Ind. Eng. Chem. Res. 2000, 39, 161-167
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Adsorption in a Centrifugal Field: Basic Dye Adsorption by Activated Carbon Chia-Chang Lin and Hwai-Shen Liu* Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan, Republic of China
The adsorption of basic yellow dye on activated carbon from aqueous solutions under a centrifugal field was explored and interpreted by both a pseudo-first-order mechanism and intraparcticle diffusion mechanism. The adsorption process, based on the assumption of a pseudo-first-order mechanism, was developed to estimate the rate constant with the effect of centrifugal force, initial dye concentration. Also, the rate parameter based on the intraparticle diffusion model was presented. In addition, the diffusion coefficients were evaluated from both models. The results showed that the centrifugal force could enhance the rate constant, the rate parameter, and the diffusion coefficient. Therefore, better mass transfer could be provided with centrifugal force. Introduction During the past few years, one of the interesting developments in the area of separation processes is the application of the centrifugal field to gas-liquid systems such as distillation, absorption, and stripping. In 1981, Ramshaw and Mallinson1 first developed a rotating packed bed which replaced gravity with centrifugal force and named it “Higee” (for high gravity). As the centrifugal acceleration, tuned by rotation speed, can be much higher than the gravitational one, some advantages may be obtained. For example, the system can be operated in a higher gas-to-liquid flow rates ratio due to the lesser tendency for flooding. Moreover, the liquid film would become thinner and consequently mass transfer may be enhanced. As a result, the size of the processing system would be greatly reduced as compared to a conventional packed bed. That represents the lower capital and perhaps operating cost. Some literature has been published to present the results about the adoption of centrifugal field in the packed bed for gasliquid systems such as distillation, absorption, stripping, and deaeration.2-10 However, the application of a centrifugal field to a liquid-solid system such as adsorption is not well-known to date. Adsorption is a well-established separation technique to remove dilute pollutants as well as to recover valuable products from aqueous streams. In the conventional adsorption process, the particle size of the adsorbent is restricted because of hydrodynamic phenomena such as pressure drop. As a consequence, the conventional adsorption equipment is relatively voluminous in general. Application of the centrifugal force becomes attractive because small particles could be used because of their low-pressure drop in the rotating packed bed. This characteristic would possibly result in a high adsorption capacity and also reduction in equipment size. A system is set up to investigate the characteristics concerning the effect of centrifugal force on adsorption. Specifically, bed adsorption with a recycle system is adopted. That is, dilute dye solution is taken from a reservoir, fed to a fixed activated carbon bed under rotation, and then recycled back to the reservoir. This study focuses on obtaining the mechanism of basic dye adsorption on activated carbon under centrif* To whom correspondence should be addressed. Fax: +8862-2362-3040. E-mail:
[email protected].
ugal force. The factors studied include the influence of the centrifugal force, initial dye concentration, and particle size on the diffusion processes and the adsorption kinetics. A rate constant, k1, has been defined and used to describe the adsorption of basic dye on activated carbon in a centrifugal field. A method for determining the intraparticle diffusion rate parameter, kr, using dataplotting techniques has been developed. These two methods are discussed for the determination of the diffusion coefficients of basic dye adsorption by activated carbon based on the rate constant and the rate parameter. Experimental Section The main purpose of this experimental work is to evaluate if the centrifugal force could affect the efficiency of adsorption. The dyestuff, Basic Yellow 2 (supplied by Acros), is used throughout in this study. The batch tests to determine the adsorption isotherms of the yellow dye solution were performed first. The activated carbons used in this work were granular-type (8-20 mesh) and cylindrical-type (0.1-1-cm length; 0.4cm diameter) (supplied by HOTAI), respectively. The activated carbon was dried at 110 °C for more than 24 h. Then, adsorbent of a certain constant amount (0.05 and 0.1 g for granular; 0.1 g for cylindrical shapes) was added to 500-mL glass flasks, each filled with 250 mL of aqueous yellow dye solutions of varying concentrations (20-260 mg/L). All the flasks were shaken in a temperature-controlled bath at a constant speed for 2 days to allow adsorption equilibrium to take place. The equilibrium dye concentrations were measured by a spectrophotometer (SPECTRONIC 20 GENESYS) with a precalibrated curve. The adsorbed amounts of yellow dye were calculated by the difference between the residual dye concentration in the solution and the initial one. Figure 1 shows the simplified schematic diagram of the adsorption bed with recirculation. The centrifugal adsorption bed consists of a rotor and stationary housing. Liquid flows outward from the inner edge of the rotor because of the centrifugal force. For visual observation, the system is made of transparent acrylic. The activated carbon with known weight is packed randomly in the rotor. The axial height of the bed is 2 cm. The inner radius and the outer radius of the bed are 2 and 4 cm, respectively. As a result, the depth (radial height) of the bed is 2 cm. In this system, the bed can be operated from 400 to 2500 rpm, which provides 5-210
10.1021/ie9902333 CCC: $19.00 © 2000 American Chemical Society Published on Web 12/14/1999
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If the rate of adsorption follows a first-order mechanism,11 the pseudo-first-order adsorption kinetic rate equation is expressed as follows:
dqt ) k1(q∞ - qt) dt
Figure 1. Centrifugal adsorption bed with recirculation.
(1)
where qt (mg/g) is the amount of dye adsorbed at time t, q∞ (mg/g) is the amount of dye adsorbed at infinite time, and k1 (1/min) is the rate constant of pseudo-firstorder adsorption. Integrating eq 1 with the boundary conditions of t ) 0, qt ) 0 and t ) t, qt ) qt, gives
qt ) q∞(1 - e-k1t)
(2)
To obtain the rate constants, the nonlinear regression of the experimental data (qt vs t) for different operating conditions should be used. The estimated values of k1 and correlation coefficients r2 of yellow dye under different conditions are given in Table 1. Theoretical analysis of intraparticle diffusion yields rather complex mathematical relationships which depend on the geometry of the adsorbent particle.13 Considering the cylindrical particles with the assumption of a constant diffusion coefficient, the following equation for the total dye adsorbed is presented by Crank.13
q t ) q∞ Figure 2. Adsorption isotherm of basic yellow dye.
gravitational force on the basis of the arithmetic mean radius. In an adsorption bed test, an aqueous dye solution of the reservoir (liquid volume ) 2.5 L) was fed to the top of the equipment, and then it flowed through the activated carbon bed, exited from the bottom of the equipment, and recycled back to the reservoir. The average temperature for all tests was 31 °C. In operation, the liquid flowed over activated carbon as a film; therefore, the radial velocity component of the liquid within the rotor would depend on the rotation speed. In all tests, the dye concentration in the reservoir as a function of time was monitored by a spectrophotometer. Result and Discussion Equilibrium Isotherms. The adsorption isotherms of the yellow dye by granular and cylindrical activated carbons are shown in Figure 2. Fitted isotherms are shown in the figure with the corresponding parameters. The nonlinear regression of the experimental data is used to determine the model parameters. The adsorption isotherm model, namely, Freundlich model, is found to give a satisfactory fit to the experimental data for the granular type. The linear isotherm is observed for cylindrical type as presented in Figure 2. It is not surprising that the adsorption capacity of granular activated carbon (small particles) is much higher than that of cylindrical activated carbon. This could be attributed to a higher surface area of small particles. Adsorption Dynamics. To investigate the mechanism of adsorption, the rate constants and the intraparticle diffusion rate parameters were determined by the models of a pseudo-first-order process11 and an intraparticle diffusion process,12 respectively. These are described below.
[ ( ) 4 Dt π1/2 a2
1/2
( )
Dt 1 Dt - 1/2 2 2 a 3π a
-
3/2
]
+ ...
(3)
where a (cm) is the radius of the adsorbent particle and D (cm2/s) is the intraparticle diffusion coefficient. In the early stage of the adsorption process, an important relationship common to most analyses of intraparticle diffusion can be reduced from the above equation with the first term.
qt )
4q∞D1,app0.5 π0.5a
t0.5 ) krt0.5
(4)
where D1,app (cm2/s) is the apparent diffusion coefficient and kr (mg/(g min0.5)) is the so-called intraparticle diffusion rate parameter. The values of kr for various conditions determined from the slopes of the initial straight line portions of qt versus t0.5 are given in Table 1. From the above equation the relationship between the apparent diffusion coefficient, D1,app, and the intraparticle diffusion rate parameter, kr, is presented as follows:
D1,app )
πkr2a2 16q∞2
(5)
An alternative determination of the apparent diffusion coefficient, D2,app, is based on the half time of the adsorption process, as shown in the following equation:13
D2,app )
0.0491a2 t1/2
(6)
where t1/2 is the half time or the time corresponding to qt/q∞ ) 0.5. The t1/2 value can be obtained from eq 2 and thus the diffusion coefficient can be calculated as
D2,app )
0.0491a2k1 ln 2
(7)
Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 163 Table 1. Kinetic Parameters for the Adsorption of Basic Yellow Dye on Cylindrical Activated Carbon under Different Operating Conditions ω (rpm)
C0 (mg/L)
k1 × 102 (1/min)
q∞ (mg/g)
r2
kr (mg/(g min0.5))
r2
D1,app × 107 (cm2/s)
D2,app × 107 (cm2/s)
0 400 1000 1600 0 400 1000 1600 0 400 1000 1600 0 400 1000 1600
205 205 205 205 165 165 165 165 125 125 125 125 85 85 85 85
0.7910 0.7595 0.9135 1.1013 0.8785 0.8846 1.0052 1.2742 1.0200 1.0509 1.2250 1.4879 1.2280 1.4105 1.7005 2.1237
13.6880 13.2883 15.1790 16.2531 11.7489 11.7737 12.5446 13.1669 9.3571 9.3346 9.6682 9.6415 6.2297 6.4101 6.4705 6.4821
0.9929 0.9916 0.9943 0.9984 0.9928 0.9940 0.9951 0.9990 0.9956 0.9953 0.9973 0.9961 0.9940 0.9961 0.9978 0.9982
0.7159 0.6835 0.8523 1.0160 0.6475 0.6514 0.7450 0.8877 0.5594 0.5646 0.6376 0.7058 0.4133 0.4516 0.5072 0.5695
0.9981 0.9984 0.9977 0.9925 0.9979 0.9976 0.9972 0.9928 0.9968 0.9967 0.9950 0.9952 0.9968 0.9972 0.9953 0.9964
3.5807 3.4632 4.1270 5.1151 3.9758 4.0069 4.6168 5.9498 4.6785 4.7888 5.6930 7.0148 5.7615 6.4971 8.0431 10.1041
3.7354 3.5867 4.3139 5.2008 4.1486 4.1775 4.7470 6.0173 4.8169 4.9628 5.7850 7.0265 5.7991 6.6610 8.0305 10.0290
Figure 3. Pseudo-first-order kinetics of dye adsorption at various rotor speeds (cylindrical activated carbon: recirculation flow rate ) 1532 mL/min; initial dye concentration ) (a) 205 mg/L, (b) 165 mg/L, (c) 125 mg/L, and (d) 85 mg/L).
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Figure 4. Effect of centrifugal acceleration on the rate constants at various initial dye concentrations.
Figure 5. Effect of initial dye concentration on the rate constants at various rotor speeds.
The values of D1,app and D2,app for different conditions were determined and listed in Table 1. The data indicate that the difference between the diffusion coefficient by two methods is negligible for all the experimental conditions. This implies that if the adsorption kinetics follows the pseudo-first-order mechanism, the diffusion coefficient can be estimated only by eq 7 on the basis of the rate constant. Four series of experiments were taken to study the influence of the centrifugal force. Experimental results for the adsorption of Basic Yellow 2 on cylindrical activated carbon with different initial dye concentrations (205, 165, 125, and 85 mg/L) are shown in Figure 3. The figure shows the plots of the adsorbed amount per gram of activated carbon, qt, versus time, t, with the rotor speed ranging from 0 to 1600 rpm. The solid lines of these figures represent the pseudo-first-order model with the parameters, k1 and q∞, listed in Table 1. For all experiments in Table 1, the content of the cylindrical activated carbon packed in the bed was 36 g and the recirculation flow rate was 1532 mL/min. The four subgraphs of Figure 3 indicate that the centrifugal force did indeed enhance the performance of the basic dye adsorption by activated carbon for all initial concentrations. Also, the enhancement of the adsorption rate by the centrifugal force becomes obvious for high initial concentrations. The rate constant, k1 as listed in Table 1, was found to increase with increasing rotor speed for the same initial dye concentration. This also implies that the centrifugal force increases the rate of dye adsorption. Besides, the experimental data show good agreement with the pseudo-first-order kinetics and the correlation coefficients are all above 0.99. Consequently, the pseudo-first-order model is applicable to describe the mechanism of basic dye adsorption by cylindrical activated carbon under a centrifugal field. As shown in Figure 4, it is clear that the centrifugal acceleration does affect the adsorption rate as the centrifugal acceleration increases from 0 to 842 m/s2 (based on the arithmetic mean radius). This is probably due to the fact that the centrifugal acceleration decreases the film resistance in mass transfer. It is also found that the variation of k1 due to centrifugal acceleration is relatively significant for low dye concentra-
tions. It is easier to recognize the effect of low dye concentrations in Figure 5, showing that k1 decreases with increasing initial dye concentrations. A similar trend was observed by Ho and McKay14,15 for dye adsorption by peat and wood in a batch system. This may be because the lower the initial dye concentration, the lower the mass-transfer resistance. It is also noted that the dependence of k1 on the initial dye concentration is also dependent on the degree of centrifugal acceleration. With higher centrifugal acceleration, the variation of mass transfer becomes obvious. Figure 6 shows the plots of the dye-adsorbed amount per unit weight of activated carbon versus the square root of time with best fit straight lines. The results indicate that the intraparticle diffusion is the ratelimiting step in the early period because of good correlation. It also suggests that the straight line portions of these plots increase with increasing initial dye concentration and decreasing rotor speed. This may be explained by the fact that the equilibrium time decreases with decreasing initial dye concentration and increasing rotor speed as shown in four subgraphs of Figure 6. The intraparticle diffusion rate parameter, kr, as presented in Table 1, increases with the rotor speed for a given initial dye concentration. The increases in the centrifugal force result in a reduction in the surface film resistance, allowing dye to reach the particle surface more rapidly. This will provide a greater driving force for adsorption. Therefore, the centrifugal force enhances the rate of dye adsorption. It is also observed that increasing the initial dye concentration causes an increase in the intraparticle diffusion rate parameter, kr, with a given rotor speed. This is similar to the results presented by McKay et al.16 for the adsorption of basic dyes onto silica in a batch system. Their data showed that kr is proportional to the initial dye concentration, C0, raised to the x power,
kr ∝ C0x
(8)
where x was 0.43 for the adsorption of Astrazone Blue on Sorbsil Silica. Our experimental data indicated that the exponent x depends on centrifugal acceleration as
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Figure 6. Intraparticle diffusion kinetics of dye adsorption at various initial dye concentrations (cylindrical activated carbon: recirculation flow rate ) 1532 mL/min; rotor speed ) (a) 0 rpm, (b) 400 rpm, (c) 1000 rpm, and (d) 1600 rpm). Table 2. Variations of the Exponents x, y, and z with Centrifugal Acceleration centrifugal acceleration (m/s2)
x
y
z
0 53 329 842
0.62 0.48 0.59 0.67
0.55 0.71 0.77 0.77
0.50 0.70 0.72 0.74
shown in Table 2. The value of x (0.67) in a high centrifugal field is higher than the ideal value of 0.5 which was obtained from the adsorption of alkylbenzene sulfonates on activated carbon in a batch system.17 As a consequence, the centrifugal force did indeed affect the mechanism of basic dye adsorption by activated carbon in the initial portion of the adsorption process. Figure 7 presents the effect of centrifugal acceleration on the intraparticle diffusion coefficient estimated by eq 5. The diffusion coefficient could be increased by increasing centrifugal acceleration. This characteristic implies better mass transfer under a high centrifugal
field. Therefore, centrifugal acceleration can enhance dye removal from an aqueous solution. Also, Figure 8 indicates that the diffusion coefficient decreases with increasing initial dye concentration. This is similar to the observation by McKay and Al-Duri18 for basic dye adsorption by activated carbon in a batch system. It can be noticed that both D1,app and D2,app are proportional to the initial dye concentration, C0, raised to the -y power and -z power, respectively.
D1,app ∝ C0-y
(9)
D2,app ∝ C0-z
(10)
The values of y and z depend on centrifugal acceleration as shown in Table 2. The values in Table 2 suggest that the variation of the diffusion coefficient due to the initial dye concentration is relatively significant with higher centrifugal acceleration. The effect of particle size on the adsorption kinetics was studied and shown in Figure 9. The rate constants,
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Figure 7. Effect of centrifugal acceleration on the diffusion constants at various initial dye concentrations.
Figure 9. Effect of particle size on adsorption kinetics.
Figure 10. Intrapaticle diffusion kinetics of dye adsorption for both activated carbons. Figure 8. Effect of initial dye concentration on the diffusion constants at various rotor speeds.
Conclusion
k1, of the granular type are 1.71 × 10-2 and 2.28 × 10-2 1/min for 0 and 1000 rpm, respectively. The results show that granular activated carbon (small particles) can remove dye faster than cylindrical activated carbon. This can be explained on the basis that the boundary layer thickness on small particles is thinner than that on large particles. It is evident that the centrifugal force could also affect the adsorption kinetics for granular activated carbon. Figure 10 shows that the intraparticle diffusion model could also describe the initial rate for the adsorption of yellow dye on granular activated carbon. The intraparticle diffusion rate parameters, kr, for the granular type are 3.40 and 3.98 mg/(g min0.5) for 0 and 1000 rpm, respectively. The intraparticle diffusion rate parameters, kr, for the granular type are much higher than those of the cylindrical type. It implies that very rapid surface adsorption occurs for granular activated carbon. It is probably due to the fact that, in large particles, the dye has a longer intraparticle diffusion path than that in small particles.
The experimental results of dye adsorption by activated carbon under a centrifugal field were investigated. The pseudo-first-order model would provide the better representation for the mechanism of adsorption of basic yellow dye on activated carbon. The data also showed that the rate of adsorption can be controlled by the degree of centrifugal force. Moreover, the initial dye concentration plays an important role in the adsorption kinetics because the dye concentration greatly affects the extent and rate of dye uptake on activated carbon. The intraparticle diffusion model could provide good correlation of the data only in the initial stages. It implies that the rate-governing step is intraparticle diffusion for this initial dye adsorption. A comparison of the diffusion coefficient evaluated was also made in terms of the rate constant and the intraparticle diffusion rate parameter. It indicated that because of the small difference between two methods the diffusion coefficient could be determined by the rate constant of the pseudo-first-order model. Moreover, the rate constants, the intraparticle diffusion rate param-
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eters, and the diffusion coefficients for the adsorption of basic yellow dye on the activated carbon could be enhanced by the centrifugal force. Therefore, the centrifugal force would improve mass transfer in adsorption. Acknowledgment Financial support from the National Science Council is greatly acknowledged. Nomenclature a ) radius of the adsorbent (cm) C0 ) initial dye concentration (mg/L) D ) diffusion coefficient based on eq 3 (cm2/s) D1,app ) apparent diffusion coefficient based on eq 5 (cm2/s) D2,app ) apparent diffusion coefficient based on eq 6 (cm2/s) k1 ) the rate constant based on eq 1 (1/min) kr ) the intraparticle diffusion rate parameter based on eq 4 (mg/(g min0.5)) qt ) amount of dye adsorbed at time t (mg of dye/g of carbon) q∞ ) amount of dye adsorbed at infinite time (mg of dye/g of carbon) t ) operating time (min) t1/2 ) time for adsorption of one-half the amount of dye (min)
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Received for review March 30, 1999 Revised manuscript received July 23, 1999 Accepted October 22, 1999 IE9902333
