Modeling of extraction of dyes and their mixtures from aqueous solution using emulsion liquid membrane

Journal of Membrane Science 360 (2010) 190–201

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Journal of Membrane Science journal homepage: www.elsevier.com/locate/memsci

Modeling of extraction of dyes and their mixtures from aqueous solution using emulsion liquid membrane Amit Kumar Agarwal a , Chandan Das b , Sirshendu De a,∗ a b

Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India Department of Chemical Engineering, Indian Institute of Technology Guwahati, Assam 781039, India

a r t i c l e

i n f o

Article history: Received 23 December 2009 Received in revised form 28 April 2010 Accepted 2 May 2010 Available online 8 May 2010 Keywords: Modeling Membrane Extraction Binary system Experimental data

a b s t r a c t Mathematical modeling of a typical batch extraction system employing emulsion liquid membrane for dyes, namely, crystal violet and methylene blue is carried out. An already available mass transfer model using spherical shell approach is used for one component dye extraction. The same model is extended for the binary system. The resultant ordinary differential equations of the model are solved using Laplace transform. The model parameters are obtained by comparing the experimental data with the calculated values of the dye concentration at various time points using an optimization algorithm. Effects of various process parameters, namely, concentration of surfactant, internal reagent, stirring speed, etc., have been analyzed for both single and binary mixtures using the model results. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Emulsion liquid membrane (ELM) is one of the potential methods for treatment of industrial wastewater aiming at recovery of various organic and inorganic solutes [1–11]. Stability of water–oil–water emulsion depends on the coalescence of internal aqueous as well as oil droplets, rupture of internal phase, swelling of membrane phase, etc. [12–18]. With the invention of emulsion liquid membrane (ELM) in late sixties, numerous mathematical models have been developed. These models can be categorized into two generic groups, namely, carrier mediated transport models for type II facilitation and diffusion-type mass transfer models for type I facilitation. Applications of these models during carrier mediated type II emulsion liquid membrane are tested for extraction of various metal ions, namely, silver [19], rare earth elements [20], chromium [21], cesium [22], nickel [23], zinc [24], gold [4,25], arsenic [26]. Acidic medium was used in most of these studies. Modeling has been carried out at various degrees of rigor in all of the above mentioned references [19–26]. A detailed rigorous model involves solution of partial differential equations [19–26]. However, numerical solutions of partial differential equations are complex and computation intensive. Liu and Zhang [20], proposed a simplified model under asymptotic cases when partial differential equations are converted

∗ Corresponding author at: Tel.: +91 3222 283926; fax: +91 3222 255303. E-mail address: [email protected] (S. De). 0376-7388/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2010.05.017

to ordinary differential equations. Using leading term approximation, perturbation method is also used to simplify the partial differential equations [25,27]. However, recently Huang et al. [26] found a closed form solution of the model for carrier mediated ELM system. Mass transfer models for type I ELM system are studied by various researchers [21,23,28–30]. In these studies also, the resulting model equations are partial differential equations, which are solved using numerical techniques. Advancing front model is a much cited and useful model for both types of transport models discussed above [21–23,25,30]. However, to circumvent complexities involved in cumbersome numerical techniques, simplifications are attempted. Pseudo-steady state was assumed by Bhowal and Datta [21] and leading order perturbation solution was carried out by Yan et al. [28]. In all the above works, various system parameters, like, effective diffusivity, reversible rate constant, etc., are estimated as fitting parameters. Ho and Sirkar developed a mathematical model to quantify the extraction including the effects of mass transfer and breakage for one component system [31]. Therefore, it may be noted that in the modeling study, concerted research efforts are directed to obtain the closed form analytical solution. It may be worth mentioning that all the modeling works in ELM are based on single component system. In this paper, we propose a diffusion-type mass transfer model for type I facilitation that produces a closed form solution based on Ho and Sirkar [31]. The model has been extended to a binary system to explain the batch extraction of two dyes, crystal violet and methylene blue, using liquid emulsion membrane. This study presents the first ever

A.K. Agarwal et al. / Journal of Membrane Science 360 (2010) 190–201

191

closed form solution for a multi-component system. This is the uniqueness and novelty of this work. The spherical shell approach is used to model the present system using Laplace and inverse Laplace transform of the model equations along with the initial and boundary conditions to get the analytical solution for the concentration of various species in the external phase. This model is capable of predicting theoretically the effects of individual parameters on overall extraction rate. The adjustable model parameters are found with special physical meanings attached to them to characterize the emulsion liquid membrane system. The model is easy to comprehend and the analytical solution can be used to get the solute recovery at various time points for a set of experimental conditions.

2.1. Diffusion-type mass transfer model for type I of facilitated mechanism

2. Theory

2.1.1. Spherical shell approach This approach assumes that the mass transfer resistance is diffusion in the spherical ‘shell’ of the membrane phase of constant thickness between the external and internal phases. The shell is shown schematically in Fig. 1(a) for the dye extraction with the internal phase containing NaOH for reaction with dye to maintain the concentration of dye, effectively zero in the internal phase. Some models consider only the extraction of the solute from the feed phase into the receiving phase while other models consider both extraction and breakage of the components from the receiving phase to the feed phase. Model proposed by Ho and Sirkar [31] considers both extraction and breakage.

The effectiveness of emulsion liquid membrane (ELM) process is a result of the facilitated mechanism that maximizes both the extraction rate, i.e., the flux through the membrane phase, and the capacity of the receiving phase (the internal phase in the case with an external feed phase) for the diffusing species. The mechanism of batch extraction can be classified into two categories: (i) diffusiontype mass transfer models for type I of facilitated mechanism and (ii) carrier-facilitated transfer models for type II of facilitated mechanism. In the first mechanism, the solute dissolves in the membrane phase near the external interface, diffuses through it to the inward region of emulsion drop in the dissolved state and is released into the internal phase. The solute reacts with a reagent in the internal aqueous phase, resulting in a membrane-insoluble product. Thus, a concentration gradient is maintained across the membrane. Recovery of dyes from aqueous solution using surfactant span 80 is a typical example of diffusion-facilitated transport [32]. In the second mechanism, i.e., carrier-facilitated transport mechanism, a carrier is incorporated in the membrane phase to increase the mass transfer rates. Recovery of zinc from wastewater using cation-exchange reagents is a typical example of carrier-facilitated transport [33].

In this type of facilitation, the reaction in the receiving phase (the internal phase if the external phase is a feed) of an emulsion liquid membrane system maintains a solute concentration of effectively zero. This maximizes of the driving force for the diffusion of solute through the membrane phase from the feed phase to the receiving phase. The reaction of the diffusing species with a chemical reagent in the receiving phase forms a product incapable of diffusing back through the membrane. The spherical shell approach for the diffusion process has been taken up in this study, as suggested by Ho and Sirkar [31].

2.1.1.1. Model with overall mass transfer coefficient for extraction and breakage. Ho and Sirkar first developed a model with overall mass transfer coefficients for extraction and breakage [31]. In the model, solute can transfer from the internal phase of an emulsion liquid membrane system to the external phase by two mechanisms: diffusional transport and breakage. But, solute can transfer from the external phase to the internal phase only by diffusional transport. The mass transfer rate, jk for the diffusional transport can be expressed as:

Fig. 1. Schematic of dye extraction (a) for single dye without breakage; (b) for single dye with breakage and (c) for binary system with breakage.

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jk = k Av (Vm + Vi ) ci −

Ke ce Ki





= k(Vm + Vi ) ci −

Ke ce Ki

 (1)

where k is the overall mass transfer coefficient based on the mass transfer area of the emulsion globules in the external phase, Av the external phase mass transfer area per unit volume of the emulsion, Vm the membrane phase volume, Vi the total volume of the internal phase, and k is the overall mass transfer coefficient based on the volume of the emulsion (Vm + Vi ). This assumes that the mass transfer area is proportional to the volume of the emulsion under a given mixing condition for contact with the external phase. The breakage of the internal phase in terms of the change of the internal phase volume with time can be assumed to be proportional to the internal phase volume under a given mixing condition. −

dVi = Vi dt

(2)

where  is the breakage coefficient and t is the extraction time. The mass transfer rate due to the breakage is, j = Vi ci

(3)

Integration of Eq. (2) gives the internal phase volume as a function of time: Vi = Vi0 exp(−t)

(4)

where Vi0 is the initial volume of the internal phase. The breakage decreases the internal phase volume but increases the external phase volume Ve , which is given in the following equation: Ve = V0 − Vi = V0 − Vi0 exp(−t)

(5)

where V0 = Ve0 + Vi0

(6)

V0 is the sum of the external and internal phase volumes and Ve0 the initial internal phase volume. 2.1.2. Modeling of extraction of single component system The transport of species involved in the model is shown schematically in Fig. 1(b). Solute A in the external phase is extracted, by the diffusion mechanism associated with the mass transfer coefficient kA , into the internal phase where the solute reacts with the reagent in the internal phase to become solute B. Solute B can transfer from the internal phase, by both the diffusion mechanism associated with the mass transfer coefficient kB and the breakage mechanism associated with the coefficient , to the external phase, where, B remains as the same species. So, here both A and B can exist in the external phase whereas B exists in the internal phase but not A. The internal reagent leaked out to the external phase can convert A into B. Solute A can exist in the external phase until it is exhausted owing to both extraction and internal reagent leaking. Transient mass balance equations for species A, B and internal reagent are written and the following sets of equations are resulted [31], For 0 ≤ t ≤ t1:



d(Ve ceA ) KeA = kA1 (Vm + Vi ) ciA − ceA KiA dt



KeB d(Ve ceB ) = kB (Vm + Vi ) ciB − ceA KiB dt







KeA d(Vi cir ) ceA = kA1 (Vm + Vi ) ciA − KiA dt



− Vi cir

(7)

and B between the membrane and internal phases at equilibrium and r is the internal reagent NaOH. With the assumption that solute accumulation in the membrane phase is negligible compared to the solute amounts in the external and internal phases, ciB is given in the following equation from the conservation of mass: Vi ciB = Ve0 ceA0 + Ve0 ceB0 + Vi0 ciB0 − Ve ceA − Ve ceB The initial conditions of Eqs. (7)–(10) (at t = 0) are: ceA = ceA0 ,

ceB = ceB0 ,

ciB = ciB0 ,

(8)

− Vi cir

(9)

Here, t1 is the time at which solute A in the external phase is just exhausted. KeA and KeB are the distribution coefficient for the solute A and B between the membrane and external phases at equilibrium, KiA and KiB are the distribution coefficient for the solute A

cir = cir0 ,

Ve = Ve0 , Vi = Vi0

A special case in this model is that the solute B cannot diffuse through the membrane phase, i.e., kB = 0. For practical purposes, kB = 0 (hence kB0 = 0) and the concentration of A in the internal phase, ciA and the concentration of B in the external phase ceB are zero, so the above set of equations reduce to: d(Ve ceA ) 0 ceA − Vi cir = −kA dt

(11)

d(Ve ceB ) = Vi ciB + Vi cir dt

(12)

d(Vi cir ) 0 ceA − Vi cir = −kA dt

(13)

Vi ciB = Ve0 ceA0 + Vi0 ciB0 − Ve ceA − Ve ceB

(14)

where 0 = kA (Vm + Vi ); kA

kA =

kB0 = kB (Vm + Vi )

(15)

KeA kA1 KiA

(16)

where kA and kB are the overall mass transfer coefficients for solutes A and B, respectively; and ceA and ciB are the concentrations for A in the external phase and for B in the internal phase, respec0 and k0 are assumed to be constant, i.e., the mass transfer tively. kA B area or the emulsion volume (Vm + Vi ) does not change significantly even though breakage of the internal phase occurs. For typical ELM systems with a reasonably good stability, the breakage is not appreciable, and the volume of the membrane phase (Vm ) is much larger than the volume of the internal phase (Vi ). Thus, the emulsion volume does not change significantly. The initial conditions of Eqs. (11)–(14), at t = 0 are: ceA = ceA0 ,

ceB = ceB0 ,

cir = cir0 ,

Ve = Ve0 ,

Vi = Vi0 ;

It is assumed that the concentration of A in the external phase is zero beyond t = t1 , i.e., solute A is exhausted in the external phase. For t ≥ t1 , species mass balance equations result as follows [31]: ceA = 0

(17)

d(Ve ceB ) = Vi ciB dt

(18)

d(Vi cir ) = −Vi cir dt

(19)

Vi ciB = Ve0 ceA0 + Vi0 ciB0 − Ve ceB

(20)

Substituting Eq. (11) into Eq. (13) and integrating the resultant equation lead to the following relationship: Vi cir = Ve0 ceA + (Vi0 cir0 − Ve0 ceA0 ),

+ Vi ciB − Vi cir

(10)

for 0 ≤ t ≤ t1

(21)

Eqs. (17)–(20) can be solved for the two cases, namely, small and large breakage. For small breakage, which is needed for the ELM systems of practical interest, i.e.,  ≤ 1.35 × 10−5 s−1 , the change of the internal phase volume is less than 5% as determined from Eq. (4) for a 1-h extraction time. Thus, Vi and Ve can be assumed constant and approximated by their initial volumes Vi0 and Ve0 , respectively. This leads to the solution of concentration profiles of A and B in external phase [31].

A.K. Agarwal et al. / Journal of Membrane Science 360 (2010) 190–201

For 0 ≤ t ≤ t1 [31]: ceA =

0c (kA eA0 0 kA

−

ceB =

+ Vi0 cir0 ) + Ve

  exp

−

+

0 kA

 

Ve

t

(Vi0 cir0 − Ve0 ceA0 )

(22)

0 + V kA e

Vi0 (c + cir0 − (ciB0 + cir0 ) exp(−t)) Ve iB0

(23)

The time t1 is obtained from Eq. (22) by letting ceA = 0: t1 =

Ve



0c kA eA0 + Vi0 cir0



Vi cir d(Ve ceC ) = Vi ciC + 2 dt

(31)

Vi cir d(Ve ceD ) = Vi ciD + 2 dt

(32)

d(Vi cir ) 0 = −kA ceA − kB0 ceB − Vi cir dt

(33)

Vi ciC = (Ve0 ceA0 + Ve0 ceC0 + Vi0 ciC0 ) − (Ve ceA + Ve ceC )

(34)

Vi ciD = (Ve0 ceB0 + Ve0 ceD0 + Vi0 ciD0 ) − (Ve ceB + Ve ceD )

(35)

The initial conditions (at t = 0) are: (24)

ceA = ceA0 ,

ceB = ceB0 ,

The solution of concentration profiles for t ≥ t1 , is presented below

ciD = ciD0 ,

cir = cir0 ,

0 + V ) (kA e

ln

(Vi0 cir0 − Ve0 ceA0 )

ceA = 0 ceB

(25)

1 = (Ve0 ceA0 + Vi0 ciB0 − Vi0 (ciB0 + cir0 ) exp(−t) Ve + (Vi0 cir0 − Ve0 ceA0 ) exp(−(t − t1 )))

(26)

The extraction of component A is evaluated as: % Extraction =



ceA + ceB 1− ceA0 + ceB0



× 100

193

(27)

In all the single component experiments, ceB0 = 0, so Eq. (27) reduces to:   ceA + ceB % Extraction = 1 − × 100 (28) ceA0 2.1.3. Modeling of extraction of binary system The model is shown schematically in Fig. 1(c). Solutes A and B in the external phase are extracted, by the diffusion mechanism associated with the mass transfer coefficient kA and kB , respectively, into the internal phase where the solutes react with the reagent in the internal phase to become solutes C and D, respectively. Solutes C and D can transfer from the internal phase, by both the diffusion mechanism associated with the mass transfer coefficient kC and kD and the breakage mechanism associated with the coefficient , to the external phase where C and D remain as the same species. So, A, B, C and D can co-exist in the external phase, whereas, C and D can only exist in the internal phase but not A and B. The internal reagent leaked out to the external phase can convert A into C and B into D. Solutes A and B can exist in the external phase until they are exhausted owing to both extraction and internal reagent leaking. For example, crystal violet (CV), the solute A, can be extracted into the internal phase where it reacts with the internal reagent NaOH to become solute C. Similarly, methylene blue (MB), the solute B, can be extracted into the internal phase where it reacts with the internal reagent NaOH to become solute D. The solutes C and D can leak out from the internal phase, by breakage (the ionic species C and D cannot diffuse through the type of membrane used for our purpose, i.e., kC = 0 and kD = 0 for our case), into the external phase where they remain as C and D. NaOH leaked out from the internal phase to the external phase can convert CV and MB, i.e., the solutes A and B into C and D, respectively, in the external phase. CV and MB will exist in the external phase until they are exhausted owing to both extraction and NaOH breakage. Transient mass balance equations for species A–D and internal reagent are written and the following set of equations are resulted: For 0 ≤ t ≤ t1 : d(Ve ceA ) Vi cir 0 = −kA ceA − 2 dt

(29)

d(Ve ceB ) Vi cir = −kB0 ceB − 2 dt

(30)

ceC = ceC0 , Ve = Ve0 ,

ceD = ceD0 ,

ciC = ciC0 ,

Vi = Vi0

It is assumed that solute A exists in the external phase up to a time t1 and the governing concentration balance equations for various species for t1 ≤ t ≤ t2 are given below: ceA = 0

(36)

d(Ve ceB ) = −kB0 ceB − Vi cir dt

(37)

d(Ve ceC ) = Vi ciC dt

(38)

d(Ve ceD ) = Vi ciD + Vi cir dt

(39)

d(Vi cir ) = −kB0 ceB − Vi cir dt

(40)

Vi ciC = Ve0 ceA0 + Ve0 ceC0 + Vi0 ciC0 − Ve ceC

(41)

Vi ciD = Ve0 ceB0 + Ve0 ceD0 + Vi0 ciD0 − (Ve ceB + Ve ceD )

(42)

After time t2 , it is assumed that both A and B are exhausted in the external phases and the governing equations of various species are presented below, For t ≥ t2 : ceA = 0

(43)

ceB = 0

(44)

d(Ve ceC ) = Vi ciC dt

(45)

d(Ve ceD ) = Vi ciD dt

(46)

d(Vi cir ) = −Vi cir dt

(47)

Vi ciC = Ve0 ceA0 + Ve0 ceC0 + Vi0 ciC0 − Ve ceC

(48)

Vi ciD = Ve0 ceB0 + Ve0 ceD0 + Vi0 ciD0 − Ve ceD

(49)

where t1 is the time at which solute A in the external phase is just exhausted, i.e., ceA = 0 and t2 is the time when solute B in the external phase is just exhausted, i.e., ceB = 0. From the experimental data, it was seen that t1 for all set of experiments, was less than t2 . So, the governing equations are designed keeping this fact in consideration. For the case of t2 being less than t1 , the governing equations for A and B can be just interchanged to get the new set of equations. It is also assumed that the internal reagent leaked out to the external phase reacts in equal proportion with A and B. For small breakage, Vi and Ve can be assumed constant and approximated by their initial volumes Vi0 and Ve0 , respectively. This leads to the solution of concentration profiles of A, B, C and D in external phase.

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A.K. Agarwal et al. / Journal of Membrane Science 360 (2010) 190–201

For 0 ≤ t ≤ t1 :

V c i0 ir0

kB0

ceA = −

Ve0

2Ve0



kB0

+

Ve0

V c i0 ir0

ceB = 



Ve0

− ceA0 − ceB0

 

− ceA0 − ceB0 (a + b exp(−˛t) + c exp(−ˇt))



+

Vi0 cir0 ceA0 − 2Ve0

+ [ceB ]t1 exp

 (a1 exp(−˛t)

+ b1 exp(−ˇt)) + ceA0 (a2 exp(−˛t) + b2 exp(−ˇt))

(50)

ceC =



ceA0 + ceC0 +

−

(kB0 /Ve0 + )



kB0 Ve0

Vi0 ciC0 Ve0

 (exp(−(k + )(t − t ) − 1) 4 1

+





(t − t1 )

(55)

(1 − exp(−(t − t1 )))

+ [ceC ]t1 exp(−(t − t1 ))

V c i0 ir0

0 kA

ceB = −



− ceA0 − ceB0 (a + b exp(−˛t)

Ve0

2Ve0



+ c exp(−ˇt)) +

0 kA

Ve0

 +

ceB0 −

Vi0 cir0 2Ve0

ceD =





−ceA0 + ceD0 +

(56)



Vi0 ciD0 V c + i0 ir0 Ve0 Ve0

((1 − exp(−(t − t1 )))

+ [ceD ]t1 exp(−(t − t1 ))

(57)

× (a1 exp(−˛t) + b1 exp(−ˇt)) + ceB0 (a2 exp(−˛t) + b2 exp(−ˇt))

ceC =

c

eA0

2  2

+ × +

V c V c ceB0 + ceC0 + i0 iC0 + i0 ir0 2 Ve0 2Ve0

−

  V c i0 iC0

a 

Ve0

2Ve0



0 kA

ceB0

Ve0

 a 1 −˛

−

×

 2

2





+

− ceA0



+

 a 2 −˛

Ve0

Ve0

ceD =





+ ceC0 exp(−t)



(52)

(1 − exp(−t))



ceA0

 a 1 −˛

kB0 Ve0

+

− ceB0

−˛

Ve0



+ ceD0 exp(−t)

(53)

For t1 ≤ t ≤ t2 : ceA = 0

% Extraction =

k1 2

k1 =

+



−ceA0 + ceD0 +



(exp(−˛t) − exp(−t))

b2 (exp(−ˇt) − exp(−t)) −ˇ

(1 − exp(−(t − t2 )) (60)



Vi0 ciD0 V c + i0 ir0 Ve0 Ve0

(1 − exp(−(t − t2 )) (61)

[ceC ]t2 can be obtained by putting t = t2 in Eq. (60) and [ceD ]t2 can be obtained by putting t = t2 in Eq. (61).

˛=

(exp(−˛t) − exp(−t))

 a 2





1−

ceA + ceC ceA0



1−

ceB + ceD ceB0





× 100

(62)

× 100

(63)

The various notations/symbols used in the above equations are:



0 kA



% Extraction =

b (exp(−˛t) − exp(−t)) −˛



Vi0 ciC0 Ve0

For B (i.e., methylene blue):

0 − ceA0 − ceB0 (kB0 − kA )



ceA0 + ceC0 +

The extraction for small breakage is evaluated as: For A (i.e., crystal violet):







+ [ceD ]t2 exp(−(t − t2 ))

(exp(−˛t) − exp(−t))

(1 − exp(−t)) +

+ (ceA0 − ceB0 ) +

ceC =

+

V c V c ceB0 + ceD0 + i0 iD0 + i0 ir0 2 Ve0 2Ve0

2Ve0



×

(59)



kB0

c + (exp(−ˇt) − exp(−t)) −ˇ +

ceB = 0

(exp(−˛t) − exp(−t))

  V c i0 ir0

a

(58)

+ [ceC ]t1 exp(−(t − t1 ))

b2 (exp(−ˇt) − exp(−t)) −ˇ

 c eA0 +

b (exp(−˛t) − exp(−t)) −˛

ceA = 0



+ (ceB0 − ceA0 )

ceD =

[ceB ]t1 can be obtained by putting t = t1 in Eq. (55), [ceC ]t1 can be obtained by putting t = t1 in Eq. (56) and [ceD ]t1 can be obtained by putting t = t1 in Eq. (57). For t ≥ t2 ;

(1 − exp(−t))



(1 − exp(−t)) +



+



0 − ceA0 − ceB0 (kB0 − kA )

c (exp(−ˇt) − exp(−t)) −ˇ

+ ×

(51)

(54)

+

k2 +

k0 +k0 A

Ve0

B

+

k2 1

4



k1 2

ˇ= k2 =

2 4

− −

a=

1 ˛ˇ

b=

c=

1 ˇ(ˇ−˛)

a1 =

1 (ˇ−˛)

b1 =

1 (˛−ˇ)

a2 =

˛ (ˇ−˛)

b2 =

ˇ (ˇ−˛)



k2 + k0

A

Ve0

k2

+

1

4  2



k0

B

Ve0

+

 2



1 ˛(˛−ˇ)

2.1.4. Validity of the model The validity of the model was checked by fitting this model to experimental data of removal of dyes from aqueous solution using emulsion liquid membrane [32]. Span 80 (sorbitan mono-oleatet) was used as the surfactant; n-heptane was used as an additive to the surfactant span 80. Methylene blue (MB) and crystal violet (CV)

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195

Table 1 Experimental scheme for single component. Span 80 (%, w/w)

NaOH (M)

Stirring speed (rpm)

Oil phase/aqueous phase (%, v/v)

1, 5 and 8

0.01, 0.05 and 0.5

280 and 430

1,2 and 4

Span 80 (%, w/w)

NaOH (M)

Stirring speed (rpm)

Oil phase/aqueous phase (%, v/v)

1, 5 and 8

0.01, 0.05 and 0.5

280 and 430

1 and 2

Table 2 Experimental scheme for binary mixture.

were the two dyes used whose extraction from aqueous solution was investigated for their single component and binary system. Sodium hydroxide (NaOH) was used as the internal reagent. The concentration of dyes in the clear solution extracted from the feed was determined by UV spectrophotometer [max for CV is 586 nm and max for MB is 660 nm]. The standard method was used to calculate the concentration of dyes in their binary mixture [34]. The operating parameters were span 80 concentration, NaOH concentration, the volume ratio of the oil phase to the aqueous phase (O/A) and stirring speed during extraction. Operating conditions for single dye system and binary mixture are shown in Tables 1 and 2, respectively. 0 and  The model presented in Section 2, has two parameters, kA 0 0 for one component system and kA , kB and  for two component system. Depending upon the system, the relevant governing equations are solved with a set of guess values of these unknown parameters. Percentage of extraction of the dye species is evaluated at various time points and the sum of the errors between calculated and experimental data for all time points are computed as shown in Eqs. (64) and (65). For one component system, S=

 Ei,cal − Ei,exp 2 i

3. Results and discussions 3.1. Effect of surfactant span 80 concentration In emulsion-type liquid membrane process, surfactant plays a very important role. It influences the emulsion stability and the transport rate of the solute. With the increase of surfactant concentration, emulsion stability improves; however, the extraction rate decreases due to the presence of more surfactant molecules at the reaction site, aqueous–organic interface. This problem may be resolved by the use of a new type of surfactant, known as bifunctional surfactant, which acts as an emulsifier and an extractant as well [3,35,36]. Surfactant concentration is an important factor as it directly affects the stability, swelling and break up of emulsion liquid membranes. Fig. 2(a) represents the variation of percentage of extraction of CV for both experimental and calculated data and Table 3 lists the model parameters for various operating conditions, in case of single component system. It is observed from the figure that the percentage of extraction of CV increases up to 5% of span 80 concentration and decreases thereafter. The model parameters in Table 3 clearly reveal that the breakage coefficient () decreases significantly from 3.45 × 10−6 s−1 to 2.2 × 10−6 s−1 with increasing surfactant concentration from 1% to 5%. The relatively low 0 ) for the lowoverall mass transfer coefficient for extraction (kA est surfactant concentration, 1% (refer Table 3) was due to a low mass transfer area associated with poor emulsion stability. For surfactant concentration up to 5%, the mass transfer coefficient increases with increasing surfactant concentration. For example, overall mass transfer coefficient increases from 1.18 × 10−4 m3 /s to 9.25 × 10−4 m3 /s as surfactant concentration increases from 1% to 5%. At lower surfactant concentrations (less than 5%) emulsions break easily leading to poor extraction. At higher surfactant concentration (beyond 5%), although the membrane stability increases,

(64)

Ei,exp

For two component system, S=

 Ei,cal − Ei,exp  i

Ei,exp



2

+ A

Ei,cal − Ei,exp



Ei,exp

2

(65) B

An optimization method is employed with an initial guess of the parameters and minimizing the above error function to obtain the values of these parameters. The obtained values of the parameters for one and two component systems are presented in Tables 3 and 4. Table 3 Model parameters for single component system. Operating conditionsa

Feed concentration CV: 20 ppm kA0 (×104 m3 /s)

MB: 20 ppm  (×106 s−1 )

kA0 (×104 m3 /s)

 (×106 s−1 )

IR = 0.05 (M) N = 280 rpm O/A = 1

Surfactant span 80 conc. (%, w/w)

1 5 8

1.18 9.25 1.53

3.45 2.20 2.80

1.09 2.00 0.83

3.00 0.10 0.01

S = 5% N = 280 rpm O/A = 1

NaOH conc. (M)

0.01 0.05 0.5

6.20 9.25 5.10

13.50 2.20 0.58

1.39 2.00 0.97

0.20 0.10 0.11

S = 5% IR = 0.05 (M) O/A = 1

Stirring speed (rpm)

280 430

9.25 13.00

2.20 6.00

2.00 2.76

0.10 0.38

S = 5% IR = 0.05 (M) N = 280 rpm

Oil to aqueous phase (O/A)

1 2 4

9.25 2.94 4.80

2.20 6.46 12.80

2.00 2.00 4.00

0.10 2.50 8.70

a

Surfactant conc., S; NaOH conc., IR; stirring speed, N; oil to aqueous phase, O/A.

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Table 4 Model parameters for binary mixture. Operating conditionsa

Feed concentration CV: 10 ppm; MB: 10 ppm kA0 (×104 m3 /s)

kB0 (×104 m3 /s)

 (×106 s−1 )

IR = 0.05 (M) N = 280 rpm O/A = 1

Surfactant span 80 conc. (%, w/w)

1 5 8

11.00 17.00 5.82

3.30 3.89 2.93

1.74 0.90 3.76

S = 5% N = 280 rpm O/A = 1

NaOH conc. (M)

0.01 0.05 0.5

26.00 17.00 7.18

4.25 3.89 2.20

14.00 0.90 0.18

S = 5% IR = 0.05 (M) O/A = 1

Stirring speed (rpm)

280 430

17.00 19.00

3.89 4.28

0.90 1.94

S = 5% IR = 0.05 (M) N = 280 rpm

Oil to aqueous phase (O/A)

1 2

17.00 12.00

3.89 2.08

0.90 1.48

a

Surfactant conc., S; NaOH conc., IR; stirring speed, N; oil to aqueous phase, O/A.

mass transfer resistance also increases due to presence of more surfactant at aqueous–organic phase interface, resulting in less transfer of dye molecules to internal phase. Thus the dye extraction is reduced. However, it can also be observed from Table 3 that

the breakage coefficient () increases with the surfactant concentration beyond 5%. Therefore, for this particular case, there exists an optimal value of surfactant dose (i.e., 5%), where, extraction is maximum.

Fig. 2. Variation of percentage of extraction with time for different span 80 concentrations (a) for CV; (b) for MB and (c) for binary mixture of CV and MB.

A.K. Agarwal et al. / Journal of Membrane Science 360 (2010) 190–201

Effect of surfactant concentration on the extraction of MB is presented in Fig. 2(b) and the model parameters are listed in Table 3. In case of MB, almost 100% extraction is achieved at the surfactant concentration of 5% at which the value of the overall mass transfer coefficient is the highest (2.2 × 10−4 m3 /s). Below 5%, the extraction is reduced as discussed earlier in the case of CV. Comparing the model parameters of MB with CV, two trends are apparent. Firstly, the overall mass transfer coefficient for CV is higher than MB for any particular surfactant concentration and so it can be observed from Fig. 2(a) and (b) that the extraction profile of CV is faster than MB. Secondly, the breakage coefficient for higher surfactant concentrations is much less for MB compared to CV. Thus, unlike CV, extraction of MB does not fall below the maximum level at higher surfactant concentration (5%). The structure of MB and CV is shown in Appendix A. The different structures of CV and MB provide an explanation for the above trend. The chloride ion in MB is surrounded by three benzene rings. These benzene rings lead to steric hindrance to any molecule trying to reach the reacting chloride ion in MB. This is a plausible explanation for the reduced reaction rates in case of MB. On the other hand, although CV molecule is bigger in size, less hindered chloride ion reacts easily. Therefore, reaction of CV in internal phase favors faster transport of CV to the internal phase which can be observed from the higher mass trans0 ) values for CV. Thus, the extraction profile of CV fer coefficient (kA stabilizes at an earlier time of operation. As the reaction with CV is very fast, NaOH present in the inner phase gets depleted at an earlier time as compared the case with MB. Therefore, the chance

197

of breakage of MB into the external phase is small which can be observed from the lower breakage coefficient values () for MB. For example, at 5% span 80 concentration, extraction of CV stabilizes at 10 min whereas; it takes 45 min for MB. As discussed earlier, the solute can transfer from the internal phase of an ELM system to the external phase by two mechanisms: diffusional transport and breakage. But, solute can transfer from the external phase to the internal phase only by diffusional transport. The model parameters obtained and the experimental results indicate that for CV, the breakage and subsequent breakage of CV into the external phase, over time, manifests itself as a drop in percentage of extraction, whereas this phenomenon is absent with MB for the time of operation used in the experiments. This is clear as breakage coefficient of MB is less than CV, as shown from Table 4. Extraction profile of the dye mixture is presented in Fig. 2(c) for various concentrations of surfactant and the model parameters are listed in Table 4. The qualitative observations are similar to those of one component system as discussed earlier. Two distinctly new observations are evident from this figure. Firstly, the extraction values of both components are slightly less than the single component system. This is due to competitive transport and reaction of two dyes. Secondly, the overall mass transfer coefficient values for CV and MB in dye mixture system are much more as compared to their values in single component system. This leads to the observation that the percentage of extraction of both CV and MB is quicker compared to one component system. The presence of three benzene rings around the reactive chloride ion in MB causes

Fig. 3. Variation of percentage of extraction with time for different NaOH concentrations (a) for CV; (b) for MB and (c) for binary mixture of CV and MB.

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steric hindrance. No such hindrance to the reaction site is present in CV and hence the extraction CV is faster as compared to MB. 3.2. Effect of NaOH concentration Fig. 3(a) represents the variation of percentage of extraction of CV for both experimental and calculated data and Table 3 lists the model parameters for various internal reagent (NaOH) concentrations for the single component system. It is observed that maximum extraction occurs at NaOH concentration of 0.05 (M). At lower concentrations, i.e., below 0.05 (M) of NaOH, almost all reactant (NaOH) is consumed in the internal phase resulting in lower extraction efficiency. This phenomenon is reflected by the fact that 0 ) decreases as the starting the overall mass transfer coefficient (kA concentration of the internal reagent NaOH decreases. It is observed 0 value decreases from 9.25 × 10−4 m3 /s to from Table 3 that kA 6.2 × 10−4 m3 /s as NaOH concentration decreases from 0.05 (M) to 0.01 (M). At lower concentrations, NaOH present in the inner phase gets depleted at an earlier time and therefore, the chance of breakage of the solute CV into the external phase is more which can be observed from the high breakage coefficient values () for CV in Table 3. For example, breakage coefficient values () decreases from 13.5 × 10−6 s−1 to 0.58 × 10−6 s−1 as NaOH concentration increases from 0.01 (M) to 0.5 (M) for CV. At higher concentrations, i.e., beyond 0.05 (M), extraction of dye 0 value decreases from 9.25 × 10−4 m3 /s decreases. For example, kA −4 3 to 5.10 × 10 m /s as NaOH concentration is increased from 0.05

(M) to 0.5 (M) for CV. This is due to two factors at higher concentration. Firstly, at higher concentrations of NaOH, the driving force for the diffusion of solute in the membrane phase from the feed phase should be maximum as the concentration gradient of the membrane soluble permeates is maximized by the reaction of the solute in the receiving phase and so the extraction efficiency should increase. Also, if the internal reagent concentration in the internal phase is high, then the chance of breakage also decreases. Secondly, at higher concentrations, excess NaOH causes swelling of emulsion leading to destabilization of liquid membrane system, causing reduction in percentage of extraction. The extraction profile and the values of overall mass transfer coefficient and the breakage coefficient is a result of which of the above factors is dominant at that particular NaOH concentration. The variation of the percentage of extraction of MB with changing the concentration of NaOH used as the internal reagent is shown in Fig. 3(b) and the corresponding model parameters are listed in Table 3. The observations are similar to those in case of CV. In this case also, the optimum value of NaOH concentration is found to be 0.05 (M). Effect of NaOH concentration on the extraction of CV–MB mixture is shown in Fig. 3(c) and the model parameters are listed in Table 4. It is interesting to note that the mass transfer coefficient values for CV is much higher than that of MB and also it is much higher when compared to their single component system. As discussed earlier, this is due to preferential reaction of CV with NaOH in the internal phase. As the concentration of NaOH in the inter-

Fig. 4. Variation of percentage of extraction with time for different stirring speeds (a) for CV; (b) for MB and (c) for binary mixture of CV and MB.

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nal phase increases, the chance of depletion of the internal reagent NaOH decreases and hence the breakage also decreases. So, with increasing NaOH concentrations, the breakage coefficient value decreases considerably. Increasing the concentration of the internal reagent causes swelling of the emulsion leading to a decrease in the diffusion rate of solute through the membrane phase to the internal phase and hence the mass transfer coefficient value decreases with increasing NaOH concentration. For example, it can be observed 0 value decreases from 26.0 × 10−4 m3 /s to from Table 4 that kA −4 3 7.18 × 10 m /s as NaOH concentration is increased from 0.01 (M) to 0.5 (M) for CV in the CV–MB mixture. 3.3. Effect of stirring speed Stirring speed during extraction is an important factor. Effect of stirring speed on the extraction of CV, MB and CV–MB mixture is shown in Fig. 4(a)–(c), respectively. The model parameters, overall mass transfer coefficient and the breakage coefficient, for single component system and the binary mixture system are listed in Tables 3 and 4, respectively. It is observed that at earlier period of operation, extraction is more at higher stirring speed. This trend is observed during initial start up of the experiment. At higher stirring speed, smaller sized emulsion droplets are formed leading to more surface area for mass transfer and hence higher overall mass transfer coefficient. But at the same time, higher stirring speed adversely

199

affects the stability of emulsion globules leading to breakage with higher breakage coefficient values. Therefore, percentage of extraction decreases in the long run. Beyond initial minutes, percentage of extraction decreases with rpm. This trend is clearly revealed by the model parameters values in Tables 3 and 4. For CV, as the stirring speed increases 0 ) increases from from 280 rpm to 430 rpm, the value of (kA −4 3 −4 3 9.25 × 10 m /s to 13.0 × 10 m /s and the () value also increases from 2.2 × 10−6 s−1 to 6.0 × 10−6 s−1 . Increase in the mass transfer coefficient value with increasing stirring speed drives the extraction efficiency at the start of the experiment but in the long run, increase in the breakage coefficient value takes over and hence decreases the percentage of extraction over the latter half of the experiment. 3.4. Effect of volume ratio of the oil phase to aqueous phase (O/A) In the removal of organic and inorganic pollutants from the solutions using the emulsion liquid membrane (ELM) technology, the volume ratio of the oil phase to the aqueous phase (O/A) plays an important role. Oil phase provides more resistance to the solute transport but at the same time it offers more stability to emulsion droplets. In general, the viscosity and the size of emulsion drop decrease with this ratio, and the total interfacial area between the external phase and emulsion drops increases. However, the

Fig. 5. Variation of percentage of extraction with time for different O/A ratios (a) for CV; (b) for MB and (c) for binary mixture of CV and MB.

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extraction rate will increase or decrease with the ratio depending on which of the two factors: increase in total interfacial area or a decrease in the capacity of internal phase for trapping dye solutes had a larger effect on extraction rate. The effect of volume ratio of the oil phase to aqueous phase on the extraction of CV, MB and CV–MB mixture is shown in Fig. 5(a)–(c), respectively. The model parameters, overall mass transfer coefficient and the breakage coefficient, for single component system and the binary mixture system are listed in Tables 3 and 4, respectively. Fig. 5(a) shows that extraction of CV is achieved best when the volume ratio of the oil phase to aqueous phase is 1. With increase in this ratio, the extraction decreases as concentration of NaOH in the aqueous phase decreases. For exam0) ple, an increase in O/A ratio from 1 to 4 results in a decrease of (kA −4 3 −4 3 from 9.25 × 10 m /s to 4.8 × 10 m /s for CV (refer Table 3). It can also be observed from Table 3 that the breakage coefficient () increases from 2.2 × 10−6 s−1 to 12.8 × 10−6 s−1 as O/A ratio increases from 1 to 4 for CV. It can also be noticed that there is little emulsion breakage in most of the cases and it is most profound in case of minimum aqueous phase volume. The effect of volume ratio of oil phase to aqueous phase for the extraction of MB is presented in Fig. 5(b). The extraction efficiency is maximum for the ratio (O/A) of 1. The trend is almost similar to that of CV. Effect of volume ratio of the oil phase to the aqueous phase (O/A) in binary mixture is shown in Fig. 5(c). It is seen that the breakage in the emulsion takes place earlier in case of mixture because of early exhaustion of the solutes in the external phase due to competitive transport and reaction. Here also best extractions of two dyes are achieved with O/A ratio of 1. 4. Conclusions

is developed considering type I facilitated transport mechanism. The model equations are generated using spherical shell approach and solved by Laplace transform. The adjustable model parameters characterize the system. The model is applied to extraction of two dyes, namely, crystal violet and methylene blue. Effects of various operating conditions are satisfactorily explained by the model. The model successfully predicts that the percentage of extraction reaches a saturated value earlier in case of CV compared to MB. In two component system, percentage of extraction decreases compared to one component system due to competitive transport. It is a general observation that for the two component system, the model underpredicts the percentage of extraction for MB and overpredicts that of CV, at a long time (beyond 30 min). However, these deviations are within ±15% for most of the operating conditions. The modeling study also provides the tuning of various model parameters (under the range of operating conditions studying herein) so that the optimum extrac0 tion is attained. For example, for two component system, kA 0 −4 3 −4 3 and kB are maximum, i.e., 17 × 10 m /s and 3.89 × 10 m /s, respectively, and  is minimum, i.e., 0.9 × 10−6 s−1 for a surfactant concentration of 5%. Thus, at this surfactant concentration, the extraction performance is optimal. Similarly, an analysis of parameters from Table 3 reveals that 0.05 (M) NaOH, 280 rpm and oil to aqueous phase ratio of 1 are suitable conditions to obtain the best extraction results for the operating conditions studied herein. The model is easy to comprehend and the analytical solution can be used to get the solute recovery at various experimental conditions. More importantly, it provides an insight into the mechanisms of diffusion and breakage and their relative importance.

A closed form analytical solution for batch extraction of a two component system is presented in this work. The physical model

Appendix A.

.

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Nomenclature Av ce ce0 ceA ceA0 ceB ceB0 ci ciB ciB0 cir cir0 k kA 0 kA kA1 kB kB0 Ke KeA KeB Ki KiB Ve0 Vi0 V0 

external phase mass transfer area per unit volume of the emulsion (m−1 ) solute concentration in the external phase (kg/m3 ) initial solute concentration in the external phase (kg/m3 ) solute A concentration in the external phase (kg/m3 ) initial solute A concentration in the external phase (kg/m3 ) solute B concentration in the external phase (kg/m3 ) initial solute B concentration in the external phase (kg/m3 ) solute concentration in the internal phase (kg/m3 ) solute B concentration in the internal phase (kg/m3 ) initial solute B concentration in the internal phase (kg/m3 ) concentration of the reagent in the internal phase (kg/m3 ) initial concentration of the reagent in the internal phase (kg/m3 ) overall mass transfer coefficient (s−1 ) overall mass transfer coefficient for solute A (s−1 ) kA (Vm + Vi ) (m3 /s) kA KiA /KeA (s−1 ) overall mass transfer coefficient for solute B (s−1 ) kB (Vm + Vi ) (m3 /s) distribution coefficient for the solute between the membrane and external phases at equilibrium distribution coefficient for solute A between the membrane and external phases at equilibrium distribution coefficient for solute B between the membrane and external phases at equilibrium distribution coefficient for the solute between the membrane and internal phases at equilibrium distribution coefficient for solute B between the membrane and internal phases at equilibrium initial volume of the external phase (m3 ) initial total volume of the internal phase (m3 ) (Ve0 + Vi0 ) = (Ve + Vi ) (m3 ) breakage coefficient (s−1 )

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