$$J\_S = -P\frac{d\mathbf{c}\_S}{d\mathbf{x}} + (\mathbf{1} - \sigma)\mathbf{c}\_S I\_V \tag{2}$$

where salt rejection *RS* is defined by the salt concentrations *cF* and *cP* in the feed and perme‐ ate streams respectively.

$$R\_S = 1 - \frac{c\_P}{c\_F} \tag{3}$$

The two electrolytes are fully dissociated as shown in Eq. (8).

librium between feed and permeate solution as:

**Figure 1.** Scheme of the system.

*NaCl* ⇔ *N a* + + *Cl* − *CxN aν* ⇔ *νN a* + + *Cx*

(*a*1*a*2)

(*a*1*a*2)

membrane. Then the equilibrium condition can be expressed as:

If we assume the salt as a single electroneutral species we can express the condition of equi‐

*F* = (*a*1*a*2)

*F* = (*a*1*a*2)

In the feed solution containing a nonpermeable multifunctional organic anion at a concen‐

tration *Cx*, the following conditions of electroneutrality can be written for each phase:

We can also consider the equilibrium between feed solution and the solution inside the

−*ν* (8)

http://dx.doi.org/10.5772/50438

141

Nanofiltration Process Efficiency in Liquid Dyes Desalination

*P* (9)

*M* (10)

*Cl* − *F* = *cSF* (11)

*X* − *F* = *CxF* (12)

*N a* + *F* = *cSF* + *νCxF* (13)

*Cl* − *M* = *N a* + *M* = *cSM* (14)

and

$$\mathbf{c}\_P = \frac{J\_S}{J\_V} \tag{4}$$

With constant fluxes, constant coefficients *P* and σ and with condition in Eq. (4), integration of Eq. (2) through the membrane thickness yields:

$$\frac{\int\_{V} (1 - \sigma) \Lambda \mathbf{x}}{P} = \ln \frac{c\_P \sigma}{c\_P - c\_F (1 - \sigma)}\tag{5}$$

and then salt rejection can be expressed as:

$$R\_S = \frac{(1 - F)\sigma}{1 - \sigma F} \tag{6}$$

where

$$F = e^{-l\_V A}, \ A = \frac{1-\sigma}{P} \Delta x = \frac{1-\sigma}{P\_S} \tag{7}$$

where *P* is the local salt permeability and *PS* is overall salt permeability.

In a mixture of electrolytes, the interactions between different ions can be very important and the behaviour of mixed solutions in NF cannot be predicted from the coefficients describing each salt separately. The differences in the permeabilities of ions lead to an electric field, which influences the velocity of each ion. Thus one needs to analyse all ion fluxes together. This anal‐ ysis for the mixture of two electrolytes with common permeable counter ion and two coions, which are the rejected and the permeable ion respectively, is presented bellow.

#### **1.2. Salt permeation in presence of retained organic ions**

Consider a system (see Figure 1) which consists of semipermeable membrane separating two aqueous solutions with mixed electrolyte sharing a common permeable cation (*1*) and two anions which anion (*2*) is permeable through the membrane and anion (*3*) is fully rejected.

For the sake of simplicity let us consider a mixture of a mono-monovalent salt (*NaCl*) and a multifunctional organic anion *Cx -ν* containing *ν* negatively charged groups per molecule in a sodium salt form.

The two electrolytes are fully dissociated as shown in Eq. (8).

*RS* = 1 − *cP*

*cP* = *JS JV*

of Eq. (2) through the membrane thickness yields:

and then salt rejection can be expressed as:

*JV* (1 − *σ*)*Δx*

*F* = *e*

**1.2. Salt permeation in presence of retained organic ions**

multifunctional organic anion *Cx*

sodium salt form.

−*JV A*

where *P* is the local salt permeability and *PS* is overall salt permeability.

*P* = ln

*RS* = (1 − *F*)*σ*

, *A* = 1 − *σ*

ions, which are the rejected and the permeable ion respectively, is presented bellow.

and

140 Advancing Desalination

where

*cF*

With constant fluxes, constant coefficients *P* and σ and with condition in Eq. (4), integration

*cPσ*

*P Δx* = 1 − *σ*

In a mixture of electrolytes, the interactions between different ions can be very important and the behaviour of mixed solutions in NF cannot be predicted from the coefficients describing each salt separately. The differences in the permeabilities of ions lead to an electric field, which influences the velocity of each ion. Thus one needs to analyse all ion fluxes together. This anal‐ ysis for the mixture of two electrolytes with common permeable counter ion and two co-

Consider a system (see Figure 1) which consists of semipermeable membrane separating two aqueous solutions with mixed electrolyte sharing a common permeable cation (*1*) and two anions which anion (*2*) is permeable through the membrane and anion (*3*) is fully rejected.

For the sake of simplicity let us consider a mixture of a mono-monovalent salt (*NaCl*) and a

*-ν* containing *ν* negatively charged groups per molecule in a

*PS*

*cP* − *cF* (1 − *σ*) (5)

1 − *σF* (6)

(3)

(4)

(7)

$$\begin{aligned} \text{NaCl} & \Leftrightarrow \text{Na}^{\text{+}} + \text{Cl}^{-} \\ \text{C}\_{\text{x}} \text{Na}\_{\text{v}} & \Leftrightarrow \text{v} \,\text{Na}^{\text{+}} + \text{C}\_{\text{x}}^{-\text{-}v} \end{aligned} \tag{8}$$

If we assume the salt as a single electroneutral species we can express the condition of equi‐ librium between feed and permeate solution as:

$$(a\_1 a\_2)\_F = (a\_1 a\_2)\_P \tag{9}$$

We can also consider the equilibrium between feed solution and the solution inside the membrane. Then the equilibrium condition can be expressed as:

$$(a\_1 a\_2)\_F = (a\_1 a\_2)\_M \tag{10}$$

**Figure 1.** Scheme of the system.

In the feed solution containing a nonpermeable multifunctional organic anion at a concen‐ tration *Cx*, the following conditions of electroneutrality can be written for each phase:

$$\mathbf{I}\mathbf{C}\mathbf{I}^{-}\mathbf{J}\_{F} = \mathbf{c}\_{SF} \tag{11}$$

$$\mathbf{\mathbf{\color{red}{L}}X^{-}}\mathbf{\color{red}{J}}\_{F} = \mathbf{\color{red}{C}}\_{xF} \tag{12}$$

$$\left[Na^{+}\right]\_{\mathrm{F}} = \mathcal{c}\_{\mathrm{SF}} + \nu \mathcal{C}\_{x\mathrm{F}} \tag{13}$$

$$\begin{bmatrix} \mathbb{C}I \ ^{-}\end{bmatrix}\_{\mathcal{M}} = \begin{bmatrix} \mathbb{C}Na \ ^{+}\end{bmatrix}\_{\mathcal{M}} = c\_{\mathbb{S}\mathcal{M}} \tag{14}$$

We assume equilibrium on the membrane solution interface, approximating activities with concentrations and substituting Eqs. (11) and (14) into Eq. (10), one obtains the value of salt concentration inside the membrane on the feed side:

$$c\_{SM} = c\_{SF} \left( 1 + \frac{\nu \mathbf{C}\_{xF}}{c\_{SF}} \right)^{0.5} \tag{15}$$

*R* =*S* 1 −

The balances for the concentration mode can be written as:

*d*(*VFρF* )

*d*(*VF cD*,*F* )

*d*(*VF cS* ,*F* )

*dVF*

*dτ* = − *JV A*\*

Expanded differential equation with using the product rule can be written as:

*i* represent dye and salt. Eq. (21) (or (22)), may be re-written as:

*d*(*VF ci*,*F* )

*dτ* = − *J A*\*

*dτ* = − *J A*\*

*dτ* = − *J A*\*

Mass balances of dye and salt are formally same and we can solve them together. Subscripts

In the concentration mode, the volume and the concentration in feed depends on the time.

(1 − *Ri*

**1.4. Mathematical modelling of diafiltration**

Donnan equilibrium.

Solvent mass balance:

where *Ri*

Mass balances of dye and salt:

Eq. (20) is possible to write in the form:

is real rejection.

(1 − *σS* )(1 +

*νMSCxF MxcSF*

*αS cSF*

1 − *σS* exp( (*σS* − 1)*JV*

Mathematical model connects together balance equations and solution-diffusion model, which is extended by dependence of salt permeability on the salt concentration in feed and

) 0.5

*βS* ) (19)

http://dx.doi.org/10.5772/50438

143

Nanofiltration Process Efficiency in Liquid Dyes Desalination

*ρP* (20)

*cD*,*P* (21)

*cS* ,*P* (22)

)*ci*,*F* (24)

*dτ* = − *JV A*\* (23)

The expression for *cSM* from Eq. (15) is now used to integrate Eq. (5). In other words, in the presence of Donnan exclusion forces, induced by the impermeable organic ions, the salt transport across the membrane proceeds as if the membrane was exposed to a salt solution having a concentration *cSM* instead of *cSF*. Thus the value of *cSM* and not of *cSF* determines the driving force for the salt passage and should be used as boundary condition during the inte‐ gration of Eq. (1) and Eq. (2).

Then the expression for salt rejection in the presence of retained organic ion can be written as:

$$R\_S = \frac{(1 - \sigma F) - (1 - \sigma) \left(1 + \frac{\nu C\_{\chi F}}{c\_{SF}}\right)^{0.5}}{1 - \sigma F} \tag{16}$$

#### **1.3. Concentration dependence of the solute permeability**

The concentration dependence of the solute permeability was proposed by Schirg and Widmer [16] as an exponential function:

$$P = \alpha \mathfrak{c}\_F \beta \tag{17}$$

where *cF* is the concentration of the permeable component in the feed [g.l-1],

α - coefficient for salt permeability [m.s-1],

β - coefficient for concentration dependence of salt permeability [-].

With introducing of Eq. (17) into Eq. (6), the retention for single electrolyte can be written as:

$$R = 1 - \frac{1 - \sigma}{1 - \sigma \exp\left(\frac{(\sigma - 1)f\_V}{\alpha c\_F \beta}\right)}\tag{18}$$

Similar, with introduction of Eq. (17) into Eq. (16), the salt retention for the system with re‐ tained organic ion can be expressed as:

#### Nanofiltration Process Efficiency in Liquid Dyes Desalination http://dx.doi.org/10.5772/50438 143

$$R\_S = 1 - \frac{(1 - \sigma\_S) \left(1 + \frac{\nu M\_S \, \mathrm{C}\_{\mathrm{xF}}}{M\_X \, \mathrm{c}\_{SF}}\right)^{0.5}}{1 - \sigma\_S \exp\left(\frac{(\sigma\_S - 1)f\_V}{\sigma\_S \, \mathrm{c}\_{SF} \, ^{\beta\_S}}\right)}\tag{19}$$

#### **1.4. Mathematical modelling of diafiltration**

Mathematical model connects together balance equations and solution-diffusion model, which is extended by dependence of salt permeability on the salt concentration in feed and Donnan equilibrium.

The balances for the concentration mode can be written as:

Solvent mass balance:

We assume equilibrium on the membrane solution interface, approximating activities with concentrations and substituting Eqs. (11) and (14) into Eq. (10), one obtains the value of salt

> *νCxF cSF* ) 0.5

The expression for *cSM* from Eq. (15) is now used to integrate Eq. (5). In other words, in the presence of Donnan exclusion forces, induced by the impermeable organic ions, the salt transport across the membrane proceeds as if the membrane was exposed to a salt solution having a concentration *cSM* instead of *cSF*. Thus the value of *cSM* and not of *cSF* determines the driving force for the salt passage and should be used as boundary condition during the inte‐

Then the expression for salt rejection in the presence of retained organic ion can be written

1 − *σF*

The concentration dependence of the solute permeability was proposed by Schirg and

With introducing of Eq. (17) into Eq. (6), the retention for single electrolyte can be written as:

1 − *σ*exp( (*σ* − 1)*JV*

Similar, with introduction of Eq. (17) into Eq. (16), the salt retention for the system with re‐

*νCxF cSF* ) 0.5

*P* = *αcF β* (17)

*αcF β* ) (18)

(1 − *σF* ) − (1 − *σ*)(1 +

where *cF* is the concentration of the permeable component in the feed [g.l-1],

*R* = 1 − 1 − *σ*

β - coefficient for concentration dependence of salt permeability [-].

(15)

(16)

*cSM* = *cSF* (1 +

concentration inside the membrane on the feed side:

*RS* =

**1.3. Concentration dependence of the solute permeability**

Widmer [16] as an exponential function:

α - coefficient for salt permeability [m.s-1],

tained organic ion can be expressed as:

gration of Eq. (1) and Eq. (2).

as:

142 Advancing Desalination

$$\frac{d\left(V\_F \rho\_F\right)}{d\tau} = -JA^\* \rho\_F \tag{20}$$

Mass balances of dye and salt:

$$\frac{d\left(V\_F c\_{D,F}\right)}{d\tau} = -\left[A\stackrel{\*}{c}\_{D,P}\right] \tag{21}$$

$$\frac{d\left(V\_{F}c\_{S,F}\right)}{d\tau} = -JA^\*c\_{S,P} \tag{22}$$

Eq. (20) is possible to write in the form:

$$\frac{dV\_F}{d\tau} = -J\_V A^\* \tag{23}$$

Mass balances of dye and salt are formally same and we can solve them together. Subscripts *i* represent dye and salt. Eq. (21) (or (22)), may be re-written as:

$$\frac{d\left(V\_F c\_{i\_{.F}}\right)}{d\tau} = -J\_V A \, ^\ast (1 - R\_i) c\_{i,F} \tag{24}$$

where *Ri* is real rejection.

In the concentration mode, the volume and the concentration in feed depends on the time. Expanded differential equation with using the product rule can be written as:

$$V\_F \frac{d c\_{i\_{,F}}}{d \tau} + c\_{i\_{,F}} \frac{d V\_F}{d \tau} = -J\_V A^\* \langle 1 - R\_i \rangle c\_{i,F} \tag{25}$$

Substituting Eq. (23) into Eq. (25) leads to:

$$V\_F \frac{d c\_{i,F}}{d \tau} = J\_V A \stackrel{\*}{\ast} \mathbb{R}\_i c\_{i,F} \tag{26}$$

*JS* = *B*(*cF* − *cP*) (31)

Nanofiltration Process Efficiency in Liquid Dyes Desalination

http://dx.doi.org/10.5772/50438

) (34)

(*cS* ,*W* − *cS* ,*P*) (35)

(32)

145

(33)

(36)

*cP* = *JS JV*

*B* = *α*( *cS* ,*F*

*cS* ,*W* = *cS* ,*F* (1 +

*JS* = *α*( *cS* ,*F*

*α cS* ,*F β*+1 *c* \**β* (1 +

and then salt concentration in permeate can be expressed as

*cS* ,*P* =

For the permeate flux these equations can be used:

*c* \* ) *β*

*JV* + *αcS* ,*F*

Eq. (37) is the osmotic pressure model. This model is used in similar form by many authors [5,10,12-14,17,18]. Parameter A (water permeability) can be concentration or viscous de‐

be 1 g/l.

as:

activities with concentrations) [17]:

mines the driving force for the salt passage.

This model can be extended by the dependence of salt permeability on salt concentration in the feed [17]. To avoid some in conveniences with units, here c\* is introduced and chosen to

> *c* \* ) *β*

Assuming equilibrium on the membrane - solution interface we can obtain (approximating

In the presence of Donnan exclusion forces, induced by the impermeable organic ions, the salt transport across the membrane proceeds as if the membrane were exposed to a salt solu‐ tion having concentration cS,W instead cS,F. Thus the value of cS,W and not that of cS,F deter‐

Then the expression for salt passage in the presence of retained organic ion can be written

*νD*.*cD*,*F* .*MS cS* ,*F* .*MD*

*β c* \*−*β*

)

*JV* = *A*(*ΔP* − *Δπs* − *δ*) (37)

*νD*.*cD*,*F* .*MS cS* ,*F* .*MD*

Dividing Eq. (26) by Eq. (23) leads to:

$$\mathbf{c}\_{i,F} = \mathbf{c}\_{i,F} \left(\frac{\mathbf{V}\_{F0}}{\mathbf{V}\_F}\right)^{\mathbf{R}\_i} \tag{27}$$

If we assume constant rejection and permeate flux (for small change of volume in feed tank, or better of yield - permeate volume divided by feed volume, it is achieved) or the average values integrations of Eq. (27) and Eq. (23) with the boundary conditions (VF0 to VF) result‐ ing in Eq. (28) and Eq. (29):

$$\mathcal{L}\_{i,F} = \mathcal{L}\_{i,F0} \left(\frac{V\_{F0}}{\overline{V}\_F}\right)^{R\_i} \tag{28}$$

$$
\tau = \frac{V\_{R0} - V\_R}{f\_V A^\*} \tag{29}
$$

On the base of Eq. (28) and Eq. (29) we can obtain the concentration in feed tank and the time for separation of certain permeate volume in concentration mode, respectively. Next process is diluting. Pure solvent (water) is used as diluant. Salt concentration in feed tank after this operation (cS´) is:

$$c\_S' = c\_{i,F0} \left(\frac{V\_F}{V\_{F0}}\right) \tag{30}$$

This concentration (cS´) is now equal to the salt concentration in feed tank (cS,F0) for the next concentration mode in the second diafiltration step.

For solving of these equations we need to know dependence of rejection and permeate flux on salt concentration in feed.

The basic equations for rejection can be written as:

Nanofiltration Process Efficiency in Liquid Dyes Desalination http://dx.doi.org/10.5772/50438 145

$$J\_S = B \left( c\_F - c\_P \right) \tag{31}$$

$$c\_P = \frac{J\_S}{J\_V} \tag{32}$$

This model can be extended by the dependence of salt permeability on salt concentration in the feed [17]. To avoid some in conveniences with units, here c\* is introduced and chosen to be 1 g/l.

$$B = \alpha \left(\frac{c\_{S,F}}{c^\*}\right)^{\beta} \tag{33}$$

Assuming equilibrium on the membrane - solution interface we can obtain (approximating activities with concentrations) [17]:

$$c\_{S,W} = c\_{S,F} \left( 1 + \frac{\nu\_D \mathcal{L}\_{D,F} \, M\_S}{c\_{S,F} \, M\_D} \right) \tag{34}$$

In the presence of Donnan exclusion forces, induced by the impermeable organic ions, the salt transport across the membrane proceeds as if the membrane were exposed to a salt solu‐ tion having concentration cS,W instead cS,F. Thus the value of cS,W and not that of cS,F deter‐ mines the driving force for the salt passage.

Then the expression for salt passage in the presence of retained organic ion can be written as:

$$J\_S = \alpha \left(\frac{c\_{S,F}}{c^\*}\right)^\beta \left(c\_{S,W} - c\_{S,P}\right) \tag{35}$$

and then salt concentration in permeate can be expressed as

$$c\_{S,P} = \frac{\alpha \frac{c\_{S,F}^{\beta+1}}{c^{\ast\beta}} \left(1 + \frac{\nu\_D \cdot c\_{D,F} \cdot \mathcal{M}\_S}{c\_{S,F} \cdot \mathcal{M}\_D} \right)}{J\_V + \alpha c\_{S,F}^{\beta} c^{\ast\beta}} \tag{36}$$

For the permeate flux these equations can be used:

*VF*

Substituting Eq. (23) into Eq. (25) leads to:

144 Advancing Desalination

Dividing Eq. (26) by Eq. (23) leads to:

ing in Eq. (28) and Eq. (29):

after this operation (cS´) is:

on salt concentration in feed.

*dci*,*F dτ*

+ *ci*,*F*

*VF dci*,*F*

*dVF*

*dτ* = − *JV A*\*

*dτ* = *JV A*\*

*ci*,*F* = *ci*,*F* 0( *VF* 0

*ci*,*F* = *ci*,*F* 0( *VF* 0

*τ* = *V R*0 − *VR*

, = *ci*,*F* 0( *VF*

*cS*

concentration mode in the second diafiltration step.

The basic equations for rejection can be written as:

*VF* ) *Ri*

If we assume constant rejection and permeate flux (for small change of volume in feed tank, or better of yield - permeate volume divided by feed volume, it is achieved) or the average values integrations of Eq. (27) and Eq. (23) with the boundary conditions (VF0 to VF) result‐

> *VF* ) *Ri*

On the base of Eq. (28) and Eq. (29) we can obtain the concentration in feed tank and the time for separation of certain permeate volume in concentration mode, respectively. Next process is diluting. Pure solvent (water) is used as diluant. Salt concentration in feed tank

*VF* 0

This concentration (cS´) is now equal to the salt concentration in feed tank (cS,F0) for the next

For solving of these equations we need to know dependence of rejection and permeate flux

*Ri*

(1 − *Ri*

)*ci*,*F* (25)

(27)

(28)

*ci*,*F* (26)

*JV A*\* (29)

) (30)

$$J\_V = A \{ \Delta P - \Delta \pi\_s - \delta \}\tag{37}$$

Eq. (37) is the osmotic pressure model. This model is used in similar form by many authors [5,10,12-14,17,18]. Parameter A (water permeability) can be concentration or viscous de‐ pended [12,14]. For our model we assume this parameter as constant. Coefficient δ repre‐ sents the effect of dye on flux. This means mainly osmotic pressure of dye. If this parameter represents only osmotic pressure of dye, then it is constant too (constant dye concentration).

The osmotic pressure gradient for salt is related to the difference of the concentration Δc by the van´t Hoff law:

$$
\Delta \pi\_{\rm S} = \frac{\nu \mathcal{R}^\* T}{M} \Delta c\_{\rm S} \tag{38}
$$

**1.5. Characterization of membranes**

feed solution to pure water [12].

**1.6. Comparison of membranes**

where *c0*

*D*, *c0*

Before diafiltration experiments characterizations of commercial membranes are carried out. For these characterizations pure water and water solutions of salt are used. From experi‐ ments with pure water model parameter *A* (water permeability) can be estimated. This pa‐ rameter is slope of the curve (straight line) J = f (ΔP) (see Eq. (37) and Δπ = δ =0 because no salt and dye are used). In our model we assume water permeability as constant. However, an increase in concentration can cause significant changes in viscosity and a consequent modification of the water permeability. According to resistance model (A = 1/(μ RM)) the de‐

Nanofiltration Process Efficiency in Liquid Dyes Desalination

http://dx.doi.org/10.5772/50438

*Aμ* = *A μREL*

where *A* is the water permeability respect to pure water and *μREL* is the relative viscosity of

In case of diafiltration fouling or gel layer effects can occur and then parameter A is depend‐ ed on dye/salt concentration ratio (in resistance model is added next resistance A=1/μREL (RM

Similar experiments are made with salt solutions. Four salt concentrations (1, 5, 10 and 35 g/l) are used. From these experiments can be obtained parameter B (salt permeability) and then α and β (plotting B versus cF). Values obtained from these experiments are not used direct but are used as first approximation values for best fit parameters (see Table 3). From results (salt rejection and flux) the suitable membranes for desalination were chosen, Desal 5DK, NF 70, NF 270 and TR 60. Membranes NF 90 and Esna 1 had higher rejection (see Fig‐

ure 4). For desalination, than membrane with small rejection of salt are suitable.

*S* =

*cD cD* 0 *cS cS* 0

= *cDcS* 0

*cD* 0 *cS*

*S* are concentrations of dye and salt at the beginning of experiment, *cD, cS* are

(39)

147

(40)

pendence of water permeability on viscosity can be expressed as:

+RF), where RM and RF are membrane and fouling resistance [14].

For comparison of membranes, three factors were used.

concentrations of dye and salt in the end of experiment.

The first factor is separation factor of diafiltration, *S*:

where *c* is concentration,

*J* - flux,

subscripts

#### **1.5. Characterization of membranes**

pended [12,14]. For our model we assume this parameter as constant. Coefficient δ repre‐ sents the effect of dye on flux. This means mainly osmotic pressure of dye. If this parameter represents only osmotic pressure of dye, then it is constant too (constant dye concentration).

The osmotic pressure gradient for salt is related to the difference of the concentration Δc by

*T*

*M ΔcS* (38)

*ΔπS* = *νR* \*

the van´t Hoff law:

146 Advancing Desalination

where *c* is concentration,

*A\** - membrane area,

*B* - salt permeability,

*J* - flux,

*R* - rejection,

subscripts

S - salt

D - dye

V - water

F - feed

P - permeate

R - retentate

W - membrane interface (wall)

0 - beginning of the concentration mode

*A* - water permeability,

*R\** - universal gas constant,

*M* - relative molecular mass,

σ - reflection coefficient

δ - coefficient for dye solution,

*α* - coefficient for salt permeability,

*ν* - valence (for NaCl is ν = 2 and for dye ν = 3).

β - coefficient for concentration dependence of salt permeability

Before diafiltration experiments characterizations of commercial membranes are carried out. For these characterizations pure water and water solutions of salt are used. From experi‐ ments with pure water model parameter *A* (water permeability) can be estimated. This pa‐ rameter is slope of the curve (straight line) J = f (ΔP) (see Eq. (37) and Δπ = δ =0 because no salt and dye are used). In our model we assume water permeability as constant. However, an increase in concentration can cause significant changes in viscosity and a consequent modification of the water permeability. According to resistance model (A = 1/(μ RM)) the de‐ pendence of water permeability on viscosity can be expressed as:

$$A\_{\mu} = \frac{A}{\mu\_{REL}}\tag{39}$$

where *A* is the water permeability respect to pure water and *μREL* is the relative viscosity of feed solution to pure water [12].

In case of diafiltration fouling or gel layer effects can occur and then parameter A is depend‐ ed on dye/salt concentration ratio (in resistance model is added next resistance A=1/μREL (RM +RF), where RM and RF are membrane and fouling resistance [14].

Similar experiments are made with salt solutions. Four salt concentrations (1, 5, 10 and 35 g/l) are used. From these experiments can be obtained parameter B (salt permeability) and then α and β (plotting B versus cF). Values obtained from these experiments are not used direct but are used as first approximation values for best fit parameters (see Table 3). From results (salt rejection and flux) the suitable membranes for desalination were chosen, Desal 5DK, NF 70, NF 270 and TR 60. Membranes NF 90 and Esna 1 had higher rejection (see Fig‐ ure 4). For desalination, than membrane with small rejection of salt are suitable.

#### **1.6. Comparison of membranes**

For comparison of membranes, three factors were used.

The first factor is separation factor of diafiltration, *S*:

$$S = \frac{\frac{c\_D}{c\_D^0}}{\frac{c\_S}{c\_S^0}} = \frac{c\_D c\_S^0}{c\_D^0 c\_S} \tag{40}$$

where *c0 D*, *c0 S* are concentrations of dye and salt at the beginning of experiment, *cD, cS* are concentrations of dye and salt in the end of experiment.

The separation factor, *S*, represents how well the dye will be desalinated. With higher sepa‐ ration factor the dye desalination is better. But it is also clear that with bigger separation fac‐ tor the loss of the dye will be bigger because real membranes have not 100% rejection of dye.

The dye loss factor, *Z*, can be defined as the rates of amount of the dye in permeate to amount of the dye at the beginning of experiment:

$$Z = \frac{V\left(c\_D^0 - c\_D\right)}{Vc\_D^0} = 1 - \frac{c\_D}{c\_D^0} \tag{41}$$

**2.2. Materials**

**Figure 2.** Structural formula of dye (free acid).

maintained by cooling system (7).

ments were analysed using potentiometric titration.

**2.3. Experimental system**

**2.4. Analytical methods**

**2.5. Separation procedure**

Dye was obtained from VÚOS a.s. Pardubice, Czech Republic. The commercial name is Re‐ active Orange 35, and a molecular weight is 748.2 Da in free acid form (three acidic groups) or 817.2 Da as the sodium salt. Figure 2 shows structural formula of the free acid form.

Nanofiltration Process Efficiency in Liquid Dyes Desalination

http://dx.doi.org/10.5772/50438

149

NaCl and MgSO4 used for all experiments were analytical grade. The demineralised water

Experiments were carried out on system depicted schematically on Figure 3. Feed (F) was pumped by pump (3) (Wanner Engineering, Inc., type Hydracell G13) from feed vessel (2) to membrane module (1). Pressure was set by valve (4) placed behind membrane module. Per‐ meate (P) and retentate (R) were brought back to feed vessel. Pressure was measured by manometer (5). Temperature was detected by thermometer (6). Stable temperature was

Dye concentrations were analysed using a spectrophotometer (SPECOL 11). NaCl and MgSO4 concentrations were calculated from conductivity measurements using a conductivi‐ ty meter (Cond 340i). Permeate and retentate salt concentrations during diafiltration experi‐

The system was operated in the full recirculation mode while both retentate and permeate were continuously recirculated to the feed tank except sampling and concentration mode of diafiltration. By changing applied pressure (from 5 to 30 bar) and concentration of salt (1, 5, 10 and 35 g/l) in characterization of membranes both the retentate and permeate were re‐ turned back to the feed tank for 0.5 h or 10 min, respectively to reach a steady state before sampling. Before first concentration mode in diafiltraton experiments and after each diluting mode the total recirculation was used 1h and minimally 5 min, respectively. The permeate

flux was measured by weighing of certain permeate volume and using a stopwatch.

with the conductivity between 4-15 μS/cm was used in this study.

The third parameter is time of diafiltration needed to reach certain separation factor, *S*. The total time of diafiltration with n steps, *τ*, can be expressed (constant permeate flux in each concentration mode) as:

$$
\pi\_{\text{total}} = \sum\_{i=1}^{n} \frac{\Delta V}{\mathbf{Q}} = \sum\_{i=1}^{n} \frac{V\_{F0} - V\_F}{AJ} \tag{42}
$$

where *Q* is flow of permeate.

#### **2. Methods**

#### **2.1. Membranes**

Eight NF membranes were chosen for this study. Properties of membranes used are given in Table 1.

**Table 1.** Properties of the membranes used.

#### **2.2. Materials**

The separation factor, *S*, represents how well the dye will be desalinated. With higher sepa‐ ration factor the dye desalination is better. But it is also clear that with bigger separation fac‐ tor the loss of the dye will be bigger because real membranes have not 100% rejection of dye.

The dye loss factor, *Z*, can be defined as the rates of amount of the dye in permeate to

0 = 1 − *cD*

The third parameter is time of diafiltration needed to reach certain separation factor, *S*. The total time of diafiltration with n steps, *τ*, can be expressed (constant permeate flux in each

Eight NF membranes were chosen for this study. Properties of membranes used are given in

**Indication Type Producer MWCO [Da] Material Module** Desal 5DK Desal 5DK GEW & PT 200 polyamide spiral-wound Esna 1 Esna 1 Hydranautics 100-300 polyamide spiral-wound NF 270 NF 270 Dow 270 polyamide spiral-wound NF 90 NF 90 Dow 90 polyamide spiral-wound NF 70 CSM NE 2540-70 Saehan 250 polyamide spiral-wound NF 45 NF 45 FILMTEC 100 polyamide spiral-wound TR 60 TR 60 - 2540 Toray 400 polyamide spiral-wound PES 10 PES 10 Hoechst 500-1000 polyether-sulphone spiral-wound

*cD*

*n VF* 0 − *VF*

0 (41)

*AJ* (42)

0 − *cD*) *V cD*

amount of the dye at the beginning of experiment:

concentration mode) as:

148 Advancing Desalination

where *Q* is flow of permeate.

**Table 1.** Properties of the membranes used.

**2. Methods**

**2.1. Membranes**

Table 1.

*Z* = *V* (*cD*

*τtotal* = ∑ *i*=1 *n ΔV Q* = ∑ *i*=1 Dye was obtained from VÚOS a.s. Pardubice, Czech Republic. The commercial name is Re‐ active Orange 35, and a molecular weight is 748.2 Da in free acid form (three acidic groups) or 817.2 Da as the sodium salt. Figure 2 shows structural formula of the free acid form.

NaCl and MgSO4 used for all experiments were analytical grade. The demineralised water with the conductivity between 4-15 μS/cm was used in this study.

**Figure 2.** Structural formula of dye (free acid).

#### **2.3. Experimental system**

Experiments were carried out on system depicted schematically on Figure 3. Feed (F) was pumped by pump (3) (Wanner Engineering, Inc., type Hydracell G13) from feed vessel (2) to membrane module (1). Pressure was set by valve (4) placed behind membrane module. Per‐ meate (P) and retentate (R) were brought back to feed vessel. Pressure was measured by manometer (5). Temperature was detected by thermometer (6). Stable temperature was maintained by cooling system (7).

#### **2.4. Analytical methods**

Dye concentrations were analysed using a spectrophotometer (SPECOL 11). NaCl and MgSO4 concentrations were calculated from conductivity measurements using a conductivi‐ ty meter (Cond 340i). Permeate and retentate salt concentrations during diafiltration experi‐ ments were analysed using potentiometric titration.

#### **2.5. Separation procedure**

The system was operated in the full recirculation mode while both retentate and permeate were continuously recirculated to the feed tank except sampling and concentration mode of diafiltration. By changing applied pressure (from 5 to 30 bar) and concentration of salt (1, 5, 10 and 35 g/l) in characterization of membranes both the retentate and permeate were re‐ turned back to the feed tank for 0.5 h or 10 min, respectively to reach a steady state before sampling. Before first concentration mode in diafiltraton experiments and after each diluting mode the total recirculation was used 1h and minimally 5 min, respectively. The permeate flux was measured by weighing of certain permeate volume and using a stopwatch.

As we can see the water permeability of PES 10 is approximately three times higher than water permeability of other membranes. It can be due to more open structure of this mem‐ brane, which can approach to the UF type. But the opened structure may cause the insuffi‐

Nanofiltration Process Efficiency in Liquid Dyes Desalination

http://dx.doi.org/10.5772/50438

151

Basic membrane characteristics are the dependence of the permeate flux and the salt rejec‐ tion on other operation parameters, i.e. the applied pressure difference and the salt concen‐

The permeate flux increases with increasing pressure and decreases as the feed concentra‐ tion of salt increases. For the lowest concentration of salt (1 g/l), the values of permeate flux were similar to the values of clean water. The lower values of permeate flux were obtained with the increasing salt concentrations in feed (increasing osmotic pressure). For membrane NF 90 fluxes were not measured at the highest salt concentration for pressure smaller than 25 bar, because the osmotic pressure was too high. Opposite problem was with membrane NF 270 at the smallest salt concentration in feed. The permeate flux was too high and pump was not able to deliver necessary volumetric flow of retentate (600 l/h) for constant condi‐

The observed rejection increases as the pressure difference increases, and decreases with the increasing salt concentration in feed for all tested membranes. However, the minimal values were obtained during experiments with membrane NF 270. Low values of the salt rejection and higher values of the permeate flux are suitable for desalting. Figure 4 shows the com‐ parison of tested membranes for the lowest (1 g/l) and the highest salt concentrations in feed

**Figure 4.** Permeate flux and rejection as a function of pressure for the lowest salt concentration; (1 g/l) - left figures

cient retention of the dye in the case of the dye-salt separation.

**3.2. Flux and salt rejection in single salt solutions**

tration in feed.

tions at all experiments.

(35 g/l), respectively.

and the highest salt concentration (35 g/l) - right figures.

**Figure 3.** Schematic diagram of the experimental set-up used: 1 membrane module, 2 feed vessel, 3 high pressure pump, 4 back pressure valve, 5 manometer, 6 temperature controller, 7 cooling system, 8 cooling water input, 9 cool‐ ing water output, F feed, P permeate, R retentate (concentrate).

#### **3. Results and discussions**

#### **3.1. Pure water flux**

Water permeability is one of the basic characteristic of NF membranes. The pure water per‐ meability of the eight membranes was determined by measuring the deionized water flux at different operating pressures. According to Darcy´s law, the permeate flux is directly pro‐ portional to the pressure difference across the membrane. The slope of this line corresponds to the water permeability (A).

**Table 2.** Water permeability of membranes used.

As we can see the water permeability of PES 10 is approximately three times higher than water permeability of other membranes. It can be due to more open structure of this mem‐ brane, which can approach to the UF type. But the opened structure may cause the insuffi‐ cient retention of the dye in the case of the dye-salt separation.

#### **3.2. Flux and salt rejection in single salt solutions**

**Figure 3.** Schematic diagram of the experimental set-up used: 1 membrane module, 2 feed vessel, 3 high pressure pump, 4 back pressure valve, 5 manometer, 6 temperature controller, 7 cooling system, 8 cooling water input, 9 cool‐

Water permeability is one of the basic characteristic of NF membranes. The pure water per‐ meability of the eight membranes was determined by measuring the deionized water flux at different operating pressures. According to Darcy´s law, the permeate flux is directly pro‐ portional to the pressure difference across the membrane. The slope of this line corresponds

> **Membrane A [l/m2.h.bar]** Desal 5DK 3.365 Esna 1 4.824 NF 90 5.845 NF 270 6.801 NF 70 2.650 NF 45 3.184 TR 60 3.952 PES 10 12.583

ing water output, F feed, P permeate, R retentate (concentrate).

**3. Results and discussions**

to the water permeability (A).

**Table 2.** Water permeability of membranes used.

**3.1. Pure water flux**

150 Advancing Desalination

Basic membrane characteristics are the dependence of the permeate flux and the salt rejec‐ tion on other operation parameters, i.e. the applied pressure difference and the salt concen‐ tration in feed.

The permeate flux increases with increasing pressure and decreases as the feed concentra‐ tion of salt increases. For the lowest concentration of salt (1 g/l), the values of permeate flux were similar to the values of clean water. The lower values of permeate flux were obtained with the increasing salt concentrations in feed (increasing osmotic pressure). For membrane NF 90 fluxes were not measured at the highest salt concentration for pressure smaller than 25 bar, because the osmotic pressure was too high. Opposite problem was with membrane NF 270 at the smallest salt concentration in feed. The permeate flux was too high and pump was not able to deliver necessary volumetric flow of retentate (600 l/h) for constant condi‐ tions at all experiments.

The observed rejection increases as the pressure difference increases, and decreases with the increasing salt concentration in feed for all tested membranes. However, the minimal values were obtained during experiments with membrane NF 270. Low values of the salt rejection and higher values of the permeate flux are suitable for desalting. Figure 4 shows the com‐ parison of tested membranes for the lowest (1 g/l) and the highest salt concentrations in feed (35 g/l), respectively.

**Figure 4.** Permeate flux and rejection as a function of pressure for the lowest salt concentration; (1 g/l) - left figures and the highest salt concentration (35 g/l) - right figures.

Figure 5 denote dependence of the transmembrane pressure on the flux for NaCl solutions with the various salt contents. As we can see this dependence for every salt concentration shows a straight line course. Thus we can assume that the concentration polarization has no significant influence and therefore we can consider the bulk concentration equal to that on the membrane [20], which is required in model equations.

tion attainable on given membrane (at the lowest concentration and the highest pressure). The parameter *β* express the concentration dependence of the salt permeability. The ana‐ lyzation of experimental data for separation of MgSO4 by Spiegler-Kedem model is less in‐

Nanofiltration Process Efficiency in Liquid Dyes Desalination

http://dx.doi.org/10.5772/50438

153

The aim of these experiments was to find dependence of salt and dye rejections on the salt and dye concentration. In every experiment carried out in this work the dye rejection was sufficient high and almost equal unity. The lowest value of the dye rejection observed was 0.9988. The salt rejection as a function of the dye and salt concentration is plotted in follow‐

It can be seen from Figure 6 that the salt rejection decreases with decreasing salt concentra‐ tion and with increasing dye concentration, corresponding to Donnan equilibrium (Eq. 15). In the case of solution without the dye or with low dye content (positive rejections) we can observe the typical decline of salt rejection with increasing salt concentration. At higher dye content we can observe increase of salt rejection with increasing salt concentration due to

It's obvious from Figure 7 that salt content has also a strong influence on the flux. In the case of single salt solution (without dye content) we can see a typical decrease of flux with in‐ creasing salt content. In the case of mixed dye-salt solutions we can observe initial increase of flux and following decrease after a maximum was reached. The initial increase of flux at high dye concentration and low salt concentration is due to negative rejection (see Figure 6), which causes the reverse osmotic pressure difference between permeate and feed side of the membrane (*Δπ>0)*. This reverse osmosis pressure difference escalates the driving force of the

The experimental dependence of the salt rejection on flux can be evaluated by extended Spiegler-Kedem model (Figure 8) in order to obtained parameters *σNaCl, αNaCl* and *βNaCl*. These parameters are characteristic for the transport of NaCl through given membrane and also characteristic for given dye in feed solution dye. The meaning of individual parameters is

Figure 8 depicted the experimental dependence of the salt rejection on the flux. The single curves represent course of the salt rejection as a function of the flux for given dye content in the feed. The pressure difference was kept constant during all experiments and flux was changed by changing of salt content in the feed (changing of osmotic pressure difference). It can be seen from Figure 8 that extended Spiegler-Kedem model isn't able to evaluate rejec‐ tion-flux data as accurately as it was in the case of the single salt transport. But realising the

We can see that the coefficient *α* is approximately four times higher than in the case of the separation of single NaCl solution, which reflect the fact that the presence of the dye escalate

range of rejection values we can consider prediction by this model still sufficient.

teresting because except PES 10 all membranes showed rejection almost equal unity.

**3.3. Flux, salt and dye rejection in mixed dye - salt solutions**

ing Figure 6.

shifting of Donnan equilibrium.

process (Eq. 1) thus flux increases.

the same as in the case of the single salt transport.

the salt permeability through the membrane.

**Figure 5.** Flux as a function of transmembrane pressure for NaCl solutions with various salt content (Desal 5DK).

Experimental data rejection-flux can be evaluated by extended Spiegler-Kedem model to ob‐ tain parameters *σ*, *α* and *β*.

**Table 3.** Coefficients of extended Spiegler-Kedem model for the transport of NaCl for various membranes.

The membrane PES 10 was not involved into Table 3 because this membrane didn't show typical course of the rejection-flux dependence. These differences are caused by another na‐ ture of this membrane near the UF type and therefore the transport through this membrane cannot be described by Spiegler-Kedem model.

On the Table 3 we can see that the water permeability and the salt permeability show the same trend for various membranes (*LP* and *α*). The parameter *σ* means the maximum rejec‐ tion attainable on given membrane (at the lowest concentration and the highest pressure). The parameter *β* express the concentration dependence of the salt permeability. The ana‐ lyzation of experimental data for separation of MgSO4 by Spiegler-Kedem model is less in‐ teresting because except PES 10 all membranes showed rejection almost equal unity.

#### **3.3. Flux, salt and dye rejection in mixed dye - salt solutions**

Figure 5 denote dependence of the transmembrane pressure on the flux for NaCl solutions with the various salt contents. As we can see this dependence for every salt concentration shows a straight line course. Thus we can assume that the concentration polarization has no significant influence and therefore we can consider the bulk concentration equal to that on

**Figure 5.** Flux as a function of transmembrane pressure for NaCl solutions with various salt content (Desal 5DK).

**Membrane LP [m.s-1.Pa-1]** σ **[-]** α **[m.s-1]** β **[-]** Desal 5DK 9.35.10-12 0.824 1.96.10-6 0.438 Esna 1 1.34.10-11 0.594 1.60.10-6 0.620 NF 90 1.62.10-11 0.685 4.39.10-6 0.266 NF 270 1.89.10-11 0.723 2.88.10-6 0.529 NF 70 7.36.10-12 0.598 1.34.10-6 0.381 TR 60 1.10.10-11 0.583 1.86.10-6 0.474

**Table 3.** Coefficients of extended Spiegler-Kedem model for the transport of NaCl for various membranes.

The membrane PES 10 was not involved into Table 3 because this membrane didn't show typical course of the rejection-flux dependence. These differences are caused by another na‐ ture of this membrane near the UF type and therefore the transport through this membrane

On the Table 3 we can see that the water permeability and the salt permeability show the same trend for various membranes (*LP* and *α*). The parameter *σ* means the maximum rejec‐

Experimental data rejection-flux can be evaluated by extended Spiegler-Kedem model to ob‐

the membrane [20], which is required in model equations.

tain parameters *σ*, *α* and *β*.

152 Advancing Desalination

cannot be described by Spiegler-Kedem model.

The aim of these experiments was to find dependence of salt and dye rejections on the salt and dye concentration. In every experiment carried out in this work the dye rejection was sufficient high and almost equal unity. The lowest value of the dye rejection observed was 0.9988. The salt rejection as a function of the dye and salt concentration is plotted in follow‐ ing Figure 6.

It can be seen from Figure 6 that the salt rejection decreases with decreasing salt concentra‐ tion and with increasing dye concentration, corresponding to Donnan equilibrium (Eq. 15).

In the case of solution without the dye or with low dye content (positive rejections) we can observe the typical decline of salt rejection with increasing salt concentration. At higher dye content we can observe increase of salt rejection with increasing salt concentration due to shifting of Donnan equilibrium.

It's obvious from Figure 7 that salt content has also a strong influence on the flux. In the case of single salt solution (without dye content) we can see a typical decrease of flux with in‐ creasing salt content. In the case of mixed dye-salt solutions we can observe initial increase of flux and following decrease after a maximum was reached. The initial increase of flux at high dye concentration and low salt concentration is due to negative rejection (see Figure 6), which causes the reverse osmotic pressure difference between permeate and feed side of the membrane (*Δπ>0)*. This reverse osmosis pressure difference escalates the driving force of the process (Eq. 1) thus flux increases.

The experimental dependence of the salt rejection on flux can be evaluated by extended Spiegler-Kedem model (Figure 8) in order to obtained parameters *σNaCl, αNaCl* and *βNaCl*. These parameters are characteristic for the transport of NaCl through given membrane and also characteristic for given dye in feed solution dye. The meaning of individual parameters is the same as in the case of the single salt transport.

Figure 8 depicted the experimental dependence of the salt rejection on the flux. The single curves represent course of the salt rejection as a function of the flux for given dye content in the feed. The pressure difference was kept constant during all experiments and flux was changed by changing of salt content in the feed (changing of osmotic pressure difference).

It can be seen from Figure 8 that extended Spiegler-Kedem model isn't able to evaluate rejec‐ tion-flux data as accurately as it was in the case of the single salt transport. But realising the range of rejection values we can consider prediction by this model still sufficient.

We can see that the coefficient *α* is approximately four times higher than in the case of the separation of single NaCl solution, which reflect the fact that the presence of the dye escalate the salt permeability through the membrane.

**Figure 9.** Comparison of rejection-NaCl concentration dependence for various membranes at dye concentration 100

Nanofiltration Process Efficiency in Liquid Dyes Desalination

http://dx.doi.org/10.5772/50438

155

The comparison with another membranes was carried out in order to determine the most suitable one of given membranes. As we can see at Figure 9 membranes Desal 5DK and PES 10 have the best course of dependence of salt rejection as a function of concentration but PES 10 shows the highest flux (Figure 10). Among given membranes PES 10 is therefore the most

**Figure 10.** Comparison of flux-NaCl concentration dependence for various membranes at dye concentration 100 g.l-1

The concentration of macrosolutes by batch NF is frequently accompanied by a diafiltration step to remove microsolutes such as salts. Batch diafiltration with periodically adding sol‐ vent at 20 bars and constant retentate flow 600 l/h was provided. Aqueous dye solutions with dye concentrations 100, 50 and 10 g/l and salt concentration between 20-23 g/l were de‐ salted at 23 C. Volume of the pure solvent added in every dilute mode was 4l (the same vol‐ ume of permeate was remove before in concentration mode). Total feed volume in tank was 52l. For every membrane and every concentration of the dye in feed fifty diafiltration steps were made. One point in Figures 11-14 is one diafiltration step before concentration mode.

g.l-1 (1.5 MPa).

(1.5 MPa).

**3.4. Diafiltration**

suitable membrane for desalination of this dye.

**Figure 6.** Salt rejection as a function of salt concentration for different dye concentration (Desal 5DK; 1.5MPa).

**Figure 7.** Flux as a function of salt concentration for different dye concentration (Desal 5DK).

**Figure 8.** Salt rejection as a function of flux for different dye concentration (Desal 5DK; 1.5 MPa); σΝaCl*=0.880;* αΝaCl*=5.38.10-6* and βΝaCl*=0.623*.

**Figure 9.** Comparison of rejection-NaCl concentration dependence for various membranes at dye concentration 100 g.l-1 (1.5 MPa).

The comparison with another membranes was carried out in order to determine the most suitable one of given membranes. As we can see at Figure 9 membranes Desal 5DK and PES 10 have the best course of dependence of salt rejection as a function of concentration but PES 10 shows the highest flux (Figure 10). Among given membranes PES 10 is therefore the most suitable membrane for desalination of this dye.

**Figure 10.** Comparison of flux-NaCl concentration dependence for various membranes at dye concentration 100 g.l-1 (1.5 MPa).

#### **3.4. Diafiltration**

**Figure 6.** Salt rejection as a function of salt concentration for different dye concentration (Desal 5DK; 1.5MPa).

**Figure 7.** Flux as a function of salt concentration for different dye concentration (Desal 5DK).

αΝaCl*=5.38.10-6* and βΝaCl*=0.623*.

154 Advancing Desalination

**Figure 8.** Salt rejection as a function of flux for different dye concentration (Desal 5DK; 1.5 MPa); σΝaCl*=0.880;*

The concentration of macrosolutes by batch NF is frequently accompanied by a diafiltration step to remove microsolutes such as salts. Batch diafiltration with periodically adding sol‐ vent at 20 bars and constant retentate flow 600 l/h was provided. Aqueous dye solutions with dye concentrations 100, 50 and 10 g/l and salt concentration between 20-23 g/l were de‐ salted at 23 C. Volume of the pure solvent added in every dilute mode was 4l (the same vol‐ ume of permeate was remove before in concentration mode). Total feed volume in tank was 52l. For every membrane and every concentration of the dye in feed fifty diafiltration steps were made. One point in Figures 11-14 is one diafiltration step before concentration mode.

Four membranes only - Desal 5DK, NF 70, NF 270 and TR 60 - were used for diafiltration experiments. Diafiltration with membrane NF 270 was provided only with dye concentra‐ tions 100 and 50 g/l and with membrane TR 60 only at the highest dye concentration, which is the best for desalination. For the reason of low values of permeate flux, membrane NF 90 and Esna 1 were not used for those experiments.

The comparisons of experimental and model data for the highest dye concentration (100 g/l) are shown in Figure 14. Salt concentrations are calculated using Eq. (28) and Eq. (30). Rejec‐ tion needed for these equations is calculated on basis of Eq. (36). Best fit parameters for pro‐

Nanofiltration Process Efficiency in Liquid Dyes Desalination

http://dx.doi.org/10.5772/50438

157

From Table 4 can be shown that δ is not only osmotic pressure (if we assume water permea‐ bility as constant), because the values of δ are different. From these results we can assume, the highest effect of dye on flux is for membrane NF 270. This membrane is the most fouled from these membranes. It is appropriate assumed the change in water permeability (A) in

In our experiments, the decrease of permeate flux was mainly caused by the effect of con‐ centration polarization and the increase of the viscosity of dye solution. The dye formed a boundary layer over the membrane surface (concentration polarization) and consequently, increased the resistance against the water flux through the membrane. At the same time, the

From Figure 14 can be shown that the experimental results in permeate fit the model very well. Due to considerably low salt concentrations in permeate, concentration polarization was minimized. The diafiltration process benefits to obtain pure salt product and this can be predicted by a mathematic model on the basis of description of discontinuous diafiltration

posed model are given in Table 4.

case of desalination of dyes.

viscosity of solution increased with higher concentration.

by periodically adding solvent at constant pressure difference.

**Figure 12.** Permeate flux as a function of salt concentration in feed.

Dependences of rejection on salt concentration in feed are given in Figure 11 for Desal 5DK, NF 70, NF 270 and TR 60, respectively. Membranes are compared at dye concentration 100 g/l. The lowest values of rejection (max. 0.29) were obtained for membrane Desal 5DK. The membrane NF 70 had the highest values.

Dependences of flux on salt concentrations are shown in Figure 12. The highest values of flux (70.3 l/m2 .h) were obtained in experiments with membrane NF 270. The permeate flux decreased while salt concentration increased. This is due to the effect of osmotic pressure along with the concentration polarization. Due to the concentration polarization phenomen‐ on, the osmotic pressure of the aqueous solution adjacent to the membrane active layer is higher than the corresponding value of the feed solution. As a result, the osmotic pressure would increase dramatically while the salt concentration increased.

In Figure 13 dependences of salt concentrations on time of diafiltration are shown.

**Figure 11.** Salt rejection as a function of salt concentration in feed

**Table 4.** Model parameters.

The comparisons of experimental and model data for the highest dye concentration (100 g/l) are shown in Figure 14. Salt concentrations are calculated using Eq. (28) and Eq. (30). Rejec‐ tion needed for these equations is calculated on basis of Eq. (36). Best fit parameters for pro‐ posed model are given in Table 4.

Four membranes only - Desal 5DK, NF 70, NF 270 and TR 60 - were used for diafiltration experiments. Diafiltration with membrane NF 270 was provided only with dye concentra‐ tions 100 and 50 g/l and with membrane TR 60 only at the highest dye concentration, which is the best for desalination. For the reason of low values of permeate flux, membrane NF 90

Dependences of rejection on salt concentration in feed are given in Figure 11 for Desal 5DK, NF 70, NF 270 and TR 60, respectively. Membranes are compared at dye concentration 100 g/l. The lowest values of rejection (max. 0.29) were obtained for membrane Desal 5DK. The

Dependences of flux on salt concentrations are shown in Figure 12. The highest values of

decreased while salt concentration increased. This is due to the effect of osmotic pressure along with the concentration polarization. Due to the concentration polarization phenomen‐ on, the osmotic pressure of the aqueous solution adjacent to the membrane active layer is higher than the corresponding value of the feed solution. As a result, the osmotic pressure

> α **[l/m2.h]**

Desal 5DK 3.365 5.379 0.623 7.503 NF 70 2.650 4.839 0.381 4.664 NF 270 6.801 10.350 0.529 8.561 TR 60 3.952 6.693 0.474 5.888

β **[-]**

δ **[bar]**

would increase dramatically while the salt concentration increased.

**Figure 11.** Salt rejection as a function of salt concentration in feed

**A [l/m2.h.bar]**

In Figure 13 dependences of salt concentrations on time of diafiltration are shown.

.h) were obtained in experiments with membrane NF 270. The permeate flux

and Esna 1 were not used for those experiments.

membrane NF 70 had the highest values.

flux (70.3 l/m2

156 Advancing Desalination

**Membrane**

**Table 4.** Model parameters.

From Table 4 can be shown that δ is not only osmotic pressure (if we assume water permea‐ bility as constant), because the values of δ are different. From these results we can assume, the highest effect of dye on flux is for membrane NF 270. This membrane is the most fouled from these membranes. It is appropriate assumed the change in water permeability (A) in case of desalination of dyes.

In our experiments, the decrease of permeate flux was mainly caused by the effect of con‐ centration polarization and the increase of the viscosity of dye solution. The dye formed a boundary layer over the membrane surface (concentration polarization) and consequently, increased the resistance against the water flux through the membrane. At the same time, the viscosity of solution increased with higher concentration.

From Figure 14 can be shown that the experimental results in permeate fit the model very well. Due to considerably low salt concentrations in permeate, concentration polarization was minimized. The diafiltration process benefits to obtain pure salt product and this can be predicted by a mathematic model on the basis of description of discontinuous diafiltration by periodically adding solvent at constant pressure difference.

**Figure 12.** Permeate flux as a function of salt concentration in feed.

 Total time of diafiltration, τtotal, the separation factor, **S**, and the loss of dye, **Z**. (subscript Z, K are start and end

of diafiltration, respectively)

**Figure 13.** Salt concentration as a function of diafiltration time for membranes Desal 5DK, NF 70, NF 270 and compar‐ ison of tested membranes at dye concentration 100 g/l.

**Figure 14.** Comparison of experimental and model data for the highest dye concentration.

From Table 5 is clearly shown, the total time of diafiltration, τtotal, decreases with decreasing dye concentration. The shortest time had membrane NF 270. Time for the highest dye con‐ centration is not two times higher than with medium dye concentration for all tested mem‐ branes (the time/amount of dye desalted ratio is the smaller for higher concentration of dye). Separation factor decreases with decreasing concentration of dye and it is the second reason why the highest dye concentration was used as the best mode for desalination. The best sep‐ aration factor had membrane Desal 5DK (very similar values, except the highest dye concen‐ tration, had membrane NF 270). The loss of dye is almost same for membrane Desal 5DK, NF 70 and NF 270 at all concentrations of dye. Only for membrane TR 60 are obtained high‐ er loss of dye.

**Figure 13.** Salt concentration as a function of diafiltration time for membranes Desal 5DK, NF 70, NF 270 and compar‐

From Table 5 is clearly shown, the total time of diafiltration, τtotal, decreases with decreasing dye concentration. The shortest time had membrane NF 270. Time for the highest dye con‐ centration is not two times higher than with medium dye concentration for all tested mem‐ branes (the time/amount of dye desalted ratio is the smaller for higher concentration of dye). Separation factor decreases with decreasing concentration of dye and it is the second reason why the highest dye concentration was used as the best mode for desalination. The best sep‐ aration factor had membrane Desal 5DK (very similar values, except the highest dye concen‐ tration, had membrane NF 270). The loss of dye is almost same for membrane Desal 5DK, NF 70 and NF 270 at all concentrations of dye. Only for membrane TR 60 are obtained high‐

**Figure 14.** Comparison of experimental and model data for the highest dye concentration.

ison of tested membranes at dye concentration 100 g/l.

158 Advancing Desalination

er loss of dye.

**Table 5.** Total time of diafiltration, τtotal, the separation factor, **S**, and the loss of dye, **Z**. (subscript Z, K are start and end of diafiltration, respectively)

### **4. Conclusions**

The separation performance of dye, salt and dye solution with six different nanofiltration membranes were investigated, followed by the study of the optimum of diafiltration and concentration process of dye solution.

**Author details**

Petr Mikulášek\*

Czech Republic

**References**

and Jiří Cuhorka

\*Address all correspondence to<EMAIL_ADDRESS>
*ration & Purification Reviews*, 37(3), 303-325.

Kluwer Academic Publishers.

Institute of Environmental and Chemical Engineering, University of Pardubice, Pardubice,

Nanofiltration Process Efficiency in Liquid Dyes Desalination

http://dx.doi.org/10.5772/50438

161

[1] Drioli, E., Laganh, F., Criscuoli, A., & Barbieri, G. (1999). Integrated Membrane Oper‐

[2] Diawara, C. K. (2008). Nanofiltration Process Efficiency in Water Desalination. *Sepa‐*

[3] Yu, S., Gao, C., Su, H., & Liu, M. (2001). Nanofiltration used for Desalination and

[4] He, Y., Li, G. M., Zhao, J. F., & Su, H. X. (2007). Membrane Technology: Reactive

[5] Mulder, M. (2000). Basic Principles of Membrane Technology. 2nd Ed., Dordrecht,

[6] Oatley, D. L., Cassey, B., Jones, P., & Bowen, W. R. (2005). Modelling the Perform‐ ance of Membrane Nanofiltration - Recovery of high-value Product from a Process

[7] Bowen, W. R., & Mohammad, A. W. (1998). Diafiltration by Nanofiltration: Predic‐

[8] Weselowska, K., Koter, S., & Bodzek, M. (2004). Modelling of Nanofiltration in Soft‐

[9] Foley, G. (2006). Water Usage in Variable Volume Diafiltration: Comparison with Ul‐ trafiltration and Constant Volume Diafiltration. *Desalination*, 196(1-3), 160-163. [10] Al-Zoubi, H., Hilal, N., Darwish, N. A., & Mohammed, A. W. (2007). Rejection and Modelling of Sulphate and Potassium Salts by Nanofiltration Membranes: Neural

[11] Wang, L., Yang, G., Xing, W., & Xu, N. (2008). Mathematic Model of Yield for Diafil‐

[12] Kovács, Z., Discacciati, M., & Samhaber, W. (2009). Modelling of Batch and Semibatch Membrane Filtration Processes. *Journal of Membrane Science*, 327(1-2), 164-173.

ations in Desalination Processes. *Desalination*, 122(2-3), 141-145.

Concentration in Dye Production. *Desalination*, 140(1), 97-100.

Waste Stream. *Chemical Engineering Science*, 60(7), 1953-1964.

Network and Spiegler-Kedem Model. *Desalination*, 206(1-3), 42-60.

tration. *Separation and Purification Technology*, 59(2), 206-213.

tion and Optimization. *AIChE Journal*, 44(8), 1799-1812.

ening Water. *Desalination*, 162(1-3), 137-151.

Dyes and Cleaner Production. *Filtration & Separation*, 44(4), 22-24.

Asymmetric and negatively charged polyamide thin-film composite membranes of near similar molecular weight cut-off were characterized for key physical and surface properties, and employed to perform the laboratory-scale experiments to investigate the impacts of membranes properties on reactive dye removal from dye/salt mixtures through NF process. It was found that properties of the NF membrane play an important role in dye removal rate, stable permeate flux and their change behaviour with operational conditions.

The electrostatic repulsive interaction between dye and membrane surface promotes the dye removal and decreases concentration polarization and dye adsorption on the membrane sur‐ face. But, the action will be weakened as the dye concentration or salt concentration increased.

The introduction of an exponential term for the concentration dependence of salt permeabil‐ ity in the Spiegler-Kedem model allows very good prediction of rejection of nanofiltration membranes for single salt solutions depending on the feed concentration and permeates flux.

In the case of separation of mixed dye-salt solutions the extended Spiegler-Kedem model in‐ cluding Donnan equilibrium term (the Perry-Linder model) and the exponential concentra‐ tion dependence term can be used for sufficient prediction of the salt rejection even at high dye concentrations typical for industrial desalination process.

From the results presented above it is clear that the best concentration of the dye in feed for desalination of reactive dye by batch diafiltration is 100 g/l. In this case the salt rejection reaches minimal value due to Donnan potential which strengthens the flow of salt through the membrane.

The best membrane for desalination is NF 270 which has smaller dye loss factor and the shortest time of diafiltration. Very suitable membrane is also Desal 5DK, which has the best separation factor and dye loss factor, but this membrane has longer time of diafiltration (see Table 5). For desalination qualitative description it is convenient to use the proposed model.

#### **Acknowledgements**

This project was financially supported by Ministry of Education, Youth and Sports of the Czech Republic, Project SGFChT05/2012.

#### **Author details**

**4. Conclusions**

160 Advancing Desalination

the membrane.

**Acknowledgements**

Czech Republic, Project SGFChT05/2012.

concentration process of dye solution.

The separation performance of dye, salt and dye solution with six different nanofiltration membranes were investigated, followed by the study of the optimum of diafiltration and

Asymmetric and negatively charged polyamide thin-film composite membranes of near similar molecular weight cut-off were characterized for key physical and surface properties, and employed to perform the laboratory-scale experiments to investigate the impacts of membranes properties on reactive dye removal from dye/salt mixtures through NF process. It was found that properties of the NF membrane play an important role in dye removal

The electrostatic repulsive interaction between dye and membrane surface promotes the dye removal and decreases concentration polarization and dye adsorption on the membrane sur‐ face. But, the action will be weakened as the dye concentration or salt concentration increased.

The introduction of an exponential term for the concentration dependence of salt permeabil‐ ity in the Spiegler-Kedem model allows very good prediction of rejection of nanofiltration membranes for single salt solutions depending on the feed concentration and permeates flux.

In the case of separation of mixed dye-salt solutions the extended Spiegler-Kedem model in‐ cluding Donnan equilibrium term (the Perry-Linder model) and the exponential concentra‐ tion dependence term can be used for sufficient prediction of the salt rejection even at high

From the results presented above it is clear that the best concentration of the dye in feed for desalination of reactive dye by batch diafiltration is 100 g/l. In this case the salt rejection reaches minimal value due to Donnan potential which strengthens the flow of salt through

The best membrane for desalination is NF 270 which has smaller dye loss factor and the shortest time of diafiltration. Very suitable membrane is also Desal 5DK, which has the best separation factor and dye loss factor, but this membrane has longer time of diafiltration (see Table 5). For desalination qualitative description it is convenient to use the proposed model.

This project was financially supported by Ministry of Education, Youth and Sports of the

dye concentrations typical for industrial desalination process.

rate, stable permeate flux and their change behaviour with operational conditions.

Petr Mikulášek\* and Jiří Cuhorka

\*Address all correspondence to<EMAIL_ADDRESS>
Institute of Environmental and Chemical Engineering, University of Pardubice, Pardubice, Czech Republic

#### **References**

[13] Das, Ch., Dasgupta, S., & De , S. (2008). Steady-state Modelling for Membrane Sepa‐ ration of Pretreated Soaking Effluent under Cross Flow Mode. *Environmental Prog‐ ress*, 27(3), 346-352.

**Chapter 8**

**Desorption of Cadmium from Porous Chitosan Beads**

Cadmium pollution of the environment has become a serious problem due to the increasing consumption of cadmium by industry in the past 20 years. Cadmium is introduced into the environment from the effluence of electroplating industry, and in solid and aqueous dis‐ charges from mining operations. Increased environmental awareness has resulted in the promulgation of more stringent legislation in several countries for water quality. For exam‐ ple, in Italy and the United States, the maximum permitted concentrations of heavy metals such as cadmium, lead, chromium, and nickel ions are 5, 50, 50, and 50 μg/l respectively [1,2]. In order to increase the concentration of exposed active sites within chitosan so that the adsorption capacity and transport rate of metal ions into the particle can be enhanced, po‐ rous chitosan beads need to be developed. Rorrer, Way, and Hsien [3]described the synthe‐ sis of 1 mm and 3 mm porous, magnetic, chitosan beads for cadmium ion separation from aqueous solutions. Complete adsorption isotherms over a large range of cadmium ion con‐ centrations (2-1700 ppm) onto the chitosan beads were obtained. Chitosan is a cationic poly‐ mer which can displace adsorbed metal ions by hydrogen ions in a low pH environment. Muzzarelli et al. [4]pointed that a packed column of mercury-adsorbed chitosan could be re‐ generated by flushing the bed with a 10 mM potassium iodide solution or other eluting agents. Randall et al. [5] regenerated chitosan powder in a packed column by flushing the bed with a 0.2 N NH4Cl solution. Nickel removal efficiencies were as high as 97 %. The pH effect on the desorption process for regeneration of cadmium-adsorbed chitosan powder was first considered by Jha et al. [6]. An economic comparison of two different processes to recycle chitosan after the adsorption process was provided by Coughlin et al. [7]. Thus, it is valuable to define the optimum regeneration parameters for chitosan beads. The recycle effi‐ ciency of the cadmium-adsorbed chitosan beads will also be considered by this study.

The hydrogen ion consumption and optimum pH range for the regeneration of chitosan beads after cadmium adsorption will be studied. Specifically, the desorption process after cadmium

> © 2012 Hsien and Liu; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Hsien and Liu; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Tzu-Yang Hsien and Yu-Ling Liu

http://dx.doi.org/10.5772/50142

**1. Introduction**

Additional information is available at the end of the chapter

### **Desorption of Cadmium from Porous Chitosan Beads**

Tzu-Yang Hsien and Yu-Ling Liu

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50142

#### **1. Introduction**

[13] Das, Ch., Dasgupta, S., & De , S. (2008). Steady-state Modelling for Membrane Sepa‐ ration of Pretreated Soaking Effluent under Cross Flow Mode. *Environmental Prog‐*

[14] Cséfalvay, E., Pauer, V., & Mizsey, P. (2009). Recovery of Copper from Process Wa‐ ters by Nanofiltration and Reverse Osmosis. *Desalination*, 240(1-3), 132-146.

[15] Hussain, A. A., Nataraj, S. K., Abashar, M. E. E., Al-Mutaz, I. S., & Aminabhavi, T. M. (2008). Prediction of Physical Properties of Nanofiltration Membranes using Experi‐

[16] Schirg, P., & Widmer, F. (1992). Characterisation of Nanofiltration Membranes for the

[17] Koyuncu, I., & Topacik, D. (2002). Effect of Organic Ion on the Separation of Salts by

[18] Kovács, Z., Discacciati, M., & Samhaber, W. (2009). Modelling of Amino Acid Nano‐ filtration by Irreversible Thermodynamics. *Journal of Membrane Science*, 332(1-2),

[19] Spiegler, K. S., & Kedem, O. (1966). Thermodynamics of Hyperfiltration (Reverse Os‐

[20] Xu, Y., & Lebrun, R. E. (1999). Comparison of Nanofiltration Properties of Two Mem‐ branes using Electrolyte and Non-electrolyte Solutes. *Desalination*, 122(1), 95-105.

ment and Theoretical Models. *Journal of Membrane Science*, 310(1-2), 321-336.

Separation of Aqueous Dye-salt Solution. *Desalination*, 89(1), 89-107.

mosis): Criteria for Efficient Membranes. *Desalination*, 1(4), 311-326.

Nanofiltration Membranes. *Journal of Membrane Science*, 195(2), 247-263.

*ress*, 27(3), 346-352.

162 Advancing Desalination

38-49.

Cadmium pollution of the environment has become a serious problem due to the increasing consumption of cadmium by industry in the past 20 years. Cadmium is introduced into the environment from the effluence of electroplating industry, and in solid and aqueous dis‐ charges from mining operations. Increased environmental awareness has resulted in the promulgation of more stringent legislation in several countries for water quality. For exam‐ ple, in Italy and the United States, the maximum permitted concentrations of heavy metals such as cadmium, lead, chromium, and nickel ions are 5, 50, 50, and 50 μg/l respectively [1,2]. In order to increase the concentration of exposed active sites within chitosan so that the adsorption capacity and transport rate of metal ions into the particle can be enhanced, po‐ rous chitosan beads need to be developed. Rorrer, Way, and Hsien [3]described the synthe‐ sis of 1 mm and 3 mm porous, magnetic, chitosan beads for cadmium ion separation from aqueous solutions. Complete adsorption isotherms over a large range of cadmium ion con‐ centrations (2-1700 ppm) onto the chitosan beads were obtained. Chitosan is a cationic poly‐ mer which can displace adsorbed metal ions by hydrogen ions in a low pH environment. Muzzarelli et al. [4]pointed that a packed column of mercury-adsorbed chitosan could be re‐ generated by flushing the bed with a 10 mM potassium iodide solution or other eluting agents. Randall et al. [5] regenerated chitosan powder in a packed column by flushing the bed with a 0.2 N NH4Cl solution. Nickel removal efficiencies were as high as 97 %. The pH effect on the desorption process for regeneration of cadmium-adsorbed chitosan powder was first considered by Jha et al. [6]. An economic comparison of two different processes to recycle chitosan after the adsorption process was provided by Coughlin et al. [7]. Thus, it is valuable to define the optimum regeneration parameters for chitosan beads. The recycle effi‐ ciency of the cadmium-adsorbed chitosan beads will also be considered by this study.

The hydrogen ion consumption and optimum pH range for the regeneration of chitosan beads after cadmium adsorption will be studied. Specifically, the desorption process after cadmium

© 2012 Hsien and Liu; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Hsien and Liu; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

adsorption will be carried out in a spinning-basket reactor with online pH measurement to de‐ termine the effect of pH and H+ consumption on cadmium desorption and bead regeneration efficiency. The objective of this study is to determine the feasible pH range and H+ consump‐ tion for regeneration of cadmium adsorbed chitosan beads. The pH affects cadmium adsorp‐ tion and desorption on the chitosan beads. In this present study, the adsorption and desorption kinetics for single stage adsorption desorption experiments are determined in a spinning bas‐ ket reactor. The hydrogen ion capacity of the chitosan beads and the pH of the cadmium solu‐ tion in the vessel are also measured as a function of time. Finally, an equilibrium model for desorption process is presented in order to describe the competitive relationships associated with displacing adsorbed cadmium ions with hydrogen ions.

Process Condition Variable and Units Temperature 25 ºC Bead loading (mb) 0.5 g Initial solution volume (V) 200 mL Initial Cd+2 concentration (Co) 200 mg Cd/L Acid (HNO3) concentration (Ca) 0.0001 - 0.1 N

Desorption of Cadmium from Porous Chitosan Beads

http://dx.doi.org/10.5772/50142

165

Agitation 150 rpm

Two control experiments were performed. In the first control experiment, the pH curve for the chitosan beads was measured to determine the extent of H+ consumed by adsorption for the case where no cadmium ions were present in the system. Specifically, 0.5 g of chitosan beads were packed in the hollow propeller cells of the spinning-basket reactor and im‐ mersed in 200 mL of deionized distilled water for 48 hours. The pH at the start of the experi‐ ment was about 7.0. The mixing speed was 150 rpm. Then, 65 mL of 0.1 N HNO3 solution was added to the vessel and the pH was measured continuously until an equilibrium pH value was reached. During this time, the pH of the bulk solution increased as hydrogen ions

In the second control experiment, the stability of chelated cadmium ions adsorbed on chito‐ san beads was tested. Specifically, the cadmium adsorbed chitosan beads were immersed in 200 mL distilled water within the reactor at 25 º C and mixed at 150 rpm. Samples were re‐

**Table 1.** Table 1. The adsorption/desorption parameters for spinning basket reactor experiments

**Figure 1.** Spinning basket reactor

adsorbed onto weakly basic -NH2 sites on chitosan.

#### **2. Materials and Methods**

#### **2.1. Chitosan Beads Synthesis**

The synthesis of chitosan beads, including chitosan solution preparation, gel beads casting, crosslinking and freeze drying was described in previous studies [3,8]. Specifically, a 5 wt % chitosan solution was casted in the precipitation bath to form chitosan gel beads and then crosslinked with a 2.5 wt % aqueous glutaric dialdehyde. The wet crosslinked chitosan beads were freeze-dried to remove the remaining humidity. The chitosan beads crosslinked with a 2.5 wt % initial glutaric dialdehyde solution were used in this study.

#### **2.2. Single Stage Desorption**

Two types of desorption experiments, single stage and multiple stage, were performed. In the single stage experiment, the adsorbed cadmium ions on chitosan beads were released back to the bulk solution by the single addition of a large amount of H+ . Batch adsorption/ desorption experiments were conducted at 25 ºC in a spinning-basket reactor (Figure 1), in‐ spired by a basket reactor from Carberry [9]. Prior to desorption, the adsorption process was carried out. Specifically, 0.5 g of chitosan beads were packed into the hollow impeller basket assembly and contacted with 200 mL of 200 mg /L cadmium ion solution at 150 rpm and 25ºC for at least 48 hours to ensure that adsorption equilibrium was achieved. After adsorp‐ tion, 65 mL of 0.1 N HNO3 solution was added to the vessel to load the bulk solution with the H+ ions needed to affect the complete desorption and to reach a final pH value of 2.0. The adsorption/desorption parameters for spinning basket reactor experiments are summar‐ ized in Table 1.

The high concentration of hydrogen ions loaded to the vessel displaced the adsorbed cadmi‐ um ions. The kinetics of cadmium release and H+ adsorption were followed by measuring the cadmium ion concentration and pH of the bulk solution phase with time. The pH was monitored continuously, whereas 0.5 mL samples were periodically removed from the reac‐ tor and analyzed for Cd+2 concentration by ion chromatography (IC).

**Table 1.** Table 1. The adsorption/desorption parameters for spinning basket reactor experiments

adsorption will be carried out in a spinning-basket reactor with online pH measurement to de‐ termine the effect of pH and H+ consumption on cadmium desorption and bead regeneration efficiency. The objective of this study is to determine the feasible pH range and H+ consump‐ tion for regeneration of cadmium adsorbed chitosan beads. The pH affects cadmium adsorp‐ tion and desorption on the chitosan beads. In this present study, the adsorption and desorption kinetics for single stage adsorption desorption experiments are determined in a spinning bas‐ ket reactor. The hydrogen ion capacity of the chitosan beads and the pH of the cadmium solu‐ tion in the vessel are also measured as a function of time. Finally, an equilibrium model for desorption process is presented in order to describe the competitive relationships associated

The synthesis of chitosan beads, including chitosan solution preparation, gel beads casting, crosslinking and freeze drying was described in previous studies [3,8]. Specifically, a 5 wt % chitosan solution was casted in the precipitation bath to form chitosan gel beads and then crosslinked with a 2.5 wt % aqueous glutaric dialdehyde. The wet crosslinked chitosan beads were freeze-dried to remove the remaining humidity. The chitosan beads crosslinked

Two types of desorption experiments, single stage and multiple stage, were performed. In the single stage experiment, the adsorbed cadmium ions on chitosan beads were released

desorption experiments were conducted at 25 ºC in a spinning-basket reactor (Figure 1), in‐ spired by a basket reactor from Carberry [9]. Prior to desorption, the adsorption process was carried out. Specifically, 0.5 g of chitosan beads were packed into the hollow impeller basket assembly and contacted with 200 mL of 200 mg /L cadmium ion solution at 150 rpm and 25ºC for at least 48 hours to ensure that adsorption equilibrium was achieved. After adsorp‐ tion, 65 mL of 0.1 N HNO3 solution was added to the vessel to load the bulk solution with

 ions needed to affect the complete desorption and to reach a final pH value of 2.0. The adsorption/desorption parameters for spinning basket reactor experiments are summar‐

The high concentration of hydrogen ions loaded to the vessel displaced the adsorbed cadmi‐

the cadmium ion concentration and pH of the bulk solution phase with time. The pH was monitored continuously, whereas 0.5 mL samples were periodically removed from the reac‐

. Batch adsorption/

adsorption were followed by measuring

with a 2.5 wt % initial glutaric dialdehyde solution were used in this study.

back to the bulk solution by the single addition of a large amount of H+

um ions. The kinetics of cadmium release and H+

tor and analyzed for Cd+2 concentration by ion chromatography (IC).

with displacing adsorbed cadmium ions with hydrogen ions.

**2. Materials and Methods**

164 Advancing Desalination

**2.1. Chitosan Beads Synthesis**

**2.2. Single Stage Desorption**

the H+

ized in Table 1.

Two control experiments were performed. In the first control experiment, the pH curve for the chitosan beads was measured to determine the extent of H+ consumed by adsorption for the case where no cadmium ions were present in the system. Specifically, 0.5 g of chitosan beads were packed in the hollow propeller cells of the spinning-basket reactor and im‐ mersed in 200 mL of deionized distilled water for 48 hours. The pH at the start of the experi‐ ment was about 7.0. The mixing speed was 150 rpm. Then, 65 mL of 0.1 N HNO3 solution was added to the vessel and the pH was measured continuously until an equilibrium pH value was reached. During this time, the pH of the bulk solution increased as hydrogen ions adsorbed onto weakly basic -NH2 sites on chitosan.

In the second control experiment, the stability of chelated cadmium ions adsorbed on chito‐ san beads was tested. Specifically, the cadmium adsorbed chitosan beads were immersed in 200 mL distilled water within the reactor at 25 º C and mixed at 150 rpm. Samples were re‐ moved from bulk solution at 123 and 171 hours and analyzed for cadmium ion concentra‐ tion by ion chromatography (IC).

equilibrium pH of the bulk solution. The cadmium ion concentration was measured by IC

where C(t) is the cadmium ion concentration in the vessel at different adsorption or desorption times (mg Cd/L), C0 is the initial cadmium concentration in the vessel before adsorption (mg Cd/L), mb is the mass (g) of chitosan beads in the spinning basket reactor impeller assembly, Q is the cadmium adsorption capacity on the chitosan beads (mg Cd/g-chitosan), and V is the cur‐

) • 100 = ( 1 - Q (t)

) • 100 = ( 1 -

where D (%) is the percentage of cadmium desorbed at a given desorption time, Cmin is the lowest cadmium concentration along the adsorption or desorption process (mg Cd/L), C0,i is the initial cadmium concentration in the spinning basket reactor at specific desorption stage " *i* " (mg Cd/L), and Cmin,i is the lowest cadmium concentration along the adsorption or de‐

measurements of the bulk solution in the vessel. The hydrogen ion adsorption capacity at ith

is the hydrogen ion adsorption capacity for chitosan beads at the *i*th desorption stage (mg

H/g-chitosan), Va is the acid volume (L) added into the spinning basket reactor, Vt

Ca Va - ( 10-pHt • Vt ) mb

is the pH value at different adsorption or desorption times, ΔQi (H+

Qf

Qi (t) Qi,f

) • 100 % (2)

Desorption of Cadmium from Porous Chitosan Beads

http://dx.doi.org/10.5772/50142

) • 100 *%* (3)

is the final cadmium adsorp‐

(4)

)

is the vol‐

) ) on the chitosan beads was based on pH

/L ) added into the spinning basket reactor

(1)

167

*Q* = ( C0 - C (t) ) V mb

rent cadmium solution volume loaded in the spinning basket reactor vessel (L).

The percentage of cadmium desorbed from the beads is calculated by

C0 - Cmin

C0,i - Cmin,i

sorption process at a specific desorption stage (mg Cd/L), Qf

) is given by

*Δ* Qi (H+

ume (L) of solution in the spinning basket reactor at a given time.

) =

tion capacity on the chitosan beads (mg Cd+2/g chitosan).

The hydrogen ion adsorption capacity ( ΔQi (H+

where Ca is the concentration of HNO3 (mole H+

desorption stage ΔQi(H+

before desorption, pHt

D (%) = ( 1 - C (t) - Cmin

D (%) = ( 1 - C (t) - Cmin,i

analysis as described earlier.

or

The cadmium adsorption capacity is calculated by

Shake flask experiments were carried out to determine the equilibrium hydrogen and cad‐ mium loading on the chitosan beads at different pH levels. Specifically, 0.1 g of chitosan beads were mixed with 40 mL of 200 mg /L cadmium ion solution in a 125 mL Erlenmeyer flask and agitated at 120 rpm and 25 ℃ for 51 hours to ensure that adsorption equilibrium was reached. After adsorption, different doses (1 to 4 mL) of HNO3 solution (10-4 to 1 N) was added to the flask to process the desorption for another 140 hours. The adsorption/desorp‐ tion parameters for shake flask experiments are summarized in Table 2.

**Table 2.** Table 2. The adsorption/desorption parameters for shake flask experiments

#### **2.3. Multiple Stage Desorption**

In the multiple stage experiment, adsorbed cadmium was gradually displaced by the series addition of small doses of H+ . A discrete volume of 0.1 N HNO3 was added to the vessel. If the equilibrium pH was above 2.0, then additional 0.1 N HNO3 was added. The experiment was completed when an equilibrium pH of 2.0 was achieved.

A modified titration procedure suggested by previous works for studying ion exchange or adsorption characteristics was modified in the present study to determine hydrogen ion ad‐ sorption on chitosan beads. Specifically, a 0.5 g of chitosan beads were packed into the hol‐ low propeller cells of the spinning-basket reactor and immersed in 200 mL of deionized distilled water at 150 rpm for 48 hours. After the chitosan beads were saturated with water, a discrete volume of 0.1 N HNO3 was added to the vessel to initiate hydrogen ion adsorp‐ tion on chitosan beads. Until an equilibrium pH value was reached, a different amount of 0.1 N HNO3 solution was sequentially added to the vessel.

#### **2.4. pH and Cadmium Ion Concentration Measurements**

The pH measurements were performed with an Orion model 91-02 combination pH elec‐ trode and Orion model 720A ion selective electrode (ISE) meter. The pH readings were re‐ corded by a computer every ten minutes during the experiment. The pH saturation curve was expressed as the amount of hydrogen ion sorbed per gram of chitosan beads versus the equilibrium pH of the bulk solution. The cadmium ion concentration was measured by IC analysis as described earlier.

The cadmium adsorption capacity is calculated by

$$Q = \frac{\left(\text{C}\_0 \cdot \text{C} \text{ (t)}\right)V}{\text{m}\_b} \tag{1}$$

where C(t) is the cadmium ion concentration in the vessel at different adsorption or desorption times (mg Cd/L), C0 is the initial cadmium concentration in the vessel before adsorption (mg Cd/L), mb is the mass (g) of chitosan beads in the spinning basket reactor impeller assembly, Q is the cadmium adsorption capacity on the chitosan beads (mg Cd/g-chitosan), and V is the cur‐ rent cadmium solution volume loaded in the spinning basket reactor vessel (L).

The percentage of cadmium desorbed from the beads is calculated by

$$\mathbf{D}\left(\%\right) = \left(1 \cdot \frac{\mathbf{C}\left(\mathbf{t}\right) \cdot \mathbf{C}\_{\min}}{\mathbf{C}\_0 \cdot \mathbf{C}\_{\min}}\right) \bullet \ 100 = \left(1 \cdot \frac{\mathbf{Q}\left(\mathbf{t}\right)}{\mathbf{Q}\_\mathbf{f}}\right) \bullet \ 100 \text{ \%} \tag{2}$$

or

moved from bulk solution at 123 and 171 hours and analyzed for cadmium ion concentra‐

Shake flask experiments were carried out to determine the equilibrium hydrogen and cad‐ mium loading on the chitosan beads at different pH levels. Specifically, 0.1 g of chitosan beads were mixed with 40 mL of 200 mg /L cadmium ion solution in a 125 mL Erlenmeyer flask and agitated at 120 rpm and 25 ℃ for 51 hours to ensure that adsorption equilibrium was reached. After adsorption, different doses (1 to 4 mL) of HNO3 solution (10-4 to 1 N) was added to the flask to process the desorption for another 140 hours. The adsorption/desorp‐

> Process Condition Variable and Units Temperature 25 ºC Bead loading (mb) 0.1 g Initial solution volume (V) 40 mL Initial Cd+2 concentration (Co) 200 mg Cd/L Acid (HNO3) concentration (Ca) 0.0001 - 0.1 N Agitation 120 rpm

In the multiple stage experiment, adsorbed cadmium was gradually displaced by the series

the equilibrium pH was above 2.0, then additional 0.1 N HNO3 was added. The experiment

A modified titration procedure suggested by previous works for studying ion exchange or adsorption characteristics was modified in the present study to determine hydrogen ion ad‐ sorption on chitosan beads. Specifically, a 0.5 g of chitosan beads were packed into the hol‐ low propeller cells of the spinning-basket reactor and immersed in 200 mL of deionized distilled water at 150 rpm for 48 hours. After the chitosan beads were saturated with water, a discrete volume of 0.1 N HNO3 was added to the vessel to initiate hydrogen ion adsorp‐ tion on chitosan beads. Until an equilibrium pH value was reached, a different amount of

The pH measurements were performed with an Orion model 91-02 combination pH elec‐ trode and Orion model 720A ion selective electrode (ISE) meter. The pH readings were re‐ corded by a computer every ten minutes during the experiment. The pH saturation curve was expressed as the amount of hydrogen ion sorbed per gram of chitosan beads versus the

. A discrete volume of 0.1 N HNO3 was added to the vessel. If

tion parameters for shake flask experiments are summarized in Table 2.

**Table 2.** Table 2. The adsorption/desorption parameters for shake flask experiments

was completed when an equilibrium pH of 2.0 was achieved.

0.1 N HNO3 solution was sequentially added to the vessel.

**2.4. pH and Cadmium Ion Concentration Measurements**

tion by ion chromatography (IC).

166 Advancing Desalination

**2.3. Multiple Stage Desorption**

addition of small doses of H+

$$\text{D (\%)}=(1 - \frac{\text{C (t)} - \text{C}\_{\text{min,i}}}{\text{C}\_{0,i} - \text{C}\_{\text{min,i}}}) \text{ + 100} = (1 - \frac{\text{Q}\_{\text{i}}(\text{t})}{\text{Q}\_{\text{i},\text{f}}}) \text{ + 100} \text{ \%} \tag{3}$$

where D (%) is the percentage of cadmium desorbed at a given desorption time, Cmin is the lowest cadmium concentration along the adsorption or desorption process (mg Cd/L), C0,i is the initial cadmium concentration in the spinning basket reactor at specific desorption stage " *i* " (mg Cd/L), and Cmin,i is the lowest cadmium concentration along the adsorption or de‐ sorption process at a specific desorption stage (mg Cd/L), Qf is the final cadmium adsorp‐ tion capacity on the chitosan beads (mg Cd+2/g chitosan).

The hydrogen ion adsorption capacity ( ΔQi (H+ ) ) on the chitosan beads was based on pH measurements of the bulk solution in the vessel. The hydrogen ion adsorption capacity at ith desorption stage ΔQi(H+ ) is given by

$$
\Delta \text{ Q}\_i \text{(H}^+ \text{)}=\frac{\text{C}\_\text{a} \text{ V}\_\text{a} \text{ -} (10^{-\text{pH}\_i} \text{ } \bullet \text{ V}\_\text{t})}{\text{m}\_\text{b}}\tag{4}
$$

where Ca is the concentration of HNO3 (mole H+ /L ) added into the spinning basket reactor before desorption, pHt is the pH value at different adsorption or desorption times, ΔQi (H+ ) is the hydrogen ion adsorption capacity for chitosan beads at the *i*th desorption stage (mg H/g-chitosan), Va is the acid volume (L) added into the spinning basket reactor, Vt is the vol‐ ume (L) of solution in the spinning basket reactor at a given time.

The accumulated hydrogen ion adsorption capacity Q(H+ ) is given by

$$Q \text{ (H}^+\text{)} = \sum\_{i=1}^n \Delta \text{ Q}\_i \tag{5}$$

**Figure 2.** a) cadmium ion concentration versus time (b) hydrogen ion capacity and the pH change in the cadmium

between the adsorbed cadmium ions with the hydrogen ions on active sites (-NH2 groups) of the chitosan beads during the desorption process requires hydrogen ions from the addi‐

In another control experiment using the spinning basket reactor, 65 mL of 0.1 N nitric acid were added to 0.5 g chitosan beads to determine the hydrogen ion capacity in cadmium-free water. Profiles for the hydrogen ion consumption and pH are presented in Figure 3. From

hours after the addition of nitric acid. It is notable that the hydrogen ion consumption of 8.9

Hydrogen ions are needed to replace the cadmium ions adsorbed on the amine groups of the chitosan beads. Therefore, different amounts of hydrogen ion were added into the vessel to determine the effect of hydrogen ion consumption on the percentage of cadmium desor‐ bed and the final pH value of the cadmium solution obtained in the single stage desorption process. The percentage of cadmium desorbed is presented in Figure 4 as a function of de‐ sorption time for different amounts of hydrogen ion initially charged to the vessel. Specifi‐ cally, after cadmium adsorption, different amounts of 0.1 N nitric acid (22.2 mL, 50 mL and

/g chitosan is consistent with the hydrogen ion consumption data presented in

per gram of chitosan and a final pH value of 2.06 were reached 140

Desorption of Cadmium from Porous Chitosan Beads

http://dx.doi.org/10.5772/50142

169

solution in the spinning basket reactor for a single stage adsorption/desorption experiment

tion of the nitric acid.

Figure 3, 8.9 mmole H+

**3.2. Optimum pH and Hydrogen Ion Consumption**

65 mL respectively) were dosed into the reactor. At a final pH

mmole H+

Figure 2 (b).

where n is the number of the desorption stage, Q(H+ ) is the accumulated hydrogen ion ad‐ sorption capacity in the present stage (mg Cd/g-chitosan).

#### **3. Results and Discussion**

#### **3.1. Kinetics of Adsorption and Desorption**

The cadmium ion concentration versus time profile in the spinning basket reactor is present‐ ed in Figure 2 (a) for a single stage adsorption/desorption experiment. The cadmium ion concentration decreased significantly from 200 to 183 mg Cd+2/L during the first four hours of adsorption and then slightly decreased to reach a final cadmium concentration of 179 mg Cd+2/L at 51 hours. The total solution volume was 196 mL. After adsorption, 65 mL of 0.1 N nitric acid was added to the vessel to initiate the desorption process. The cadmium concen‐ tration increased sharply during the first 12 hours of desorption following the addition of nitric acid, and then leveled off after 75 hours of desorption. The hydrogen ion capacity for the chitosan beads and the pH change in the cadmium solution are provided in Figure 2 (b) for both the adsorption and desorption processes. Similarly, the hydrogen ion capacity grad‐ ually increased and reached a final value between 8.6 and 9.5 mmole H+ /g chitosan. The pH of the cadmium solution also decreased with the addition of nitric acid and then rose to a final value of 2.17.

**Table 3.** Table 3. Stability of the adsorbed cadmium ion in distilled water at pH 6.0

The stability of the adsorbed cadmium ions in the chitosan beads was determined. Specifi‐ cally, the cadmium-adsorbed chitosan beads were immersed in 200 mL of distilled water within the spinning basket reactor at 25 ºC and mixed at 150 rpm for 93 hours. Only a trace amount of cadmium ions were released back into the water during the desorption (Table 3). Form this control experiment, we conclude that the exchange

**Figure 2.** a) cadmium ion concentration versus time (b) hydrogen ion capacity and the pH change in the cadmium solution in the spinning basket reactor for a single stage adsorption/desorption experiment

between the adsorbed cadmium ions with the hydrogen ions on active sites (-NH2 groups) of the chitosan beads during the desorption process requires hydrogen ions from the addi‐ tion of the nitric acid.

In another control experiment using the spinning basket reactor, 65 mL of 0.1 N nitric acid were added to 0.5 g chitosan beads to determine the hydrogen ion capacity in cadmium-free water. Profiles for the hydrogen ion consumption and pH are presented in Figure 3. From Figure 3, 8.9 mmole H+ per gram of chitosan and a final pH value of 2.06 were reached 140 hours after the addition of nitric acid. It is notable that the hydrogen ion consumption of 8.9 mmole H+ /g chitosan is consistent with the hydrogen ion consumption data presented in Figure 2 (b).

#### **3.2. Optimum pH and Hydrogen Ion Consumption**

The accumulated hydrogen ion adsorption capacity Q(H+

where n is the number of the desorption stage, Q(H+

**3. Results and Discussion**

168 Advancing Desalination

final value of 2.17.

**3.1. Kinetics of Adsorption and Desorption**

sorption capacity in the present stage (mg Cd/g-chitosan).

*Q* (H+

ually increased and reached a final value between 8.6 and 9.5 mmole H+

**Table 3.** Table 3. Stability of the adsorbed cadmium ion in distilled water at pH 6.0

Form this control experiment, we conclude that the exchange

) = ∑ i=1 n

The cadmium ion concentration versus time profile in the spinning basket reactor is present‐ ed in Figure 2 (a) for a single stage adsorption/desorption experiment. The cadmium ion concentration decreased significantly from 200 to 183 mg Cd+2/L during the first four hours of adsorption and then slightly decreased to reach a final cadmium concentration of 179 mg Cd+2/L at 51 hours. The total solution volume was 196 mL. After adsorption, 65 mL of 0.1 N nitric acid was added to the vessel to initiate the desorption process. The cadmium concen‐ tration increased sharply during the first 12 hours of desorption following the addition of nitric acid, and then leveled off after 75 hours of desorption. The hydrogen ion capacity for the chitosan beads and the pH change in the cadmium solution are provided in Figure 2 (b) for both the adsorption and desorption processes. Similarly, the hydrogen ion capacity grad‐

of the cadmium solution also decreased with the addition of nitric acid and then rose to a

Time (h) Q (mg Cd/g) pH Cd+2 concentration

51 9.86 6.73 0.00 87 9.55 6.31 0.78 144 9.18 6.20 1.71

The stability of the adsorbed cadmium ions in the chitosan beads was determined. Specifi‐ cally, the cadmium-adsorbed chitosan beads were immersed in 200 mL of distilled water within the spinning basket reactor at 25 ºC and mixed at 150 rpm for 93 hours. Only a trace amount of cadmium ions were released back into the water during the desorption (Table 3).

) is given by

*Δ* Qi (5)

) is the accumulated hydrogen ion ad‐

/g chitosan. The pH

(mg Cd+2/L)

Hydrogen ions are needed to replace the cadmium ions adsorbed on the amine groups of the chitosan beads. Therefore, different amounts of hydrogen ion were added into the vessel to determine the effect of hydrogen ion consumption on the percentage of cadmium desor‐ bed and the final pH value of the cadmium solution obtained in the single stage desorption process. The percentage of cadmium desorbed is presented in Figure 4 as a function of de‐ sorption time for different amounts of hydrogen ion initially charged to the vessel. Specifi‐ cally, after cadmium adsorption, different amounts of 0.1 N nitric acid (22.2 mL, 50 mL and 65 mL respectively) were dosed into the reactor. At a final pH

also used the shake flask experiment to evaluate the effect of the hydrochloric acid concentra‐ tion on the adsorption of platinum group metal ions onto chemically modified chitosan.

Desorption of Cadmium from Porous Chitosan Beads

http://dx.doi.org/10.5772/50142

171

**Figure 4.** The percentage of cadmium desorbed versus desorption time for different amounts of hydrogen ion initially

**Figure 5.** The experimental and predicted percentages of cadmium desorbed versus equilibrium pH for shake flask

Shake flask desorption experiments were also performed in this present study and com‐ pared to the results from the spinning basket reactor experiments and to previous works. Data for the percentage of cadmium desorbed is plotted as a function of the equilibrium pH in Figure 5. At an equilibrium pH of 2.1, 100 % cadmium desorption was achieved. Increas‐ ing the equilibrium pH decreased the percentage of cadmium desorbed according to an S-

charged to the vessel

experiments

**Figure 3.** The hydrogen ion consumption and pH versus time for cadmium-free water saturation experiment

value of 2.0, 94 % of cadmium desorption was achieved and 8.3 mmole H+ per gram of beads were consumed. It is interesting to note that even at a final pH of 4.7, 80 % of cadmium de‐ sorption was accomplished.

**Table 4.** Table 4. The effect of pH adjustment on the % of cadmium desorbed (D) for the multiple stage desorption experiment

The multiple stage desorption experiment was carried out by a series addition of nitric acid solution into the spinning basket reactor. The effect of pH on the percentage of cadmium desorbed is given in Table 4. After 6 stages of desorption in series, 95.7 % of the cadmium desorption was achieved at a final pH of 3.0.

Even at an equilibrium pH of 4.36, 84.6 % of cadmium desorption was reached, consistent with the single stage desorption process Figure 4

Previous researchers used shake flask experiments to study the effect of pH on heavy metal ion adsorption capacity. Eric and Roux (1992) used the shake flask experiment to study the influ‐ ence of pH on the heavy metal ion binding onto a fungus-derived bio-sorbent. Inoue et al. [10] also used the shake flask experiment to evaluate the effect of the hydrochloric acid concentra‐ tion on the adsorption of platinum group metal ions onto chemically modified chitosan.

**Figure 4.** The percentage of cadmium desorbed versus desorption time for different amounts of hydrogen ion initially charged to the vessel

**Figure 3.** The hydrogen ion consumption and pH versus time for cadmium-free water saturation experiment

were consumed. It is interesting to note that even at a final pH of 4.7, 80 % of cadmium de‐

Stage Time (h) pH D (%)

D-1 67 6.80 7.01 D-2 78 6.64 27.42 D-3 90 5.80 39.75 D-4 101 5.48 39.33 D-5 119 4.36 84.66 D-6 141 3.00 95.72

**Table 4.** Table 4. The effect of pH adjustment on the % of cadmium desorbed (D) for the multiple stage desorption

The multiple stage desorption experiment was carried out by a series addition of nitric acid solution into the spinning basket reactor. The effect of pH on the percentage of cadmium desorbed is given in Table 4. After 6 stages of desorption in series, 95.7 % of the cadmium

Even at an equilibrium pH of 4.36, 84.6 % of cadmium desorption was reached, consistent

Previous researchers used shake flask experiments to study the effect of pH on heavy metal ion adsorption capacity. Eric and Roux (1992) used the shake flask experiment to study the influ‐ ence of pH on the heavy metal ion binding onto a fungus-derived bio-sorbent. Inoue et al. [10]

per gram of beads

value of 2.0, 94 % of cadmium desorption was achieved and 8.3 mmole H+

A-1 48 7.00

sorption was accomplished.

170 Advancing Desalination

desorption was achieved at a final pH of 3.0.

with the single stage desorption process Figure 4

experiment

**Figure 5.** The experimental and predicted percentages of cadmium desorbed versus equilibrium pH for shake flask experiments

Shake flask desorption experiments were also performed in this present study and com‐ pared to the results from the spinning basket reactor experiments and to previous works. Data for the percentage of cadmium desorbed is plotted as a function of the equilibrium pH in Figure 5. At an equilibrium pH of 2.1, 100 % cadmium desorption was achieved. Increas‐ ing the equilibrium pH decreased the percentage of cadmium desorbed according to an S- shaped profile. This S-shaped profile was also observed by Schultz et al. [11] and Aldor et al. [12]. Jha et al. [6] also found that 88 % of cadmium desorption was obtained 24 hours after addition of 0.01 N hydrochloric acid to 100 mg of cadmium-loaded chitosan. Also, 80 % cad‐ mium desorption occurred at pH 3.0, a similar result as the present study. Hayes and Leckie [13] presented an S- shaped profile for Cd+2 and Pb+2 adsorption on goethite, which has a complimentary profile to the present desorption study.

ions displaces the adsorbed cadmium ions. A Langmuir-Freundlich equation for multiple components is developed below to model the competition between the hydrogen ions and

Desorption of Cadmium from Porous Chitosan Beads

http://dx.doi.org/10.5772/50142

173

*Model Development.* Three major assumptions are made for the equilibrium model. First, the adsorption of cadmium ions on the crosslinked chitosan beads may follow the chelation binding mechanism validated by Inoue et al. [15], which shows that divalent cadmium ions adsorb onto amine groups of chitosan to form metal-chelate complexes with composition of 1 mole of cadmium to 2 mole of glucosamine unit. Second, the Cd+2 ions chelate only with imino (-CH=N-) groups in the outer shell of the crosslinked chitosan. In Chapter 3, it was shown that the crosslinked chitosan bead contains a crosslinked outer shell where all amine

(-CH=N-) crosslinks, and an inner core of uncrosslinked chitosan containing free amine (- NH2) groups. In the present desorption experiments, the maximum adsorption capacity was around 15 mg Cd+2/g chitosan. Thus, the value for rM from previous study [8] is 1.32 mm, which is larger than rc value of 1.29 mm for the crosslinked chitosan beads used in the de‐ sorption experiments. Consequently the adsorbed cadmium is only localized in the cross‐ linked outer shell of the chitosan beads where only imino chelation sites are present.

KCd

on the chitosan beads may follow the acid/base neutralization reactions of the form

Ka ′

− *C* = *NH* + H+ ⇔ -C=NH2

The third assumption is that the equilibrium constants for the adsorption of hydrogen ions

2 − *C* = *NH* + Cd+2 ⇔ 2 -C=NH • Cd+2 (6)

+ (7)

the adsorbed cadmium ions on the crosslinked chitosan beads.

groups are derivativized to imino

Therefore, the chelation reaction is expressed as

**Figure 7.** The competitive ion exchange scheme

Results of the percentage of cadmium desorbed from the shake flask desorption experiment were consistent with the spinning basket desorption experiment. However, the results for hy‐ drogen ion consumption were quite different. The inconsistent hydrogen ion consumption may be due to the sensitivity of the pH measurement. A small change in pH near 2 resulted in a significant difference in hydrogen ion consumption. Also the modes of mixing between the spinning basket reactor experiment and the shake flask experiment were different. The mixing in the spinning basket reactor was more uniform and resulted in more repeatable and reliable pH measurements. Therefore, the measurements for H+ adsorption on the chitosan beads for the shake flask experiments at low pH need to be interpreted with caution.

**Figure 6.** The titration curve for crosslinked chitosan beads

The titration curve describing the equilibrium relationship between the pH and hydrogen ion capacity on the crosslinked chitosan beads is presented in Figure 6. A similar titration curve was observed by Yoshida et al. [14] for adsorption of hydrochloric acid on poly(ethyl‐ ene imine) chitosan. The titration curve in Figure 6 apparently has two equivalent points. For the first equivalent point of 4.0, hydrogen ions exchange with the imino groups (=NH) on the chitosan beads within the crosslinked outer shell. The second equivalent point at pH of 2.5 shows that hydrogen ions penetrate deeper to the un-crosslinked core of bead to ex‐ change with the free amine groups (-NH2).

#### **3.3. Exchange Between Cadmium Ions and Hydrogen Ions**

The proposed competitive ion exchange scheme for cadmium ions and hydrogen ions with nitrogen atoms on crosslinked chitosan is presented in Figure 7. The addition of hydrogen ions displaces the adsorbed cadmium ions. A Langmuir-Freundlich equation for multiple components is developed below to model the competition between the hydrogen ions and the adsorbed cadmium ions on the crosslinked chitosan beads.

*Model Development.* Three major assumptions are made for the equilibrium model. First, the adsorption of cadmium ions on the crosslinked chitosan beads may follow the chelation binding mechanism validated by Inoue et al. [15], which shows that divalent cadmium ions adsorb onto amine groups of chitosan to form metal-chelate complexes with composition of 1 mole of cadmium to 2 mole of glucosamine unit. Second, the Cd+2 ions chelate only with imino (-CH=N-) groups in the outer shell of the crosslinked chitosan. In Chapter 3, it was shown that the crosslinked chitosan bead contains a crosslinked outer shell where all amine groups are derivativized to imino

(-CH=N-) crosslinks, and an inner core of uncrosslinked chitosan containing free amine (- NH2) groups. In the present desorption experiments, the maximum adsorption capacity was around 15 mg Cd+2/g chitosan. Thus, the value for rM from previous study [8] is 1.32 mm, which is larger than rc value of 1.29 mm for the crosslinked chitosan beads used in the de‐ sorption experiments. Consequently the adsorbed cadmium is only localized in the cross‐ linked outer shell of the chitosan beads where only imino chelation sites are present. Therefore, the chelation reaction is expressed as

**Figure 7.** The competitive ion exchange scheme

shaped profile. This S-shaped profile was also observed by Schultz et al. [11] and Aldor et al. [12]. Jha et al. [6] also found that 88 % of cadmium desorption was obtained 24 hours after addition of 0.01 N hydrochloric acid to 100 mg of cadmium-loaded chitosan. Also, 80 % cad‐ mium desorption occurred at pH 3.0, a similar result as the present study. Hayes and Leckie [13] presented an S- shaped profile for Cd+2 and Pb+2 adsorption on goethite, which has a

Results of the percentage of cadmium desorbed from the shake flask desorption experiment were consistent with the spinning basket desorption experiment. However, the results for hy‐ drogen ion consumption were quite different. The inconsistent hydrogen ion consumption may be due to the sensitivity of the pH measurement. A small change in pH near 2 resulted in a significant difference in hydrogen ion consumption. Also the modes of mixing between the spinning basket reactor experiment and the shake flask experiment were different. The mixing in the spinning basket reactor was more uniform and resulted in more repeatable and reliable

The titration curve describing the equilibrium relationship between the pH and hydrogen ion capacity on the crosslinked chitosan beads is presented in Figure 6. A similar titration curve was observed by Yoshida et al. [14] for adsorption of hydrochloric acid on poly(ethyl‐ ene imine) chitosan. The titration curve in Figure 6 apparently has two equivalent points. For the first equivalent point of 4.0, hydrogen ions exchange with the imino groups (=NH) on the chitosan beads within the crosslinked outer shell. The second equivalent point at pH of 2.5 shows that hydrogen ions penetrate deeper to the un-crosslinked core of bead to ex‐

The proposed competitive ion exchange scheme for cadmium ions and hydrogen ions with nitrogen atoms on crosslinked chitosan is presented in Figure 7. The addition of hydrogen

adsorption on the chitosan beads for

complimentary profile to the present desorption study.

172 Advancing Desalination

pH measurements. Therefore, the measurements for H+

**Figure 6.** The titration curve for crosslinked chitosan beads

change with the free amine groups (-NH2).

**3.3. Exchange Between Cadmium Ions and Hydrogen Ions**

the shake flask experiments at low pH need to be interpreted with caution.

$$\text{K}\_{\text{Cd}}$$

$$\text{2 }-\text{C}=\text{NH} + \text{Cd}^{\cdot 2} \Leftrightarrow \text{2 }-\text{C=NH} \text{ }\bullet \quad \text{Cd}^{\cdot 2} \tag{6}$$

The third assumption is that the equilibrium constants for the adsorption of hydrogen ions on the chitosan beads may follow the acid/base neutralization reactions of the form

$$\text{K}\_{\text{a}}^{\text{'}}$$

$$\text{C}-\text{C}=\text{NH} + \text{H}^{+} \iff \text{-C=NH}\_{2}{\text{A}}^{\text{-}} \tag{7}$$

$$\begin{array}{ll} \text{K}\_{\text{a}}^{\text{'}} \\\\ \text{or} & \text{-C-NH}\_{2} + \text{H}^{+} \quad \Leftrightarrow & \text{-C-NH}\_{3}{^{\text{+}}} \end{array} \tag{8}$$

In other words, the equilibrium constant Ka ′ is assumed to be the same for either imino or amine groups. Consequently, Figure 6 is assumed to have only one apparent pKa value at pH 3.0. From equations (6) and (7), Kcd and Ka ′ are defined as

$$K\_{\text{Cd}} = \frac{\mathbf{I} \cdot \mathbf{C} \text{=NH} \; \bullet \; \text{Cd}^{\ast 2} \; \mathbf{J}}{\mathbf{I} \cdot \text{C=NH} \; \mathbf{J} \; \text{Cd}^{\ast 2} \; \mathbf{J}^{1/2}} \tag{9}$$

The sum of qCd and qH is expressed as q, given by

*q* = qCd + qH = KCd Ce

In equations (12) and (14), QM/2 is equal to 3.1 mmole Cd+2/g chitosan.

*D* (%) = ( 1- qCd

KCd Ce

on the relationship between pKa and Ka (pKa = - log Ka), the value of Ka

1+KCd Ce

cadmium solution during the desorption process is expressed as

*D* (%) = ( 1 -

Therefore, the Ka

substitution of Ka

Once Ka

11.0 (Snoeyink and Jenkins, 1982 [17]). In this study Ka

et al. [14] are similar with the results of this present work.

1/2 QM /2 + Ka

′ Cae + KCd Ce

1+Ka

Recall from equation (3) that the percentage of cadmium desorbed (D) is given by

qCd,f

where qCd,f is the final cadmium adsorption capacity before the desorption process is initiat‐ ed (mmole Cd+2/g chitosan). Therefore, the percentage of the cadmium desorbed into the

1/2 QM / 2

1/2 + Ka

*Estimation of Equilibrium Constants.* The pKa value of the crosslinked chitosan beads was ob‐ tained from the pH value at which 50 % of the active sites were protonated. The pKa value estimated from Figure 6 was 3.0. In other words, the pKb value of the conjugated base was

tosan was 6.3. Similarly, the pKb for the base -C-NH2 was 7.7. The pKb differences may sug‐ gest that the crosslinked imino group (=NH) on chitosan is a weaker base than the uncrosslinked amine group (-NH2). Both the titration curve for adsorption of hydrochloric acid onto poly(ethylene imine) chitosan beads and the derived pKa value of 4.0 by Yoshida

mmole Cd+2/L) and pH at 6.5 to 7 were between 0.13 and 0.17 mmole Cd+2/g chitosan. After

the minimum sum of squares between the data points given in Figure 4.5 for the percentage of cadmium desorbed (D) and the predicted values from equation (15) was achieved. The Kcd value was estimated to be 0.57 (mole/L)-1/2. This chelation reaction constant was also compared to the stability constant data for metal complexes on organic ligands (IUPAC, 1979) which showed that the binding constant of cadmium on pyridine (imine ligand) and sterotonin (amine ligand) were 10 1.36 and 10 3.6 (mole/L)-1/2 respectively. Therefore, the value for estimated Kcd indicated that the cadmium did not bind very strongly to imino groups on chitosan. This low binding constant facilitated the desorption process as the hydrogen ions

′was obtained, Kcd was estimated. The qCd,f values at Ce around 200 mg Cd+2/L (1.79

′ Cae

1 qCd,f

′value was 1000 (mole/L)-1. Muzzarelli [18] found that the pKa value for chi‐

′, Cae, Ce, QM, and qCd,f values into equation (15), Kcd was determined when

′ Cae QM

1/2 (15)

http://dx.doi.org/10.5772/50142

175

Desorption of Cadmium from Porous Chitosan Beads

) • 100 % (17)

′is defined as the inverse of Ka. Based

′was equal to 10pKa.

) • 100 % (16)

$$K\_a \text{'} = \frac{\text{I - C=NH\_2} \text{'} \text{J}}{\text{I - C=NH} \text{J } \text{I } \text{H}^+ \text{J}} \tag{10}$$

If the overall active number of adsorption sites on the crosslinked chitosan bead is con‐ served, then the equilibrium constants Kcd and Ka ′can be expressed as

$$K\_{\rm Cd} = \frac{2 \,\mathrm{q\_{\rm Cd}}}{\left(\mathrm{Q\_M} \cdot 2 \,\mathrm{q\_{\rm Cd}} \cdot \mathrm{q\_H}\right) \,\mathrm{C\_e}^{-1/2}} \tag{11}$$

$$K\_a \text{ = } \frac{\text{q}\_{\text{H}}}{\left(\text{Q}\_{\text{M}} \cdot 2 \,\text{q}\_{\text{Cd}} \cdot \text{q}\_{\text{H}}\right) \,\text{C}\_{\text{ae}}} \tag{12}$$

where Ce is the equilibrium cadmium ion concentration in the vessel (mole /L), Cae is the equilibrium hydrogen ion concentration in the cadmium solution (mole/L), Ka ′ is the equili‐ brium constant (mole/L)-1 for the neutralization reaction, Kcd is the equilibrium constant (mole/L)-1/2 for chelation, QM is the theoretical maximum capacity of chitosan (6.2 mmole ac‐ tive sites/g chitosan), qCd is the equilibrium cadmium ion capacity of the crosslinked chito‐ san beads (mmole Cd+2/g chitosan), and qH is the equilibrium hydrogen ion capacity of the crosslinked chitosan beads (mmole H+ /g chitosan).

By solving for qCd and qH from equations (10) and (11), the following Langmuir-Freundlich equations were derived, based on the binary mixture model presented by Ruthven [16]:

$$q\_{\rm Cd} = \frac{\mathbf{K\_{Cd}} \; \mathbf{C\_e}^{1/2} \; \mathbf{Q\_M}/2}{1 + \mathbf{K\_a}' \; \mathbf{C\_{ae}} + \mathbf{K\_{Cd}} \; \mathbf{C\_e}^{1/2}} \tag{13}$$

$$q\_H = \frac{\text{K}\_\text{a}\text{ }^\circ\text{C}\_\text{ae}\text{ Q}\_\text{M}}{1 + \text{K}\_\text{a}\text{ }^\circ\text{C}\_\text{ae} + \text{K}\_\text{Cd}\text{ C}\_\text{e}^{-1/2}}\tag{14}$$

The sum of qCd and qH is expressed as q, given by

Ka ′

174 Advancing Desalination

In other words, the equilibrium constant Ka

pH 3.0. From equations (6) and (7), Kcd and Ka

served, then the equilibrium constants Kcd and Ka

crosslinked chitosan beads (mmole H+

*or* -C-NH2 + H+ ⇔ -C-NH3

*Ka*

*Ka*

amine groups. Consequently, Figure 6 is assumed to have only one apparent pKa value at

+

If the overall active number of adsorption sites on the crosslinked chitosan bead is con‐

( QM -2qCd - qH ) Ce

( QM -2qCd - qH ) Cae

where Ce is the equilibrium cadmium ion concentration in the vessel (mole /L), Cae is the

brium constant (mole/L)-1 for the neutralization reaction, Kcd is the equilibrium constant (mole/L)-1/2 for chelation, QM is the theoretical maximum capacity of chitosan (6.2 mmole ac‐ tive sites/g chitosan), qCd is the equilibrium cadmium ion capacity of the crosslinked chito‐ san beads (mmole Cd+2/g chitosan), and qH is the equilibrium hydrogen ion capacity of the

/g chitosan).

By solving for qCd and qH from equations (10) and (11), the following Langmuir-Freundlich equations were derived, based on the binary mixture model presented by Ruthven [16]:

1/2 QM / 2

′ Cae + KCd Ce

′ Cae + KCd Ce

*KCd* = -C=NH • Cd+2

′ = -C=NH2

*KCd* = 2 qCd

′ = qH

equilibrium hydrogen ion concentration in the cadmium solution (mole/L), Ka

*qCd* = KCd Ce

1+Ka

*qH* = Ka ′ Cae QM 1+Ka

′ are defined as

+ (8)

′ is assumed to be the same for either imino or

1/2 (11)

1/2 (13)

1/2 (14)

(12)

′ is the equili‐

′can be expressed as

$$q = q\_{\rm Cd} + q\_{\rm H} = \frac{K\_{\rm Cd} \, \text{C}\_{\rm e}^{-1/2} \, \text{Q}\_{\rm M} / \text{2} + K\_{\rm a} \, ^\circ \text{C}\_{\rm ae} \, \text{Q}\_{\rm M}}{1 + K\_{\rm a} \, ^\circ \text{C}\_{\rm ae} + K\_{\rm Cd} \, \text{C}\_{\rm e}^{-1/2}} \tag{15}$$

In equations (12) and (14), QM/2 is equal to 3.1 mmole Cd+2/g chitosan.

Recall from equation (3) that the percentage of cadmium desorbed (D) is given by

$$D \text{ (\%)}=(1 - \frac{\text{q}\_{\text{Cd}}}{\text{q}\_{\text{Cd},\text{f}}}) \text{ } \text{ } \text{ } 100 \text{ \%} \text{ } \tag{16}$$

where qCd,f is the final cadmium adsorption capacity before the desorption process is initiat‐ ed (mmole Cd+2/g chitosan). Therefore, the percentage of the cadmium desorbed into the cadmium solution during the desorption process is expressed as

$$D\left(\%\right) = \left(1 \cdot \frac{\text{K}\_{\text{Cd}}\text{C}\_{\text{e}}^{-1/2}\text{Q}\_{\text{M}}/2}{1 + \text{K}\_{\text{Cd}}\text{C}\_{\text{e}}^{-1/2} + \text{K}\_{\text{a}}^{'}\text{C}\_{\text{ae}}}\frac{1}{\text{q}\_{\text{Cd},\text{f}}}\right) \bullet 100\,\%\tag{17}$$

*Estimation of Equilibrium Constants.* The pKa value of the crosslinked chitosan beads was ob‐ tained from the pH value at which 50 % of the active sites were protonated. The pKa value estimated from Figure 6 was 3.0. In other words, the pKb value of the conjugated base was 11.0 (Snoeyink and Jenkins, 1982 [17]). In this study Ka ′is defined as the inverse of Ka. Based on the relationship between pKa and Ka (pKa = - log Ka), the value of Ka ′was equal to 10pKa. Therefore, the Ka ′value was 1000 (mole/L)-1. Muzzarelli [18] found that the pKa value for chi‐ tosan was 6.3. Similarly, the pKb for the base -C-NH2 was 7.7. The pKb differences may sug‐ gest that the crosslinked imino group (=NH) on chitosan is a weaker base than the uncrosslinked amine group (-NH2). Both the titration curve for adsorption of hydrochloric acid onto poly(ethylene imine) chitosan beads and the derived pKa value of 4.0 by Yoshida et al. [14] are similar with the results of this present work.

Once Ka ′was obtained, Kcd was estimated. The qCd,f values at Ce around 200 mg Cd+2/L (1.79 mmole Cd+2/L) and pH at 6.5 to 7 were between 0.13 and 0.17 mmole Cd+2/g chitosan. After substitution of Ka ′, Cae, Ce, QM, and qCd,f values into equation (15), Kcd was determined when the minimum sum of squares between the data points given in Figure 4.5 for the percentage of cadmium desorbed (D) and the predicted values from equation (15) was achieved. The Kcd value was estimated to be 0.57 (mole/L)-1/2. This chelation reaction constant was also compared to the stability constant data for metal complexes on organic ligands (IUPAC, 1979) which showed that the binding constant of cadmium on pyridine (imine ligand) and sterotonin (amine ligand) were 10 1.36 and 10 3.6 (mole/L)-1/2 respectively. Therefore, the value for estimated Kcd indicated that the cadmium did not bind very strongly to imino groups on chitosan. This low binding constant facilitated the desorption process as the hydrogen ions easily displaced the cadmium ions to accomplish the neutralization reaction. However, hy‐ drogen ions were still required for desorption because water alone could not desorb the bound cadmium.

Chemical modifications of chitosan were considered. First, the linear chitosan chains within gel beads were heterogeneously crosslinked by glutaric dialdehyde solution. The chitosan