesulfonic Acid with Respect to Detergent Granulation Marek Sch€ongut, Zdenek Grof, and Frantisek Stepanek* Department of Chemical Engineering, Institute of Chemical Technology, Prague, Technicka 5, 166 28 Prague 6, Czech Republic ABSTRACT: Sodium dodecyl-benzenesulfonate, a common anionic surfactant used in powder detergents, is a product of the socalled “dry neutralization” reaction between dodecyl-benzenesulfonic acid and sodium carbonate. The acid acts not only as a reactant but also as a binder in a granulation process; the carbonate particle wetting by the acid droplets and the neutralization reaction occur simultaneously. In this work the reaction and wetting kinetics have been investigated by a macroscopic method of observing the behavior of an acid drop on a substrate pellet made from sodium carbonate. Wetting kinetics at three temperatures (20, 40, and 60 °C) were measured and expressed as a relationship between the three-phase contact line velocity and the instantaneous contact angle. The reaction rates were evaluated from the volume of CO2 gas evolved during the reaction. The kinetic parameters (temperature-dependent reaction rate constant and apparent diffusion coefficients) have been evaluated using a numerical model of coupled reaction and diffusion processes in the passivation layer. The results indicate that because of diffusion limitations the neutralization reaction takes place predominantly in the “wet” product layer rather than at the solidliquid interface.
1. INTRODUCTION Sodium dodecyl-benzenesulfonate is a common anionic surfactant, used in a wide range of detergents such as laundry washing powders, dishwasher tablets, and other household or industrial detergents.13 It is produced by the neutralization of dodecylbenzenesulfonic acid, which is often supplied as a mixture of C10C13 isomers and therefore denoted as HLAS in the literature, where LAS stands for Linear Alkylbenzene Sulfonate (NaLAS then denotes its sodium salt). NaLAS has earned its popularity through good washing efficiency, favorable cost/performance ratio, and environmental friendliness.4 If the base used for HLAS neutralization is in the solid phase (in this case sodium carbonate) the reaction is called “dry neutralization” and its stoichiometric equation can be written as 2HLAS þ Na2 CO3 f 2NaLAS þ H2 O þ CO2
ð1Þ
Fully neutralized NaLAS is a hygroscopic5 soft-solid material which can form various mesophases (e.g., liquid crystals of lamellar type) at room temperature.6 The phase behavior is illustrated in Figure 1. Industrially, dry neutralization typically occurs in a reactive granulator where HLAS is contacted with sodium carbonate powder (and possibly other formulation components) under intense mixing, and granules are formed.710 In a typical granulator the acid is fed to the mixer and sprayed onto a fluidized or mechanically agitated powder bed. With ongoing neutralization, a layer of reaction products grows on the surface of unreacted sodium carbonate particles and forms bridges strong enough to bind the particles together in larger agglomerates.11 The final granule properties such as size distribution and porosity, as well as the overall degree of neutralization are determined by the elementary process of binder spreading on the primary particles (wetting) and binder solidification due to a chemical reaction.12 It has been shown both computationally13 and experimentally1416 that the relative rates of these elementary processes jointly determine granule attributes such as porosity and subsequently influence their end-use behavior such as dissolution rate.1719 A challenge r 2011 American Chemical Society
is to correlate the properties of the final product with changes in process conditions and feed material properties.20 What makes this particular process complex to describe is the fact that agglomeration and an exothermic chemical reaction occur simultaneously. Properties of the liquid bridges (e.g., viscosity) are changing continuously with time and the process of wetting is directly dependent on a chemical reaction between the binder and carbonate particles. At the same time, the reaction rate depends on the liquidsolid contact area. An accurate analysis of microscale wetting11,14,21 and reaction-diffusion processes is therefore crucial for understanding and rational design of reactive granulation. Wettability does influence not only the degree and rate of binder spreading over particles but also the shape and strength of liquid bridges.2224 Wetting kinetics can be evaluated from an observation of a contact angle between the solid substrate and the liquid during wetting and the velocity of the three-phase contact line.25,26 For a constant volume and homogeneous substrates, analytical expressions such as the Tanner’s law can be used for describing the wetting kinetics.27 Spreading accompanied by a phase change or a chemical reaction in the liquid phase is more difficult to describe and often requires a numerical solution.28 Experimentally determined dependence between the threephase contact line velocity and the instantaneous contact angle is then necessary for model validation or parameter estimation. Beyond detergent granulation, the investigation of the kinetics of reactive wetting and noncatalytic solidliquid interfacial reactions is significant also in other diverse application areas29 such as the fabrication of microfluidic devices, the dissolution of pharmaceutical tablets,30 or the acid stimulation of porous carbonate reservoirs for permeability enhancement.31 The aim of the present study is to quantify the reactive wetting kinetics of HLAS acid on a sodium carbonate substrate as a Received: May 16, 2011 Accepted: September 7, 2011 Revised: September 4, 2011 Published: September 07, 2011 11576
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Figure 1. Layer of a liquid-crystalline phase of NaLAS/H2O present between HLAS (dark bottom layer) and a Na2CO3/H2O solution (top clear layer).
Figure 2. Scheme of an acid drop spreading over a substrate pellet.
function of temperature, and simultaneously to evaluate the kinetics of the dry neutralization reaction. By means of a numerical model of coupled reaction and diffusion, the ratelimiting step of the neutralization reaction will be determined and the relevant parameters (temperature-dependent rate constants and apparent diffusion coefficients) evaluated.
Figure 3. SEM image of the surface of a freshly prepared Na2CO3 pellet.
2. METHODOLOGY 2.1. Experimental Section. To quantify the rates of elementary processes that take place during reactive wetting, it is necessary to decouple them from other phenomena that may occur during reactive granulation such as particle agglomeration and surface renewal due to granule breakage. To investigate wetting kinetics, the three-phase contact line velocity and the instantaneous contact angle must be observable, and to quantify the rate of a heterogeneous chemical reaction, the solidliquid contact area and the extent of reaction must be measurable. Conditions prevailing in a mechanically agitated powder bed do not facilitate such direct observation, therefore the following approach has been taken. A small drop of HLAS (purchased from Acros Organics, mixture of C10C13 isomers) with a volume of approximately 4 μL was placed on a substrate pellet (Figure 2) which has been prepared from anhydrous sodium carbonate fine powder (purchased from Lach-ner, mean particle size 14 μm) and compacted on a Carver pellet press at 7000 psi resulting in an essentially nonporous tablet with a microscopically smooth surface. A SEM image of a freshly prepared unreacted tablet can be seen in Figure 3. The absence of surface roughness or porosity is important to allow the
Figure 4. Experimental setup: (a) light source, (b) heater, (c) digital camera, (d) heated cell.
calculation of solidliquid contact area from the measured base diameter of the spreading droplet. Prior to their use, tablets were kept in a desiccator to avoid absorption of atmospheric moisture. During an experiment the tablet was placed into an insulated measurement cell with controlled temperature (Figure 4), and the acid was dropped using a standard medical syringe equipped with a needle of 0.8 mm internal diameter. Both the tablet and the syringe were kept in the measurement cell for a sufficiently long time to allow their temperatures to equilibrate. Although the neutralization reaction 11577
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is exothermic, the thermal mass of the tablet and the unreacted volume of the droplet is large compared to the evolved heat, and the system can be regarded as isothermal. This assumption was confirmed by monitoring the tablet surface temperature near the three-phase contact line by an infrared thermometer throughout several experiments. The distance between the needle tip and the pellet surface was 15 mm, which is small enough to neglect the effect of gravity on the droplet deposition and its spreading on the substrate, leaving only capillary forces to be taken into account (low Weber number deposition). With these conditions, a spherical cap approximation can be used for the droplet shape fitting during wetting. The spreading experiment itself takes approximately 30 s, which was found to be long enough for the contact line between the drop and the pellet to arrest (contact line pinning). In the course of spreading, droplet images were recorded using a Canon EOS 40D camera with Sigma EX 105 mm macro-lens, at a frequency of approximately 6 frames per second. The images were subsequently cropped and adjusted in the image processing software ImageJ and merged into a single file suitable for further image analysis. The droplet shape was evaluated by the Sessile Drop Fit method (SDF) using the Drop Shape Analysis software from Kruss, Inc. The desired parameters, namely, drop base diameter, drop height, drop volume, and contact angle, were thus obtained for each point in time. The velocity of the three-phase contact line was then calculated from the time change of the droplet base diameter. The relationship between the contact line velocity and the dynamic contact angle was used for the description of wetting kinetics. Reaction kinetics and passivation layer growth were calculated from the volume of evolved CO2 (increase in the overall droplet volume with time). During the reaction rate estimation, the following simplifying assumptions were used: (i) ideal gas equation of state, (ii) the volume of CO2 evolved equals the increase in the drop volume (i.e., negligible contribution of dissolved CO2), (iii) all evolved CO2 forms bubbles with atmospheric pressure that do not leave the droplet interior, (iv) the net volume change attributable to the consumption of acid and formation of the passivation layer is negligible. Under these assumptions, the reaction kinetics can be estimated from the measured change in droplet volume. The extent of reaction (eq 1) obtained by experiment ξexp is therefore dξexp dnCO2 p dV p V ðti Þ V ðti1 Þ z ¼ ¼ RT dt RT ti ti1 dt dt
ð2Þ
where ti1 and ti are two subsequent points in time, V is the measured droplet volume, p is atmospheric pressure, T is temperature, and R is the molar gas constant. The assumption that no CO2 gas bubbles leave the droplet for the duration of the experiment was found to be valid for all three temperatures reported in this work (20, 40, and 60 °C). When the experiment was attempted at 80 °C, the viscosity of HLAS acid became too low and the partial pressure of CO2 too high to prevent the bubbles from escaping the droplet, meaning that drop shape analysis could no longer be used as a method for measuring the reaction rate. 2.2. Mathematical Model. A pseudo-steady state model describing the growth of a product (passivation) layer has been formulated. The layer is composed of the neutralization reaction
Figure 5. Model of the passivation layer with concentration profiles and boundary conditions.
products NaLAS (further denoted C) and H2O (denoted D) separating the pure reactants, HLAS acid (denoted A) and the solid base Na2CO3 (further denoted B), cf. Figure 2. In line with the macroscopic observation (Figure 1), the passivation layer consisting of the NaLAS-H2O liquid crystals is assumed to be separated from the unreacted HLAS acid by a sharp interface that is not affected by diffusion of the time course of the experiment. As the passivation layer is just a small fraction of the whole droplet, no CO2 presence is assumed within the passivation layer in the form of bubbles. This assumption is based on the fact that compared with the highly viscous liquid crystalline phase of the NaLAS-H2O product layer, a more favorable environment for bubble nucleation at a given CO2 supersaturation is the lower-viscosity bulk HLAS droplet above the passivation layer. Upon the initial contact of the acid and the carbonate surface, an interfacial reaction can be expected, but as soon as some reaction products form, the location of the reaction front is a priori unknown. For further reaction to occur, either HLAS or dissolved Na2CO3 (or both) must diffuse into the product layer where the neutralization reaction can take place. Interfacial reaction at either end of the product layer would occur in the limiting case of a very fast diffusion of one reactant across the layer or a very low solubility of the other reactant in the layer. Otherwise, the neutralization reaction must occur in the volume of the product layer, with both reactants (HLAS and dissolved sodium carbonate) diffusing against each other, cf. Figure 5. Assuming that the density of the product layer is constant and using the additivity of molar volumes for NaLAS and water components, the following equation can be written for the layer growth rate: ! dL 3 2 MC 1 MD dξ ¼ ð3Þ þ dt A 3 FC 3 FD dt where L is the layer thickness, ξ is the extent of reaction, MC, MD, FC, and FD are molar weights and densities of NaLAS and water, respectively. The contact area A = πr2 is assumed constant as L is small compared to the droplet height and base radius r. Note that the volumetric effect of diffusing reactants is neglected in eq 3. The overall neutralization rate is obtained by integration over the product layer and adding the contribution of possible interfacial 11578
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reactions at the boundaries Z L dξ R ¼A kCA ðxÞ CB ðxÞ dx þ AðRs, A þ Rs, B Þ dt 0
Table 1. List of Model Parameter Values Used model parameter
ð4Þ Here k is the reaction rate constant, CA and CB are HLAS and Na2CO3 concentrations in the product layer, and Rs,i represent rates of reactions taking place at each boundary. At this point, let us neglect both surface terms and assume that the neutralization reaction takes place only in the bulk of the product layer. This approximation may seem to be a crude one; however, it is actually justified as will be explained later in the Results section. The reaction-diffusion equations representing the mass balance of HLAS and Na2CO3 need to be solved to obtain their concentration profiles in the product layer (Figure 5). If the characteristic time of the layer growth is sufficiently long compared to the characteristic time of concentration profile evolution within the layer, then the pseudo-steady state assumption can be used, and the mass balance equations reduce to a boundary value problem for the following two ODEs: 0 ¼ Di
d2 C i jνi jkCA CB dx2
i ∈ fA, Bg
ð5Þ
where DA and DB are diffusion coefficients of HLAS and Na2CO3, respectively, in the product (NaLAS/water mixture) and νi is the stoichiometric coefficient. The boundary conditions are CB ðx ¼ 0Þ ¼ 0
ð6Þ
¼ 0 CB ðx ¼ LÞ ¼ CB0 ,
ð7Þ
CA ðx ¼ 0Þ ¼ CA0
HLAS side :
Na2 CO3 side :
dCA dx
x¼L
where CA0 = FA/MA and CB0 is the concentration of saturated Na2CO3 solution in the product mixture. The zero-flux boundary condition at x = L (Na2CO3 side) follows from the condition of no diffusion into the solid phase, and the boundary condition at (x = 0) is a definition of the interface between unreacted acid and the product layer (i.e., all dissolved carbonate is consumed and its concentration therefore drops to zero). 2.2.1. Mathematical Model in Dimensionless Form. Let us ^B = ^ A = CA/CA0 and C define dimensionless concentrations C CB/CB0, and a dimensionless length ^x = x/L. Equation 5 then becomes 0¼
^i d2 C ^A C ^B Da2i ðLÞC d^x2
i ∈ fA, Bg
ð8Þ
with boundary conditions ^ A ð^x ¼ 0Þ ¼ 1 C
HLAS side :
Na2 CO3 side :
^ A dC d^x
¼0
^ B ð^x ¼ 0Þ ¼ 0 C ^ B ð^x ¼ 1Þ ¼ 1 C
ð9Þ ð10Þ
^x ¼ 1
and two Damk€ohler numbers, which are ratios between the reaction and the diffusion rates, respectively, Da2A ðLÞ ¼
jνA jkCB0 L2 DA
Da2B ðLÞ ¼
jνB jkCA0 L2 DB
ð11Þ
symbol
value
HLAS (component A) stoichiometric coefficient
νA
2
molecular weight
MA
326.49 g mol1
density
FA
1200 kg m3
diffusivity ratio
DA/DB
0.53
Na2CO3 (component B) stoichiometric coefficient
νB
1
molecular weight
MB
105.99 g mol1
density saturated concentration
FB cB0
2540 kg m3 2076 mol m3
NaLAS (component C) molecular weight
MC
348.48 g mol1
density
FC
≈ 1000 kg m3
H2O (component D) molecular weight
MD
18.02 g mol1
density
FD
1000 kg m3
The overall neutralization reaction rate, eq 4, written in terms of the dimensionless concentrations becomes Z 1 ^ B ð^xÞ d^x ^ A ð^xÞ C ð12Þ C R ¼ ALkCA0 CB0 0
The model is completed by substituting R into eq 3 to obtain Z 1 dL 3kCA0 CB0 ^ B ð^xÞ d^x ^ A ð^xÞ C ¼ L ð13Þ C dt CCD 0 In the last equation, the constant CCD is the molar density of the NaLAS/water mixture 1 2 MC 1 MD ¼ þ CCD 3 FC 3 FD
ð14Þ
2.2.2. Estimation of Model Parameters from Experimental Data. The model in dimensionless form has three independent parameters: Da2A/L2, Da2B/L2, and 3kCA0CB0/CCD. As the saturation concentrations of all components can be estimated relatively easily (cf. Table 1), the unknowns left to be found by fitting experimental data are k, DA and DB. To further reduce the number of unknowns, the ratio between the diffusion coefficients DA/DB was assumed constant and equal to 0.53. This ratio is based on a scaling expressed by the StokesEinstein equation DA MB FA ð1=3Þ ≈ ð15Þ DB MA FB The growth of the passivation layer is obtained by integrating eq 13. The boundary value problem (eq 8) has to be solved to obtain the concentration profiles required for the evaluation of the integral reaction rate from eq 13. The value of the integral in eq 13 depends on Da2A and Da2B and therefore changes with growing layer thickness L. The passivation layer thickness as function of time was evaluated from experimental data using the combination of eq 2 and eq 3. The actual values of the two unknown parameters (rate constant k and diffusion coefficient DA) 11579
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Figure 6. Example of droplet shape evolution during reactive wetting at 20 °C. Note that the CO2 bubbles remain trapped within the droplet.
Figure 7. Change of base diameter and instantaneous contact angle evaluated from a wetting experiment at 20 °C.
were then found by minimization of the sum of squared errors between experimental and modeled data for a period of 30 s from the moment when an increase of the droplet was detected. The time interval of 30 s was chosen so as to provide a sufficiently long time series for statistically robust evaluation of the adjustable parameters.
3. RESULTS AND DISCUSSION The evolution of droplet shape in the course of one experiment is shown in Figure 6. Note the gradual emergence of CO2 bubbles in the droplet volume. The droplet base radius, droplet height and the instantaneous contact angle were evaluated at each point in time. The dependence of the contact line velocity and dynamic contact angle on time (Figure 7) was used for the wetting kinetics characterization, while the time dependence of drop volume (Figure 8), which was calculated from the base radius and droplet height based on the spherical cap approximation,21 was used for the evaluation of reaction kinetics. Experiments were carried out at 20, 40, and 60 °C, and at least five repeats were done at each temperature (depending on the statistical spread of the data).
Figure 8. Change of drop volume with time evaluated from a wetting experiment at 20 °C.
3.1. Wetting Kinetics. The wetting phase starts with the drop touching the substrate and ends with the contact line arrest. While the chemical reaction (thus the associated drop volume increase) continues beyond this point, the three-phase contact line pinning occurs after a relatively short time presumably because of the layer of a semisolid liquid crystalline phase that forms as a reaction product. The contact line velocity was calculated as the time derivative of the drop base radius using the finite difference formula
U ¼
dr rðti Þ rðti1 Þ z dt ti ti1
ð16Þ
where U is the contact line velocity, r is the droplet radius, and t is time. The wetting kinetics equation is usually defined as a relationship between the contact line velocity and the instantaneous contact angle. For nonreactive wetting of an ideal surface this relationship is often found to be linear when the contact angle approaches its equilibrium value. Wetting of nonhomogeneous substrates or wetting coupled with other phenomena (heat transfer, reactive wetting, etc.) can generally follow more complex relationships; however, the system considered in this work was also found to satisfy a linear relationship UðθÞ ¼ αðθ θ0 Þ 11580
ð17Þ
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where α is the spreading rate prefactor and θ0 is the value of contact angle at contact line arrest. Note that θ0 cannot be called “equilibrium” contact angle as equilibrium in the thermodynamic sense is not yet reached because of the ongoing chemical reaction. The two unknown parameters, α and θ0, were found by linear regression of experimental data obtained from the droplet shape evolution at each temperature. Figure 9 shows an example of one such experiment at 20 °C. The mean values and standard deviations of the regression parameters α and θ0 based on at least five repeats of each measurement at 20, 40, and 60 °C are given in Table 2. The times of contact line arrest were 16.3 ( 3.0 s, 10.8 ( 4.2 s, and 5.4 ( 1.1 s for 20, 40, and 60 °C, respectively. The data show that increasing temperature leads to a faster spreading over the substrate, which can be explained by the fact that the viscosity of the acid decreases with increasing temperature. The asymptotic contact angle drops significantly when temperature is increased from 20 to 40 °C but then remains more-or-less constant, considering the experimental error. This is consistent with the fact that the wettability of most substrates generally increases with increasing temperature. The reason why the decrease of the contact angle does not continue (or may even be slightly reversed) beyond 40 °C in this case can be attributed to the chemical reaction. The evolving CO2 gas leads to an increase in the droplet volume, which manifests itself as an increase in the apparent contact angle when the contact line is pinned. This process competes with the decrease of contact angle which would occur if there were no reaction. The observed value of θ0 is the result of a combination of these two competing processes, and therefore a faster reaction at higher temperatures may prevent the contact angle from reaching a lower value. 3.2. Reaction Kinetics. Experimental values of the passivation layer growth at different temperatures, calculated from the droplet volume using eqs 2 and 3 are summarized in Figure 10. The time is taken as a relative time from the moment when the droplet volume started to increase (induction time). This time
Figure 9. Estimation of wetting kinetics parameters for experimental data measured at 20 °C.
was 5.0 s, 3.5 s, and 0.2 s for 20, 40, and 60 °C, respectively. Each experimental data series was used for finding the rate constant k and diffusion coefficient DA according to the procedure described in Sec. 2.2.2 above. An example of fitting the experimental data (in this case at 60 °C) by the numerical model is shown in Figure 11. A summary of the mean values of the kinetic parameters and their standard deviations at each temperature is provided in Table 2. From these experimental data it is clear that the reaction rate constant k increases with increasing temperature, and as Figure 12 shows, this increase is in line with the Arrhenius law. On the other hand, the estimated diffusion coefficient DA does
Figure 10. Experimental data on passivation layer growth at different temperatures. The time is relative from the on-set of reaction at each temperature.
Figure 11. Experimental data at 60 °C fitted by the numerical model. The time is relative from the on-set of reaction.
Table 2. Wetting and Reaction Kinetics Parameters Evaluated from Experiments T/°C
α/(mm s1 deg1)
θ0/deg
k/(m3 mol1 s1)
DA/(m2 s1)
20
(2.83 ( 0.41) 102
67.4 ( 5.4
(6.05 ( 1.13) 105
(1.88 ( 0.74) 1014
40.2 ( 5.5
(4.73 ( 3.47) 10
4
(3.04 ( 0.83) 1014
(1.78 ( 0.41) 10
3
(1.48 ( 0.37) 1014
40 60
(3.31 ( 0.70) 10
2
(4.42 ( 0.95) 10
2
48.8 ( 5.7 11581
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Figure 12. Dependence of the reaction rate constant on temperature (Arrhenius plot).
not appear to follow any obvious pattern as temperature changes. Although diffusion coefficient on its own should slightly increase with temperature, the phase behavior of the passivation layer made from sodium salt liquid crystals is more complex, and it can act to either enhance or suppress any underlying trends in diffusion coefficients at various temperature intervals. In any case, it can be concluded that compared to the exponential rise of the rate constant with temperature, the diffusion coefficients remain essentially unchanged. This in turn means that with increasing temperature, diffusion limitations can be expected to play a more significant role in the overall progress of the reaction, as will be analyzed in more detail in the following section. From the granulation point of view, diffusion limitations may result in an incomplete neutralization of the original HLAS acid, which is undesirable. Conversion can be improved by providing a stoichiometric excess of carbonate, by intense mechanical agitation for surface renewal, by reducing the HLAS droplet size, or by other methods that enhance its spreading (e.g., viscosity reduction). 3.3. Parametric Analysis of the Model. To gain a deeper understanding of the rate-limiting step under different conditions and also to verify that the initial model assumptions are consistent with the experimentally observed behavior, let us discuss the HLAS and Na2CO3 concentration profiles in the product layer for a range of Da numbers as shown in Figure 13a. Two limiting cases can be identified: (i) reaction-limited regime for low Da numbers and (ii) diffusion-limited regime for high Da numbers. The neutralization rate depends on the product of both acid and base concentrations in the layer, as shown in Figure 13b. In the reaction-limited regime (i.e., fast diffusion and/or slow reaction), the reaction takes place throughout the layer as both species can diffuse at a sufficient rate. However when the Damk€ohler number is increased toward the diffusion-limited regime, the reaction becomes localized in a narrower section within the layer where both diffusing species meet and react instantaneously (large Da means fast reaction compared to diffusion). The exact position of the reaction peak depends on the ratio Da2A/Da2B. The value of Da2A at which the neutralization reaction becomes hindered by mass transport limitations can be identified by plotting the dependence of the integral appearing in eq 13 on the Damk€ohler number, as shown in Figure 14. The dependence reveals a typical sigmoidal shape, which can be divided into three regions:
Figure 13. Solutions of eq 8 for Da2A/Da2B = 2.71 and parametrized by Da2A = 10a, where a was varied in the range with stepsize 0.5. Data corresponding to Da2A = 1 are highlighted as a dashed line. (a) Concentration profile of HLAS (red color) and Na2CO3 (blue color). (b) Profiles of the local neutralization rate.
R ^ AC ^ B dx on Da2A. Points Figure 14. Dependence of the integral I = 10C denoted by circles on the line correspond to individual profiles shown in Figure 13.
kinetically limited regime (Da2A < 0.1), transition regime (0.1 < Da2A < 10), and diffusion-limited regime (Da2A > 10). Let us recall that on deriving the model, terms accounting for the contribution of possible surface reactions in eq 4 were neglected. As is evident 11582
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Figure 15. Dependence of Da2A on the layer thickness L calculated using values of k and DA obtained from the experimental data. Horizontal lines mark the diffusion-limited (top), transition (middle) and reactionlimited (bottom) regimes.
from Figure 13, in the reaction-limited regime (limit of low Da number) both reactants are still present at opposite borders of the passivation layer, suggesting that surface reactions could in principle take place. On the other hand, as soon as the passivation layer thickness, L, increases above approximately 0.1 μm and the system enters the transition regime, the concentration of each reactant at the interface with the bulk of the other reactant significantly decreases. Finally, in the diffusion-limited regime the interfacial reactions can be ruled out as each reactant is consumed within the passivation layer well before it can reach the opposite end, which is also manifested by the localized peak of reaction rate (cf. Figure 13). In this case the passivation layer effectively separates both reactants, and the surface reaction terms Rs,i therefore become insignificant. From this analysis it can be concluded that the present model would probably underestimate the reaction rate at the very early stages when the passivation layer thickness is small (low Da number) and interfacial reactions may be present, but should describes the reaction rate accurately at later stages after the product layer is sufficiently thick for diffusion to be the rate-limiting step. To assess whether the use of this model was indeed justified in our case, the dependence of Da2A on the layer thickness L was calculated using k and DA parameters found by fitting experimental data, and it is shown in Figure 15. The horizontal lines in Figure 15 delimit the reaction- and diffusion-limited regimes together with a transition regime between them. Comparing the values of L with those seen in Figure 10 it can be concluded that the majority of the experimental data points indeed lie in the transition or the diffusion-limited regions where the model is valid.
4. CONCLUSIONS From the experiments it appears that the kinetics of reactive wetting of sodium carbonate by HLAS has two phases. The first phase is associated with rapid spreading, meaning a fast decrease of the drop height and contact angle, and an increase of the drop base diameter until an asymptotic value is reached at which the three-phase contact line is pinned. The wetting kinetics was found to follow a linear relationship between the contact line velocity and the instantaneous contact angle. The spreading rate systematically increased with increasing temperature. During the second (reaction) phase, which overlaps with the wetting phase to some extent, the drop volume increase becomes clearly visible because of carbon dioxide formation by the neutralization reaction.
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At 20 °C the onset of the reaction becomes visible after an induction time of about 5 s, while at 60 °C the onset of the reaction is practically immediate. A mathematical model taking into account the reaction and diffusion in the passivation layer was developed and used for the evaluation of kinetic parameters from experimental data. The obtained rate constant was found to follow the Arrhenius law, and the validity of the model assumptions was further confirmed by analyzing the concentration profiles and localization of the reaction front in the passivation layer. With the exception of the very early phases of the reaction, the reaction front was found to be contained within the product layer (a mixture of NaLAS salt and H2O, with dissolved HLAS acid and sodium carbonate base). Our results indicate that although the base that participates in the “dry” neutralization reaction initially starts as a solid, the reaction itself actually occurs as a homogeneous reaction within the “wet” product phase rather than as a heterogeneous reaction at the solidliquid interface. The reaction and wetting kinetics obtained by this work will be used as input parameters for a particle-level model of granule microstructure formation during reactive granulation.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work has been supported by the Czech Science Foundation (104/08/H055) and by the grant of the Specific University Research (MSMT no. 21/2011). F.S. would like to acknowledge support by the European Research Council (project no. 200580Chobotix). ’ REFERENCES (1) de Groot, W. H.; Adami, I.; Moretti, G. F. The Manufacture of Modern Detergent Powders; H. de Groot Academic Publisher: Wassenaar, The Netherlands, 1995. (2) Scheibel, J. J. The Evolution of Anionic Surfactant Technology to meet the Requirements of the Laundry Detergent Industry. J. Surfactants Deterg. 2004, 7, 319. (3) Yu, Y.; Jin, Z.; Bayly, A. E. Development of Surfactants and Builders in Detergent Formulations. Chin. J. Chem. Eng. 2008, 16, 517. (4) Mungray, A. K.; Kumar, P. Fate of Linear Alkylbenzene Sulfonates in the Environment: A Review. Int. Biodeterior. Biodegrad. 2009, 63, 981. (5) Cohen, L.; Soto, F.; Roberts, D. W.; Emery, D. Hygroscopicity of Linear Alkylbenzene Sulfonate Powders. Tenside, Surfactants, Deterg. 2003, 40, 1. (6) Ramaraji, S. M.; Carroll, B. J.; Chambers, J. G.; Tiddy, G. J. T. The Liquid Crystalline Phases formed by Linear-dodecylbenzene Sulphonic Acid during Neutralization with Sodium Carbonate. Colloids Surf., A 2006, 288, 77. (7) Appel, P. W. Modern Methods of Detergent Manufacture. J. Surf. Deterg. 2000, 3, 395. (8) Borchers, G. Design and Manufacturing of Solid Detergent Products. J. Surf. Deterg. 2005, 8, 123. (9) Smulders, E.; Rybinsky, W.; Sung, E.; R€ahse, W.; Steber, J.; Wiebel, F.; Nordskog, A. Laundry Detergents; Wiley: Weinheim, Germany, 2007. (10) Germana, S.; Simons, S. J. R.; Bonsall, J. Reactive Binders in Detergent Granulation: Understanding the Relationship between Binder Phase Changes and Granule Growth under different Conditions of relative humidity. IEC Res. 2008, 47, 6450. 11583
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