Kinetic model for the immobilised biosorbents: Uptake of cationic dyes

Chemical Engineering Journal 254 (2014) 571–578

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Kinetic model for the immobilised biosorbents: Uptake of cationic dyes Nityanand Singh Maurya a, Atul Kumar Mittal b,⇑ a b

Department of Civil Engineering, National Institute of Technology Patna, 800 005, India Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India

h i g h l i g h t s  A kinetic model has been developed using the concept of Chemically Active Available Binding Sites.  It has been validated using immobilized F. carnea in polyvinyl alcohol (PVA) matrix and two cationic dyes.  It is compared with first order kinetic, Pore diffusion, single resistance and pseudo second order kinetic models.  Effect of temperature, mixing speed and sorbent dose has shown applicability of the model.

a r t i c l e

i n f o

Article history: Received 18 April 2014 Received in revised form 14 May 2014 Accepted 15 May 2014 Available online 12 June 2014 Keywords: Biosorption Immobilization Macro fungus Safranin O Polyvinyl alcohol Kinetic model

a b s t r a c t A sorption kinetic model has been developed using concept of Chemically Active Available Binding Sites (CAABS). Dead ‘‘Fomitopsis carnea’’ immobilized on polyvinyl alcohol (PVA) matrix has been employed as the immobilized sorbent. Safranin O and Alcian Blue are the representative sorbates. Results indicate that CAABS model described the kinetics with high degree of correlation coefficient (R2 P 0.99) for under different environmental conditions, viz., mixing speed (60, 200 and 500 revolutions per minutes), and biosorbent doses. Student’s t-test also revealed that the predicted data using Chemically Active Available Binding Sites (CAABS) model were significantly correlated with the experimental data. The CAABS model was also compared with well known kinetic models such as Lagergren’s model (first order kinetic model), Single resistance model, Pore diffusion model, and Pseudo-second order kinetic model. The comparative study of these models also confirmed high efficacy of the CAABS model to depict the experimental data. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Biosorption of inorganic [1–4] and organic species [5–7] has been extensively reported in the literature. However, field application of the biosorptive processes remained very limited. It may be due to poor engineering properties of the biosorbents. Immobilisation process has been quoted to improve the improve engineering properties of virgin biomass [8]. To design and/or to evaluation a biosorption system, suitable sorption kinetic model is warranted, which could simulate actual biosorption kinetics efficiently. Therefore, various sorption kinetic models have been proposed, i.e., Lagergrn’s model (first order kinetic model) [9], Single resistance model [10,11], Pore diffusion model [12] and Pseudo-second order model [13]. These models were developed for metal surfaces, different types of coals and activated carbons. Physical and chemical characteristics of a ⇑ Corresponding author. Tel.: +91 11 25691239. E-mail addresses: [email protected] (N.S. Maurya), [email protected] (A.K. Mittal). http://dx.doi.org/10.1016/j.cej.2014.05.064 1385-8947/Ó 2014 Elsevier B.V. All rights reserved.

biosorbent differ from the activated carbon. Surface of a biosorbent generally consists of biopolymers studded with a number of complex functional groups. Many researchers have indicated that the biosorptive processes involve chemical complexation, ion exchange, covalent and hydrogen bonds, and physio-sorption, besides involving oxidation–reduction and micro precipitation etc. The kinetic model proposed by Mittal [14] is based on virgin biomass without considering immobilization process. Immobilisation of a biomass may affect the surface of the biosorbent and its morphology. There is no study available in the literature which has specifically developed a sorption kinetic model for the immobilized biosorbent. This paper reports a sorption kinetic model which is based on the basic principles of chemi-sorption and physi-sorption. Data generated from sorption kinetic experiments, employing immobilized biomass of a dead macro fungus namely ‘‘Fomitopsis carnea’’ in polyvinyl alcohol (PVA) matrix as a biosorbent and two cationic dyes namely Safranin O and Alcian Blue as sorbate under various environmental conditions viz., mixing speed and bisorbent dose, have been used to validate the developed kinetic model.

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Glossary CAABS Qe M C0 Ce Ct Qt

Chemically Active Available Binding Sites Quantity of dye transferred (mg g1) onto the biosorbent at equilibrium condition Dose of the biosorbent (g L1) Initial liquid phase concentration (mg L1) of the sorbate Liquid phase concentration (mg L1) of the sorbate (dye) at equilibrium, Sorbate concentration (mg L1) in bulk solution at time t Solid phase concentration (mg g1) of the dye (sorbate) at time t

Nt Kpm Kpm max E F N Kpm

min

Number of Chemically Active Available Binding Sites, CAABS present on the surface of the biosorbent Kinetic coefficient, (L g1 h1) Maximum possible mass transfer rate per unit time per unit weight of the biosorbent Model constant related to the mixing speed Model constant related to the dose of the biosorbent Mixing speed in rpm Minimum possible mass transfer rate coefficient per unit time per unit weight of biosorbent

2.3.2. Effect of dose Biosorbent doses were 0.50, 1.05, 1.50 g L1 for Safranin O and 2.00, 5.00, 9.24 g L1 for Alcian Blue. Mixing speed in all these experiments was 500 rpm.

2. Materials and methods 2.1. Biosorbent preparation Dried powdered biomass of F. carnea – a macro fungus, was immobilized as per the method described elsewhere [15,16]. 5.0 g PVA (average molecular weight 89,000–98,000, Aldrich, USA) was dissolved in 50 mL distilled water at 80 ± 2 °C. After 16 h of stirring, pre-determined powder biomass was added to the cooled PVA solution. The completely mixed solution of PVA and biomass was extruded in the liquid nitrogen. As soon as solution drop came in contact with liquid nitrogen, instantly bead was formed. Beads were kept in liquid nitrogen overnight, and then were frozen and thawed for four cycles. Beads were kept at 40 ± 2 °C till the difference in weight between two consecutive days became negligible. 2.2. Sorbate Cationic dye namely Safranin O (Basic Red 2, CI 50240) and Alcian Blue (C.I. No. 74240) were used as sorbate. Aqueous solution having dye concentration of 100 mg/L were used in all the experiments.

3. Model development Biosorption could be considered as a result of unbalance forces acting upon the sorbate molecule. The unbalance forces may arise due to (1) liquid phase concentration gradient at the time of equilibrium, and (2) presence of Chemically Active Available Binding Sites (CAABS) on the outer surface of immobilised biomass and within the pores (micro and macro) of the biosorbent. Finally, the attachment of the sorbate occurs at these Chemically Active Sites (CAABS). So, biosorption rate for a specific sorbatan can be considered as a combined effect of the concentration gradient and CAABS. Graphically, this concept is presented in Fig. 1. The total dye uptake by the sorbent can be considered as a result of (1) physi-sorption which is a function of liquid phase concentration gradient of the sorbate, and (2) chemi-sorption which is assumed to be the function of CAABS. Surface of the immobilised biosorbent can be considered as studded with CAABS, graphically shown in Fig. 1. Chemi-sorption including chemical complexation, ion exchange, electrical forces, and different types of chemical bonding occurs at the CAABS.

2.3. Batch biosorption kinetic experiments 3.1. Physi-sorption Kinetic experiments were carried out in an acrylic vessel having 140.0 mm internal diameter and 180.0 mm height as described elsewhere [17]. At predetermined time intervals, samples were withdrawn from the adsorber and were analysed for residual dye concentration. Mass of dye transferred from the aqueous phase to the sorbent was determined by applying the mass balance on the reaction vessel as follows:

Q e  M ¼ ðC 0  C e Þ

ð1Þ

or Q e ¼ ðC 0  C e Þ=M

ð2Þ

where Qe is quantity of sorbate transferred (mg g1) onto the biosorbent (or solid phase sorbate concentration) at equilibrium condition, C0 and Ce are initial and equilibrium liquid phase sorbate concentration (mg L1) respectively and M is dose of the biosorbent (g L1). 2.3.1. Effect of mixing speed A number of kinetic experiments were undertaken at various mixing speeds, i.e., 60, 200 and 500 rpm. Biosorbent doses were 1.05 and 5.00 g L1 for Safranin O and for Alcian Blue respectively.

Rate of change in concentration of the sorbate on the solid phase (biosorbent) is directly proportional to the liquid phase concentration difference, which is assumed as the first order reaction. Mathematically, it can be represented as follows:

Liquid film boundary Biosorbent particle Biosorption site boundary

Bulk solution concentration, Ct (Ct varies from C0 to Ce)

Fig. 1. Conceptual diagram for sorbate transport and attachment on to the sorbent particle.

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dQ t =dt aðC t  C e Þ

ð3Þ

where, dQt/dt is the mass transfer rate of the sorbate (dye). It would depend on several factors, including physical and chemical characteristics of biosorbent, chemical structure of sorbate (dye), initial liquid phase sorbate concentration, pH, ionic strength and temperature of the sorbate solution. Apart from these, mixing speed and biosorbent dose are also an important factor affecting equilibrium-dye-concentration [18]. 3.2. Chemi-sorption Finally, the dye molecule (sorbate) is transferred at the CAABS. Rate of change of the solid phase concentration of the sorbate is directly related to the CAABS. Assuming that numbers of CAABS at any time t are Nt, the rate of change in sorbate concentration on the sorbent can be expressed as:

dQ t =dt aNt

ð4Þ

Nt að1  Q t =Q e Þ

ð5Þ

Combining, Eqs. (4) and (5),

dQ t =dt a ð1  Q t =Q e Þ

ð6Þ

Eq. (3) can also be presented as follows,

dQ t =dt a MðQ e  Q t Þ

ð7Þ 1

where, M is the dose of biosorbent in g L Combining Eqs. (6) and (7),

.

dQ t =dt ¼ K pm  M  ðQ e  Q t Þ ð1  Q t =Q e Þ

ð8Þ

where, Kpm is the kinetic coefficient, (L g1 h1). Separating the variables in Eq. (8),

dQ t =ðQ e  Q t Þ2 ¼ ðK pm  M=Q e Þdt

ð9Þ

Integrating Eq. (9) for the boundary conditions, at a = t, Qt = 0, and t = t, Qt = Qt

1=ðQ e  Q t Þ ¼ ðK pm  M=Q e Þ t þ 1=Q e

ð10Þ

Eq. (10) can be rearranged as follows,

Q t ¼ t=ð1=ðK pm  M  Q e Þ  t=Q e Þ which can be linearized as follows:

Absorbance

where Nt is the number of Chemically Active Available Binding Sites (CAABS) present on the surface of the biosorbent. A number of functional groups which may constitute the biopolymers, are present on the surface of the biosorbent, which in turn interact with the dye cation (sorbate). These groups could be phosphate, carboxyl, amine, hydroxyl, chitin (R2-NH), chitosan (R-NH2), melanins and other pigments [19]. It is also evident from Fig. 2 (FT-IR of the biomass used in the preparation of immobilised biosorbent of the present study) that a number of surface groups like OH (K1), methylene (K2), carbonyl (K3), amides/nitro (K4), methyl/nitro (K5), amines (K7), C-O bond (K8 & K9), sulfoxides (K11 & K12), C-X (K13) etc are present on the surface of the biosorbent. Sorption of the dye onto the biosorbent is a result of various interactions between the dye (sorbate) and the sorbent, such as ion-exchange, chemical complexation and different types of bandage due to electrostatic forces, hydrogen bonding etc. CAABS are

basically sites, which represent various types of all such interactions between the dye and the sorbent. It is assumed that the CAABS are proportional to the sorption capacity of the biosorbent at any given time, t. For a given dose of the biosorbent, maximum sorption capacity of the biosorbent could be measured in terms of the solid phase concentration (mg g1) of the sorbate at equilibrium, Qe. If the solid phase concentration of the biosorbate at a given time t is Qt, than the fractional sorption capacity of the biosorbent at time t, could be represented by Qt/Qe. Thus, the remaining sorption capacity would be (1  Qt/Qe). Hence,

Wave numbers (cm-1) Fig. 2. FTIR of the biosorbent, Fomitopsis carnea.

ð11Þ

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N.S. Maurya, A.K. Mittal / Chemical Engineering Journal 254 (2014) 571–578

100

100

(a)

80

(a)

Ct (mg/L)

Ct (mg/L)

80

60

60

40

40

20 0

20

40 t (h)

60

80

20

100

0

100

(b)

20

t (h) 40

60

80

60

80

60

80

100

(b)

80 60

Ct (mg/L)

Ct (mg/L)

80 60

40

40

20 0

20

40

100

t (h) 60

80

100

20 0

(c ) 100

80

t (h) 40

(c )

80

60

Ct (mg/L)

Ct (mg/L)

20

40

60 40

20 0

20

t (h)

40

60

80

20 Fig. 3. Variation in mixing speed (a) 60 (b) 200 (c) 500 rpm; Experimental data (N), Pore diffusion ( ), Furusawa and Smith ( ), Lagergren’ model ( ) and CAABS model ( ) for the sorption of Safranin O.

t=Q t ¼ 1=ðK pm  M Q e Þ þ t=Q e

20

t (h) 40

Fig. 4. Variation in mixing speed (a) 60 (b) 200 (c) 500 rpm; Experimental data (N), Pore diffusion ), Furusawa and Smith ( ), Lagergren’s model ( ) and CAABS model ( ) for the sorption of Alcian Blue.

ð12Þ

t/Qt could be plotted against t. The linear fit of the kinetic data to this plot (t/Qt vs t) could be used to obtain the kinetic coefficient, Kpm. Expression for the Pseudo-second order kinetic model as described by Ho et al. [13] is given below:

t=Q t ¼ 1=ðK so  Q 2e Þ þ t=Q e

0

ð13Þ

Mathematically, Pseudo-second order model (Eq. (13)) is very similar to the proposed biosorption kinetic model, CAABS (Eq. (12)). Linearised solutions of both the models (Eqs. (12) and (13)) consist of plotting same parameters as ordinate (t/Q) and abscissa (t). However, the constant term of the CAABS model is different from the Psuedo-second order model. The kinetic constant (Kpm) of the CAABS model is a function of the dose of the biosorbent (M), whereas the coefficient of the Pseudo-second order model does not use the biosorbent dose. It is obvious that the biosorption kinetics will must be affected by the dose of the biosorbent for a given set of system parameters. Thus, the kinetic coefficient obtained from the CAABS would be a better representative of the biosorption kinetics.

the widely used models namely the Lagergren’s model [9], Pore diffusion model [12], Single resistance model [10] and Pseudosecond order model [13]. These models are based on the different mechanism of the sorption. Lagergren’s model is the most frequently cited kinetic models involving first order reaction kinetics; the Single resistance model proposed by Furusawa and Smith in 1973 [10] considers film diffusion along with the equilibrium data; Pore diffusion model is based on the rate limiting resistance to the diffusion of the sorbate within the pores of the sorbent; and Pseudo-second order model is the second order model which is the latest in the series of sorption kinetic models. 4.1.1. Lagergren’s model The Lagergren’s model is based on first order reaction kinetics [9,20]. It is given below:

ln ðQ e  Q t Þ ¼ ln Q e  kad  t

ð14Þ

Here, Qt and Qe are the solid phase concentration of sorbate at any time and at equilibrium, respectively. kad is the Lagergren’s kinetic constant.

4. Results and discussion 4.1. Model validation: determination of mass transfer coefficient The kinetic profiles generated at different mixing speeds and biosorbent doses using the CAABS model were compared with

4.1.2. Pore diffusion model Pore diffusion model [2,12] is given below:

Q t ¼ K p  t 0:5 Here, Kp is pore diffusion kinetic constant.

ð15Þ

575

N.S. Maurya, A.K. Mittal / Chemical Engineering Journal 254 (2014) 571–578 Table 1 Effect of mixing speed on kinetic parameter during biosorption of Safranin O, sorbent dose 1.05 g/L, Dye concentration 100 mg/L. Mixing speed (rpm)

CAABS kinetic model Kpm

60 200 500 *

2

*

0.133 0.196 0.254

Pseudo second order

Lagergren’s equation +

R

kso**

kad

0.986 0.991 0.991

0.00241 0.00404 0.00447

0.043 0.040 0.051

R

2

0.947 0.874 0.947

Pore diffusion

Furusawa and Smith

Kp++

R

kf#

R2

7.095 6.665 8.690

0.844 0.635 0.496

0.0097 0.0072 0.0150

0.820 0.739 0.753

2

Kpm (L g1 h1); kso (h1); + kad (h1); ++ Kp (h0.5); # kf (L h1).

**

Table 2 Effect of mixing speed on kinetic parameter during biosorption of Alcian Blue; sorbent dose 5.0 g/L, dye concentration 100 mg/L. Mixing speed (rpm)

60 200 500 *

Pseudo second order

Lagergren’s equation

Kpm*

CAABS kinetic model R2

kso**

kad+

R2

Kp++

Pore diffusion R2

kf#

Furusawa and Smith R2

0.043 0.056 0.062

0.977 0.987 0.996

0.01704 0.02096 0.02315

0.047 0.041 0.081

0.965 0.902 0.961

1.831 1.926 1.932

0.887 0.715 0.613

0.0160 0.0133 0.0111

0.928 0.850 0.705

Kpm (L g1 h1); kso (h1); + kad (h1); ++ Kp (h0.5); # kf (L h1).

**

4.1.3. Furusawa and Smith model Furusawa and Smith [10] proposed a kinetic model assuming resistance due to film diffusion as presented below:

ln ðC t =C 0  1=ð1 þ ms  KÞ ¼ ln ðms  K=ð1 þ ms  KÞÞ þ ðð1 þ ms  KÞ ðkf  SB  tÞ=ðms  KÞ

ð16Þ

Here, C0 and Ct are the liquid phase sorbate concentrations at initial time and at any time, t. ms, kf, K and SB are the dose of the sorbent, model constant, Henry’s Law constant and specific surface area of the sorbent respectively.Performance of these models to predict the sorption kinetics was evaluated on the basis of coefficients of correlation, and Student’s t-test. Kinetic profiles for the Pseudo-second order model have not been plotted separately because, it would have the same presentation as CAABS model, though the values of the constants for the Pseudo-second order model would be different which were obtained using Eq. (13). 4.2. Effect of mixing speed Concentration profiles, for the sorption of Safranin O (Fig. 3) and Alcian Blue (Fig. 4) as predicted by the Lagergren’s model, and Furusawa and Smith model, approach the experimental data as the as the sorption reaches equilibrium. However, the profiles generated by the CAABS model are close to the experimental data from the start of the sorption to the equilibrium. Initially, chemi-sorption may be the dominating dye sorption mechanism. Since, it has been accounted in the development of the CAABS model, so the predictions are better. CAABS model also considers the film diffusion in the form of concentration gradient, which is reflected in better predictions by the CAABS model towards the final stages of the sorption. Performance of the Pore diffusion model improved at low mixing speeds with coefficient of correlation varying from 0.844 to 0.496 as mixing speed varied from 60 to 500 rpm (Table 1). It is quite understandable since at low mixing speeds pore diffusion could be pre-dominating. However, poor performance of this model as compared to the CAABS model can be explained on the

basis of inclusion of chemi-sorption in the CAABS model, which is not considered in the Pore diffusion model. During initial phase of the sorption, CAABS model predicted profiles are much better as compared to other employed models (Figs. 3 and 4). This could be explained on the basis that in the initial stages of sorption, kinetics is much fast and none of the models could match the rapid uptake of dye by the biosorbent. It could be inferred that the conventional theories of sorption kinetics, i.e., pore diffusion, film diffusion or the single resistance mass transfer (Furusawa and Smith model) which describe mass transfers across the two phases based on the physical processes are not applicable for the biosorptive processes on the immobilised biomass. It indicates that in the biosorptive uptakes, site based chemical complexation may be dominating mechanism during the initial phase of the sorption, which is considered in the proposed CAABS model. Kinetic data were also analysed using the Student’s t-test to check if the model predictions were significantly correlated with the experimental data. Paired Student’s test was used since same data set was employed. For t-test to be significant, the probability (95%) should be less than 0.05. Otherwise, p-value more than 0.05, indicates that the observed values and predicted values were not significantly different. Statistically, CAABS model provided significant correlations (at 95%, p > 0.05) for the sorption of Safranin O (Table 1), and sorption of Alcian Blue (Table 2). The correlations provided by other models are not significantly correlated (at 95%, p < 0.05). The values of kinetic constant of CAABS model, Kpm for both the dyes, i.e., Safranin O (Table 1) and Alcian Blue (Table 2) are affected by the mixing speed. Better correlations of the kinetic constant provided by the Pore diffusion model at low mixing speeds for both the dyes, i.e., Safranin O (Table 1) and Alcian Blue (Table 2) indicated that mixing speed may affect the kinetics at lower speeds, with minimal effects at higher speeds. Further the values Kpm and their corresponding mixing speed were regressed using the expression in Eq. (17).

K pm ¼ ðK pm max  E NÞ=ð1 þ E NÞ

ð17Þ

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N.S. Maurya, A.K. Mittal / Chemical Engineering Journal 254 (2014) 571–578

where, Kpm max represents the maximum possible mass transfer rate per unit time per unit weight of the biosorbent, E is the model constant, and N is the mixing speed in rpm. Figs. 5 and 6 present change in Kpm values as mixing speed varies from 60 to 500 rpm for Safranin O and Alcian Blue respectively. It is evident from the Figs. 5 and 6, Kpm increases to a maximum value, ‘Kpm max’ at high speeds, and becomes asymptotic for both the dyes. Thus, it is assumed that a function as described in Eq. (17) can be used to describe the effect of the mixing speed on the kinetic constant of the CAABS model. Kpm max and E for Safranin O are 0.272 and 0.0157 respectively at coefficient of correlation as 0.985. For Alcian Blue, Kpm max and E are 0.066 and 0.0132 at coefficient of correlation as 0.998. Higher value of Kpm max for Safranin O as compared to the Alcian Blue is supported from the observations that Safranin O is better sorbed (Figs. 3 and 4), further validating the physical significance of the Kpm max.

0.3

Kpm

0.2 Expt. data

0.1

Model fit 0 0

200 400 Mixing speed (rpm)

600

Fig. 5. Effect of mixing speed on the Kpm: Sorbate–Safranin O.

0.07

Kpm

0.06 0.05 0.04

4.3. Effect of biosorbent dose

Expt. data

0.03

Model fit

CAABS model assumes that transfer of sorbate from aqueous phase to the solid surface of the biosorbent depends upon the number of CAABS. These sites are proportional to the mass of the biosorbent. Thus, at higher sorbent dose, the rate of sorption would be high.

0.02 0

200 400 Mixing speed (rpm)

600

Fig. 6. Effect of mixing speed on the Kpm: Sorbate–Alcian Blue.

110

(a)

110

(a)

90

Ct (mg/L)

Ct (mg/L)

90 70

70 50 30

50

10

30 0

20

t (h) 40

60

0

80

20

110

t (h) 40

60

80

(b)

(b) 90 Ct (mg/L)

Ct (mg/L)

80 60 40

50 30 10

20 0

20

100

t (h) 40

60

0

80

20

t (h)

40

60

80

60

80

100

(c)

(c)

80

80

60

60

Ct (mg/L)

Ct (mg/L)

70

40 20

40 20

0

0

20

t (h) 40

60

80

Fig. 7. Effect of biosorbent dose (a) 0.5 (b) 1.05 (c) 1.5 g/L; Experimental data (N) Pore diffusion ( ), Furusawa and Smith ( ), Lagergren’s model ( ) and CAABS model ( ) for the sorption of Safranin O.

0 0

20

t (h) 40

Fig. 8. Effect of biosorbent dose (a) 2.0 (b) 5.0 (c) 9.24 g/L, Experimental data (N), Pore diffusion ( ), Furusawa and Smith ( ), Lagergren’s model ( ) and CAABS model ( ) for the sorption of Alcian Blue.

577

N.S. Maurya, A.K. Mittal / Chemical Engineering Journal 254 (2014) 571–578 Table 3 Effect of biosorbent dose on kinetic parameters during biosorption of the Safranin O, mixing speed 500 rpm, dye concentration 100 mg/L. Dose (g/L)

CAABS model

0.5 1.05 1.5 *

Pseudo second order 2

Kpm*

R

0.323 0.254 0.216

0.993 0.991 0.996

kso

**

Lagergren’s equation kad

0.002571 0.004473 0.005589

+

0.063 0.051 0.066

R

Pore diffusion

2

Kp

0.985 0.947 0.957

++

8.869 8.690 7.771

Furusawa and Smith R

kf#

R2

0.800 0.496 0.707

0.0040 0.0150 0.0219

0.736 0.753 0.858

2

Kpm (L g1 h1); kso (h1); + kad (h1); ++ Kp (h0.5); # kf (L h1).

**

Table 4 Effect of biosorbent dose on kinetic parameter during the biosorption of Alcian Blue, mixing speed 500 rpm, dye concentration 100 mg/L. Dose (g/L)

CAABS model

2.0 5.0 9.24 *

Pseudo second order

Lagergren’s equation

Kpm*

R2

kso**

kad+

R2

Kp++

Pore diffusion R2

kf#

Furusawa and Smith R2

0.083 0.062 0.067

0.979 0.996 0.999

0.008533 0.023152 0.060307

0.060 0.081 0.106

0.978 0.961 0.949

1.926 1.932 1.696

0.715 0.613 0.369

0.0064 0.0111 0.0425

0.827 0.705 0.837

Kpm (L g1 h1); kso (h1); + kad (h1); ++ Kp (h0.5); # kf (L h1).

**

0.1

0.06

0.04 0.0

Expt. data Model fit

Kpm

0.3

0.2

0.1 0.0

0.5

1.0 Dose (g/L)

1.5

2.0

Fig. 9. Effect of biosorbent dose on the Kpm: sorbate–Safranin O.

5.0 Dose (g/L)

10.0

Fig. 10. Effect of biosorbent dose on the Kpm: sorbate–Alcian Blue.

is high. But, when CAABS have been increased to a level where CAABS are not rate limiting, any further increase in the CAABS would not increase the rate of transfer of the biosorbate, i.e., the rate constant becomes asymptotic, and kinetic constant rate Kpm approaches a minimum value Kpm min (Figs. 9 and 10). This phenomenon may be well described by the Eq. (18) as given bellow:

K pm ¼ ðK pm min  F  MÞ=ð1 þ F  MÞ

0.4

Expt. data Model fit

0.08 Kpm

Figs. 7 and 8 present the experimental data along with the kinetic profiles generated employing all kinetic models considered in the study at various doses for Safranin O and Alcian Blue respectively. At all sorbent doses, the CAABS model generated kinetic profiles correlated with the experimental data better as compared to other models. Observed correlation coefficients were greater than 0.99 (Table 3), and 0.97 (Table 4) for Safranin O and Alcian Blue respectively. High correlation coefficients for the CAABS model as compared to other models indicate the applicability of the CAABS model at high as well as at low biosorbent doses. Thus, it validates the concept of CAABS. The Student’s t-test showed that kinetic profiles, generated by the CAABS model are significantly correlated (p > 0.05 at 95%) with the experimental data for all dosage. In general, other models were not statistically significant (p < 0.05 at 95%). Variation of Kpm (rate constant of the CAABS model) with biosorbent dose is presented in Figs. 9 and 10 for Safranin O and Alcian Blue respectively. In all cases, as biosorbent doses increases, Kpm decreases, and finally gets asymptotic. This could be explained on the basis that initially, at a low dose, the CAABS are limited in numbers, so the dye to CAABS ratio is high, thus rate of dye uptake

ð18Þ

where, Kpm min represents the minimum possible mass transfer rate coefficient per unit time per unit weight of biosorbent, F is a model constant and M is the biosorbent dose in g L1. Kpm min and F for Safranin O are 0.193 and 4.882 respectively with coefficient of correlation as 0.937. For Alcian Blue, Kpm min and F are 0.059 and 11.868 with coefficient of correlation as 0.800. The maximum of the minimum rate constant corresponds to the sorbate–sorbent system which shoed maximum sorption capacity, i.e., Safranin O, and the least of the minimum rate constant corresponds to the sorbate–sorbent system which shoed minimum sorption capacity, i.e., Alcian Blue. Probably, the minimum rate constant could be used as indicator to compare the biosorption intensity of different sorbate–sorbent systems.

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5. Conclusions The CAABS kinetic model developed in this study showed better correlation with the experimental data as compared to other models. Model constants are well correlated at various mixing speed and sorbent dose. Existing models like Lagergren model, Pore diffusion model and Furusawa and Smith model are not able to correlate from start of the kinetics to the end. It may be attributed to the fact these models consider only one of the characteristic of the sorption process, i.e., either film diffusion or pore diffusion. The CAABS model showed its superiority over others as it is based on the concept of Chemically Active Available Binding Sites besides considering the concentration gradient. The developed CAABS model formulations can be used for the design of an adsorber which uses immobilised biomass as the biosorbent.

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