Water Research 38 (2004) 2559–2570
Adsorption kinetics of polyethylene glycol fromaqueous
solution onto activated carbon
Chiung-Fen Chang
a, Ching-Yuan Chang
a,*, Wolfgang H
.oll
b, Markus Ulmer
c,
Yi-Hung Chen
a, Hans-J
.ugen GroX
caGraduate Institute of Environmental Engineering, National Taiwan University, 71 Chou-Shan Road, Taipei 106, Taiwan bForschungszentrum Karlsruhe Technik und Umwelt, Institute for Technical Chemistry, Section WGT, P.O. Box 3640,
Karlsruhe D-76021, Germany
cDVGW-Technologiezentrum Wasser (TZW) Karlsruhe, Heinrich-Sontheimer-Laboratory for Water Technology, Karlsruher Str. 84, Karlsruhe D-76139, Germany
Received 1 September 2003; received in revised form 13 February 2004; accepted 4 March 2004
Abstract
The adsorption equilibrium and kinetics of polyethylene glycol (PEG) in three aqueous systems were examined in this study. Langmuir isotherm was used to satisfactorily predict the adsorption capacity of PEG on activated carbon F-400 and applied to the investigation of adsorption kinetics. The surface diffusion, pore diffusion, and branched pore kinetics models successfully described the adsorption behavior of PEG on F-400 in the completely stirred tank reactor. The pore diffusion coefficients obtained from the pore diffusion model were compared with those computed by the experimental data of the short fixed-bed reactor combined with the assumption of non-hindered pore diffusion. In addition, the effects of initial concentrations of PEG and the relative importance of external and internal mass transfers for the adsorption were also taken into account and discussed in this study.
r2004 Elsevier Ltd. All rights reserved.
Keywords: Polyethylene glycol; Activated carbon; Adsorption isotherm; Adsorption kinetics; Film mass transfer; Intraparticle mass transfer
1. Introduction
Printed wiring board (PWB) plays a decisive impor-tant role in the electronic systems, which are essential to the improvement in the information and communication technologies. Therefore, many countries put a lot of emphasis on the development of the PWB industry in the recent decade and result in a huge amount of wastewater. To effectively treat the wastewater is a challenge to be deal with nowadays. Polyethylene glycol (PEG) is used as the disperse agent in the electroplating solution and at low concentration of 0–50 g/m3[1]. The previous study showed that it is feasible to use the
adsorption process to remove PEG from the electro-plating solution, thereby, achieving the goal of recycling the electroplating bath[2]. In addition, PEG is one of non-ionic surfactants and widely used in the industries, such as metal forming, cosmetics, food, etc., due to the advantage that they can be compatible with ionic and amphoteric surfactants. Therefore, PEG is one of abundant organic surfactants commonly found in the industrial wastewater, and needs to be dealt with.
Adsorption using activated carbon (AC) for removing the organics fromthe aqueous solution is an effective separation technology and widely applied in the water treatment. There are two common adsorption designs for wastewater treatment, namely, stirred-batch- and fixed-bed adsorber systems. The former is certainly simple and allowed to reach equilibrium quickly. In
*Corresponding author. Tel./fax: +886-2-2363-8994. E-mail address:cychang3@ntu.edu.tw (C.-Y. Chang).
0043-1354/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2004.03.001
ARTICLE IN PRESS
Nomenclature
AC activated carbon
ACS anthraquinone-2-sulfonate
as specific external surface area, m2/kg
Bis biot number, kLdpCb0=ð2Dsrpq0Þ
Cb concentration of adsorbate in effluent in
SFBR or in bulk solution in CSTR, mg/dm3 Cb0 value of Cb at inlet in SFBR or at t ¼ 0 in
CSTR, mg/dm3
Ce adsorbate concentration in the liquid phase
at equilibrium
Cp adsorbate concentration of liquid in pores,
mg/dm3
Cs adsorbate concentration of liquid on the
external surface of the adsorbent, mg/dm3 CSTR completely stirred tank reactor
D diffusivity of adsorbate in particle, m2/s DL liquid diffusivity or liquid diffusion
coeffi-cient, m2/s
Dp pore diffusion coefficient, m2/s
Dpc Dp obtained by using pore diffusion model
simulation, m2/s
Dpnh Dp estimated by Dpnh¼ epDL=t ¼ e2pDLwith
no hindered diffusion, m2/s Ds surface diffusion coefficient, m2/s
DSMa surface diffusion coefficient on macropore
surface, m2/s
dp mean particle size, mm
fMa volume fraction occupied by macropores
fb correction factor for particle shape (ratio of
experimental to correlation values of bLas; ¼ ðbLasÞexp=ðbLasÞcor)
KL Langmuir isotherm constant, dm3/mg
K Bolzmann constant, 1.381 1023J/K kbp branch pore rate constant, 1/s
kL external mass transfer coefficient, film mass
transfer coefficient gained fromCSTR ex-periments, m/s
MW molecular weight
mmass of adsorbent, kg
NL mass transfer rate per unit surface area, kg/
m2s
PEG polyethylene glycol
PNP p-nitrophenol
PWB printed wiring board
QL liquid volumetric flow rate, cm3/h
q adsorbate concentration in solid phase, mg/g qe adsorbate concentration in solid phase at
equilibrium, mg/g
qL Langmuir isotherm constant, mg/g
qMa; qmi q in macropores and micropores, mg/g
q0 q at equilibriumwith Cb0 calculated by
adsorption isotherm, mg/g
qs q at surface of particle, mg/g
%q average solid phase concentration given by ð3=ðdp=2Þ3Þ
Rdp=2
0 qr2dr; mg/g
R solute radius, hydrodynamic radius, equiva-lent radius, (A
Rb rate of transfer of adsorbate fromm
acro-pores network to microacro-pores or branch pores, mg/g/s
Re Reynolds number, ðudpÞ=n:
R2 determination coefficient, R2¼ 1 ½Pðy e
ycÞ2=Pðye ymÞ2
r intraparticle radial coordinate r2 correlation coefficient
SPEG;6:5 distilled water with dissolution of PEG at
various concentrations. The pH value of SPEG;6:5is around 6.5
SPEG;0:25 distilled water containing concentrated
hy-drochloric acid (HCl(conc)) of 30 g/m3, with the same pH value as electroplating solution adjusted by concentrated sulfuric acid (H2SO4(conc)). The only organic compound in SPEG;0:25 is PEG at various concentrations
SPEG;e electroplating solution containing H2SO4(conc), of 60 kg/m3, CuSO4 5H2O of 200 kg/m
3 , and HCl(conc), of 30 g/m3. The pH value of SPEG;e
is around 0.25. The only organic compound in the solution SPEG;e is PEG at various
concentrations
Sc Schmidt number, n=DL
SFBR short fixed-bed reactor
Sh Sherwood number
Shlam Sh in Eq. (2) represents contribution of
laminar flow to external mass transfer Shturb Sh in Eq. (3) represents contribution of
turbulent flow to external mass transfer ShE Sh in Eq. (4) for isolated single particle
ShFB Sh for single particle in adsorption bed,
ðbLdpÞDL T absolute temperature, K t adsorption time, h u interstitial velocity, m/h uFB filter velocity in SFBR, m/h VL volume of solution in CSTR, dm3
yc dimensionless concentration calculated from
model
ye dimensionless concentration gained from
experiment
ym average value of dimensionless concentration
gained fromexperiment
bL filmmass transfer coefficient gained from SFBR, m/s
bLas specific value of bL; m
3/s/kg ep particle porosity of adsorbent
eFB filter bed porosity
C.-F. Chang et al. / Water Research 38 (2004) 2559–2570 2560
contrast, the latter involves the mass transfer, which consists of two main mechanisms: external- (i.e., film diffusion) and internal (e.g., surface diffusion, pore diffusion, and a combination thereof) mass transfers. The study of stirred-batch adsorption kinetics can provide the design parameters of the internal mass transfer coefficients (surface diffusion coefficient, Ds;
pore diffusion coefficient, Dp), which are also greatly
related to fixed-bed adsorption systems.
To economically design the adsorption process for the removal of PEG, it is necessary to know the specific parameters, such as isotherm and kinetic constants, related to the adsorption of PEG on the activated carbon. The aims of this work were, therefore, (1) to study the adsorption equilibriumand kinetics of PEG fromthree different aqueous solutions onto activated carbon, (2) to evaluate the diffusivities in the liquid and carbon phases, and (3) to elucidate the relative importance of external and internal mass transfers for the development of adsorption.
2. Materials and methods 2.1. Adsorbate
Reagent-grade PEG supplied by Merck was applied in this study. The average molecular weight (MW) of PEG is 6000 with an MW range from5000 to 7000, and belongs to polydisperse system. The standard com-pounds (reagent-grade supplied by Merck) used to obtain the correction factor of particle shape, fb; in
the short fixed-bed reactor (SFBR) experiments are p-nitrophenol (PNP) and anthraquinone-2-sulfonate (ACS).
2.2. Adsorbent
Activated carbon, F-400 (Calgon), with a particle size range between 0.42 and 1.68 mm was used as the
adsorbent. The mean particle size of AC,
dp¼ 1:04 mm, was calculated from the sieve analysis
of the representative samples obtained by using a rotating sample-splitting device by means of the weight percentages of particles in the different sieve sizes. The physical characteristics of F-400 are summarized in
Table 1. The pretreatment of the adsorbent comprised several steps. Firstly, the adsorbent is washed with
distilled water to remove the crushed carbon. Secondly, it is dried at 383 K in a vacuumoven overnight and then stored in the desiccator. Finally, it is wetted in the specific solutions under vacuumbefore the adsorption experiments.
2.3. Aqueous systems
Three kinds of aqueous solvents were used to investigate the adsorption behaviors of the PEG by F-400 as listed below:
SPEG;6:5: Distilled water with dissolution of PEG at
various concentrations. The pH value of SPEG;6:5is around 6.5.
SPEG;0:25: Distilled water containing concentrated
hydro-chloric acid (HCl(conc)) of 30 g m–3, with the same pH value as electroplating solution adjusted by concentrated sulfuric acid (H2SO4(conc)). The only organic compound in SPEG;0:25is PEG at various concentrations.
m dynamic viscosity, cp
mB m of solvent, cp
n kinetic viscosity, m=r; m2/s
r density, kg/m3
PFB filter bed density, kg/m3
rp apparent particle density, kg/m3 rs average true particle density, kg/m3
t tortuosity d Nernst filmthickness Table 1 Physical characteristics of F 400 Property F 400 Mesh size 12–40
Average particle diameter, dp(mm) 1.044
Langmuir specific surface areaa(m2/g) 1363 Total pore volumea(cm3/g) 0.616 Specific external surface areab, a
s(m2/kg) 5.76
Average true particle densitya, r s(kg/m
3) 2180
Apparent particle densityc, r p(kg/m
3) 1000
Filter bed densityd, r FB(kg/m
3) 530
Particle porositye, e
p(—) 0.54
Filter bed porosityd,f, e
FB(—) 0.47
Average pore diameterg( (A) 18 a
Data fromthe surface area determined by N2adsorption at 77 K in the volumetric equipment, ASAP 2010.
b
Assumed as spherical particle and calculated using as¼
6=ðrpdpÞ: c
Data from the experiments of pycnometer. d In a water-filled bed. e Calculated using ep¼ 1 ðrp=rsÞ: fCalculated using e FB¼ 1 ðrFB=rpÞ:
gCalculated by 4 total pore volume/Langmuir specific surface area.
SPEG;e: Electroplating solution containing H2SO4(conc) of 60 kg/m3, CuSO4 5H2O of 200 kg/m3, and HCl(conc)of 30 g/m
3
. The pH value of SPEG;eis
around 0.25. The only organic compound in the solution SPEG;e is PEG at various
concen-trations.
Some properties of PEG in various aqueous solutions are listed inTable 2.
2.4. Analytical measurements
For measurements of adsorption equilibria and experiments in a completely stirred tank reactor (CSTR), all samples were filtrated through a 0.45 mm membrane, prior to the analysis. PEG concentrations were measured by means of a total organic carbon analyzer (O.I.C. M-700). For experiments in an SFBR reactor another Carbon Analyzer (Dohrmann DC-80) and a UV spectrophotometer (Perkin-Elmer UV/VIS Lambda 3) were employed. The wavelengths used in UV spectrophotometry for PNP and ACS analyses in distilled water are 315 and 253 nm, respectively. 2.5. Adsorption equilibrium
For evaluation of the adsorption equilibrium, 0.1 dm3 matrix solutions containing PEG of various initial concentrations were mixed with 0.05 g of adsor-bent and shaken at 298 K until the concentrations of filtrate did not change more than 3%. The initial concentrations of PEG in different levels are specially designed to obtain adsorption isotherms covering suitable concentration ranges, which allow the inter-pretation of the experimental data obtained in the following kinetic experiments (i.e., data gained from the CSTR). Because it is preferable to use the weight concentration units for investigating the removal effi-ciency of the target substance in wastewater treatment, concentrations are given with units in g/m3(or mole/m3) and g/kg (or mole/kg3) for the liquid and solid phases, respectively.
2.6. SFBR experiments
SFBR was used to investigate the external mass transfer coefficient (i.e., filmtransfer coefficient), bL; which is determined by means of the plateau concentra-tion of the first part of the breakthrough curve of the operation of the reactor [3]. The concentration of the solution fed into the SFBR should be kept constant and low enough being not to cause intraparticle diffusion. In this study, the length and diameter of the SFBR were 20 and 2 cm, respectively. The temperature for the solutions containing the organic additive and standard com-pounds were kept constant at 298 and 293 K, respec-tively, which were carefully controlled by noting that the effect of the temperature is significant for the kinetics of adsorption[4]. To obviate air bubbles in the carbon bed, the column was packed under specific wetting solutions. 2.7. CSTR experiments
For the CSTR experiments, a basket reactor of 3.705 dm3 was adopted to this systemto avoid the attrition of adsorbent, which may be encountered in the slurry reactor. The various stirrer revolutions from300 to 700 rpmwere examined in order to ensure the complete mixing and to reduce the film resistance to a minimum. The ratio of adsorbent mass to solution volume was 1 g/dm3and the temperature was adjusted and controlled at 298 K. The initial concentrations of PEG were from50 to 450 g/m3.
3. Results and discussion 3.1. Adsorption isotherm
Hydrophobic attraction mainly contributes the ad-sorption of the non-polar segments of PEG on the hydrophobic surface of F-400, resulting in the removal of PEG fromthe aqueous phase. At lower coverage of PEG on F-400, the conformation of PEG at the adsorbing interface is isolated and the lateral interaction between adsorbed PEG can be ignored. The lateral interaction becomes significant with increasing coverage of PEG on F-400. The Langmuir isotherm can be applied to describe the adsorption equilibriumof PEG in SPEG;e solution, which was previously performed[2].
The mathematical relationship of the isotherm is: qe¼
qLKLCe
1 þ KLCe
: ð1Þ
In Eq. (1), qeand Ceare the adsorbate concentrations
in solid and liquid phases at equilibrium, respectively. qL
and KL are the Langmuir isotherm constants. All
isothermconstants and equilibria for the adsorption systems with solutions of SPEG;6:5; SPEG;e; and SPEG;0:25
ARTICLE IN PRESS
Table 2Some properties of PEG in various aqueous solutions Solution DLat 298 K (1010m2/s) DL e2p (1010m2/s) Hydrodynamic diametera( (A) SPEG;6:5 1.15b 0.34 38 SPEG;0:25 1.03c 0.30 34 SPEG;e 0.90c 0.26 30
aCalculated by the Stokes–Einstein equation.
bPredicted value with assumption of monodisperse system of PEG[10].
cExperimental data from SFBR.
C.-F. Chang et al. / Water Research 38 (2004) 2559–2570 2562
are summarized in Table 3 and illustrated in Fig. 1, respectively.
At equilibriumconcentrations lower than 0.0025 mol/ m3, the uptake of PEG on F-400 seems similar in three solutions, interpreting that the effect of ionic strength and the pH value of the solution on the adsorption of isolated PEG on F-400 was negligible. However, when the adsorption approaches the plateau, the effects of the properties of solution on adsorption of PEG become significant, resulting in the reduction of adsorption capacity at high concentrations of PEG in SPEG;e and
SPEG;0:25which exhibit high ionic strength and lower pH
value, respectively. The hydrophilic tendency of the non-ionic surfactants is essentially due to oxygen in the molecule, which can be hydrated by hydrogen bonding to water molecules[5]. Therefore, the hydrated chain of PEG in the conformation of coil spreads into the aqueous phase and causes great steric repulsion. In addition, the copper (II) may bond to the oxygen and formthe PEG–copper (II) complex in SPEG;e; which
causes the electrostatic repulsion between adsorbed complexes and significantly reduces the adsorption capacity in the plateau. Although the high ionic strength can bring the shield effect to lower the electrostatic repulsion between the complexes in SPEG;e; the
adsorp-tion capacity at plateau poradsorp-tion may be reduced dominantly by the strong steric repulsion. Therefore, both electrostatic and steric repulsions play important roles on the adsorption of PEG in SPEG;e and SPEG;0:25;
then reducing the adsorption capacity in the plateau portion.
3.2. External mass transfer in SFBR and liquid diffusivity There are two possible formulations of the SFBR model, the plug-flow film diffusion and dispersed-flow diffusion models, respectively[3]. The value of the film mass transfer coefficient ðbLÞ in the SFBR calculated fromthe former was only 5% lower than that fromthe latter[6]. Therefore, the plug-flow filmdiffusion, due to its simplicity, is chosen in this study as the main model to obtain bLvalues by neglecting the axial dispersion. In addition, the Gnielinski correlations [7], which are suitable for Sc (Schmidt number) o12,000 and ScRe (Reynolds number)>500, are adopted in this study to calculate the liquid diffusivity ðDLÞ by noting the good
agreement with the measured data [6]. The Gnielinski correlations, which assume the spherical shape of particles, are Shlam¼ 0:664 Sc1=3Re1=2; ð2Þ Shturb¼ 0:037 Re0:8Sc 1 þ 2:443 Re0:1ðSc2=3 1Þ; ð3Þ ShE¼ 2 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sh2 lamþ Sh2turb q ; ð4Þ ShFB¼ bLdP DL ¼ ½1 þ 1:5ð1 eFBÞShE: ð5Þ
In the above equations, the dimensionless parameters are defined as: Re ¼ ðdpuÞ=n with u ¼ uFB=eFB; Sc ¼
n=DL; and ShFB¼ ðbLdpÞ=DL: Typical values of uFB; eFB;
and dp in this study are 5, 8, 10, 15, and 20 m/h ðuFBÞ;
0.47 ðeFBÞ; and 1.04 mm ðdpÞ; respectively. The density
and viscosity of SPEG;6:5; SPEG;0:25; and SPEG;e are
998.2 kg/m3 and 1.005 cp [8], 1050 kg/m3 and 1.24 cp, and 1130 kg/m3and 1.64 cp, respectively, at 293 K.
The fundamental mathematical relationship for eva-luation of the SFBR results assuming plug-flow film diffusion is as follows: bLjt-0¼ QL maS lnCb Cb0 ; ð6Þ
where bL; QL; m; and as are the filmmass transfer
coefficient (m/s), liquid flow rate (cm3/s), mass of the adsorbent applied, and specific external surface area of the adsorbent, respectively. The Cb and Cb0 represent
the bulk concentrations of effluent at time t; and of inlet, respectively. The term bL as may be called the specific
filmmass transfer coefficient. Because the Gnielinski correlations assume the spherical shape of particles, correction with respect to the geometry of the particles is necessary for non-regularly shaped particles. The correction factor, fb; depending on the shape of the
adsorbent, can be determined by the difference between the experimental data and the Gnielinski correlation results of known adsorbates (i.e., standard compounds in this study) as follows[3]:
fb¼
ðbLaSÞexp
ðbLaSÞcor
: ð7Þ
In Eq. (7), the indices exp and cor indicate the values obtained fromthe experimental data, and those calculated fromthe Gnielinski correlations, respectively. The value of fb for F-400 is 2.18, averaged from2.11 of
PNP and 2.25 of ACS, of which the values were calculated fromthe reported DL values of PNP
(7.8 1010m2/s) and ACS (6.4 1010m2/s) [4]. It signifies that the relative errors of the DL recalculated
via Eqs. (2)–(5) with fb; which employs bL¼
ðbLasÞexp=ðfbðasÞcorÞ; and without fb; which gives bL¼
ðbLasÞexp=ðasÞcorto the reference value (6.4 10
10m2/s) for ACS are approximately 4% and 39%, respectively. Therefore, the effect of the geometry of the adsorbent has to be taken into account in the calculation of DLvia
Eqs. (2)–(5).
Fig. 2 presents the ratio of Cb=Cb0 for the PEG
adsorption from SPEG;e in the SFBR as a function of
time. For the A–B portion of the breakthrough curve, the effluent concentration increases only slightly after point A as a result of the gradual displacement of the lower MW fractions by the higher MW fractions present in the polydisperse systemof PEG. Therefore, the
AR
TI
CL
E
IN
P
RE
S
S
Table 3Langmuir isotherm constants and transport quantities of PEG in the aqueous system
Condition Isothermconstants Filmmass
transfer coefficient
Internal diffusion coefficients
qL(mole/kg) KL(m3/mole) r2 kL(105m/s) Ds(m2/s) R2a Dp(m2/s) R2a DSma(m2/s),
kbp(1/s), fMa R2a Case I: Initial concentration ðCb0Þ ¼ 50 g/m3in bright electroplating solution, SPEG;e 0.064b 1051b 0.9798 5.26 4.5 1012 0.98 2.9 109 0.98 1.06 1013, 1.99 106, 0.67 0.999 Case II: Cb0¼ 50 g/m3in aqueous solution of SPEG;6:5at pH ¼ 6:5 0.337 83.59 0.8642 10.0 2.2 1013 0.99 6.2 109 0.98 2.0 1013, 9.0 106, 0.92 0.999 In aqueous solution of SPEG;0:25at pH ¼ 0:25 0.093 336 0.8164 Case III: Cb0¼ 50 g/m3 9.55 1.3 1013 0.99 7.7 109 0.99 5.3 1013, 2.1 105, 0.96 0.99 Case IV: Cb0¼ 100 g/m3 6.83 2.5 1013 0.99 3.8 109 0.99 3.4 1013, 1.4 105, 0.99 0.99 Case V: Cb0¼ 200 g/m3 3.55 3.9 1013 0.99 1.6 109 1.00 1.2 1013, 1.3 105, 0.99 0.99 Case VI: Cb0¼ 450 g/m3 0.78 1.8 1012 0.97 1.1 109 0.98 1.5 1013, 1.3 106, 0.25 0.99 a R2¼ 1 ½Pðy e ycÞ2=Pðye ymÞ2: b Ref.[2]. C.-F. Chang et al. / Water Research 38 (2004) 2559 – 2570 2564
Cb=Cb0 in the plateau portion (A–B) was viewed as
staying constant, which was used to compute the experimental value of bLas fromEq. (6). Sequentially,
the Gnielinski correlations of Eqs. (2)–(5) were used to
calculate the liquid diffusivity values of PEG in dif-ferent solution, as shown in Table 2. A more detailed discussion of the calculations and the demonstration of its validity can be referred to our previous study[9]. The values of DL fromexperiments in SPEG;e and SPEG;0:25
are 0.9 and 1.03 1010m2/s, respectively. The D
Lvalue
of SPEG;6:5 can be obtained by the Stokes–Einstein
equation combined with the assumption of monodis-perse of PEG[10,11], and is equal to 1.15 1010m2/s.
3.3. External mass transfer in CSTR
In order to eliminate the film mass transfer resistance in the CSTR experiments, the influence of the intensity of mixing is examined, and illustrated inFig. 3. When the speed of the stirrer rotation is higher than 500 rpm, the effect of filmmass transfer resistance is greatly reduced and the internal mass transfer resistance is predominantly important for the adsorption kinetics. The external mass transfer coefficient ðkLÞ
predomi-nantly depends on the hydrodynamic flow across the surface of the adsorbent particles and other factors that may affect the diffusivity DL and filmthickness d: For
short times, it can be assumed that adsorption is exclusively controlled by the external mass transfer and that the surface concentration ðCÞ is zero or negligible with respect to the bulk concentration ðCbÞ:
Hence, kL can be calculated by
lnCb Cb0 t-0¼ kL maS VL t; ð8Þ 0 4 8 12 16 20 Time, min 20 40 60 80 100 X, % A — B
Fig. 2. Variation of dimensionless effluent concentration (X ; with X ¼ CbðtÞ=Cb0) with time for experiments using SFBR.
(J): Experimental data of PEG adsorption in SPEG;e at filter
velocity uFB¼ 10 m/h. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time, hours 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Cb / C b0 ,
-Fig. 3. Effects of stirring speed on the adsorption rate of PEG in SPEG;6:5 on F-400 in CSTR. (m), (}), (n), (J), and (&):
experimental data with stirring speeds of 300, 400, 500, 600, and 700 rpm, respectively. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Ce, mol/m3 0.00 0.02 0.04 0.06 0.08 0.10 0.12 qe , mol/kg
Fig. 1. The simulation of Langmuir isotherm for polyethylene glycol (PEG) adsorption in aqueous systemon activated carbon F-400. (&) and (—), (}) and (- -), and (J) and (— -): experimental data and simulation results at 298 K in aqueous systemof SPEG;6:5 at pH ¼6:5; aqueous systemof SPEG;0:25 at
pH ¼ 0:25 adjusted by concentrated H2SO4; and electroplating solution of SPEG;e; respectively.
In Eq. (8), Cb and Cb0 are the concentrations in the
bulk solution at time t ¼ t and 0, kL is the external
mass transfer coefficient, m is the mass of the adsorbent employed, as is the specific external surface
area of the adsorbent, VL is the volume of the solution
employed.
For the experiments performed under the stirring speed of 600 rpm, the results of kLare listed inTable 3.
Comparing kL at the same Cb0 of 50 g/m3 in SPEG;6:5;
SPEG;0:25; and SPEG;e; the mass transfer resistance of
PEG was higher in the case of SPEG;e possessing the
smaller kL value. Besides, the kL decreases with
increasing Cb0 in the case of SPEG;0:25at various values
of Cb0: Note that kL resulting fromFick’s first law is
given by kL¼ DL=d; in which d is the Nernst film
thickness. The dependency of kLon the concentration of
PEG can be attributed to that DL is inversely
propor-tional to the viscosity of the solution according to Wilke and Chang correlation[12], and that the filmthickness ðdÞ increases with increasing viscosity at the identical hydrodynamic operation conditions (flow rate in terms of L=h) [13–15]. Both phenomena lead to decreasing mass transfer coefficients at the increasing PEG concentration. Furthermore, it is also mentioned that the diffusion coefficient in liquid varies with the solute concentration[10].
3.4. Modeling of the adsorption kinetics in CSTR In this study the intraparticle diffusion is interpreted as the surface diffusion, pore diffusion, and branched pore kinetics models, respectively. The intraparticle diffusion is usually dependent on the particle size of the adsorbent unless for very fine particles. However, the surface diffusion may strongly depend on the initial concentration of the solution. Thus, for modeling the usual cases, this study did not investigate the effect of the particle size but that of initial concentrations on the mass transfer of PEG. Mass transfer from the liquid to solid phases (i.e., external filmtransfer) for the three models can be described as[3]
NL¼ kLðCb CsÞ ¼ D
qCp
qr at r ¼ dp
2: ð9Þ
In Eq. (9), NLis the mass transfer rate per unit surface
area, Cb is the adsorbate concentration in the bulk
liquid, Csis the value of Cbon the external surface of the
adsorbent ðr ¼ dp=2Þ; Cp is the adsorbate concentration
of liquid in the pores at r ¼ dp=2; D is the diffusivity of
adsorbate in particles, r is the intraparticle radial coordinate. The governing Eqs. (10)–(13) listed are valid for the surface diffusion (Eq. (10)), pore diffusion (Eq. (11)), and branched pore kinetics models (Eqs. (12)–(13)), respectively. Additionally, the corre-sponding initial and boundary conditions are listed in Appendix. A more detailed discussion of these equations
is given in the literature[3,16,17]
ep rp ! qCp qt þ qq qt¼ Ds q2q qr2þ 2 r qq qr ; ð10Þ ep qCp qt þ rp qq qt¼ Dp q2Cp qr2 þ 2 r qCp qr ; ð11Þ fMa qqMa qt ¼ fMaDSMa r2 q qr r 2qqMa qr Rb; ð12Þ ð1 fMaÞ qqmi qt ¼ kbpðqMa qmiÞ ¼ Rb: ð13Þ In Eqs. (10)–(13), q is the solid concentration of the adsorbate, r is the intraparticle radial coordinate, Dsand
Dp are the surface and pore diffusion coefficients,
respectively, Cpis the adsorbate concentration of liquid
in the pores, fMais the volume fraction occupied by the
macropore region, DSMa is the surface diffusion
coeffi-cient on the macropore surface, qMaand qmiare the solid
concentrations of the adsorbate in the macropores and micropores, respectively, Rb is the rate of transfer of
adsorbate from the macropores network to the micro-pores or branch micro-pores, kbp is the branch pore rate
coefficient. The model results are shown inTable 3and
Figs. 4 and 5.
Fig. 4 indicates that, for all the three models used in this study, the branched pore kinetics model gives the best fit of the CSTR experimental data in the whole experimental period. Either the surface or pore diffusion model is able to describe well the early period of the adsorption kinetics, due to the neglect of the other part of the adsorption mechanism contributing to the adsorption capacity. Nevertheless, all three models satisfactorily fitted the data of the CSTR experiments with sufficient accuracy. The determination coefficients R2 are between 0.98 and 0.999. If the tortuosity ðtÞ of the activated carbon is estimated by using t ¼ 1=ep;
then the value of Dp for the case of non-hindered
diffusion (denoted as Dpnh) may be computed applying
Dpnh¼ epDL=t ¼ e2pDL: In Case I of SPEG;e; substituting
ep¼ 0:54 and DL¼ 0:9 1010m2/s gives Dpnh¼ 0:26
1010m2/s, which is smaller than Dpobtained by model
simulation (denoted as Dpcwith Dpc¼ 2:9 109m2/s).
Similar results were obtained in Cases II–VI. The higher value of Dpc reflects the contribution of the additional
intraparticle mass flux mechanism caused by the surface diffusion. In other words, the pore diffusion coefficient ðDpcÞ calculated by using the pore diffusion model in this
study should be better regarded as the effective diffusion coefficient. Moreover, for large molecules (e.g., PEG), the surface diffusion may be of importance, due to multiple points of attachment of the molecule on the surface, which may lead to a decreased mobility of the molecule on the surface [3]. Therefore, it is not appropriate to describe the adsorption kinetics of PEG
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C.-F. Chang et al. / Water Research 38 (2004) 2559–2570 2566
by using the pore diffusion model accompanied with the pore diffusion coefficient ðDpÞ; unless Dp is regarded as
an effective diffusion coefficient of the intraparticle diffusion including the contribution of both surface and pore diffusion.
The average pore diameter of F-400 of 18 (A is smaller than the hydrodynamic diameters of PEG in all the three solutions (seen inTable 2). Although the multiple points of attachment of the hydrophobic segments on the surface may primarily contribute the adsorption of polymer PEG on F-400, the unadsorbed end of PEG may enter the pore with its front of smallest size facing the pore, then contact the surfaces of pores and also be adsorbed in the pore. As a result, a certain amount of PEG proceeds the adsorption in the micropores (i.e., 1 fMa fraction in branched pore kinetics model).
Comparing the results of Cases I–III, the fraction of
PEG adsorbed in the micropores in SPEG;e is largest.
This may be due to the repulsion of adsorbed PEG molecules on the macropore surface which then forces the transport of PEG from macropore into micropore region.
Fig. 5 shows the effects of various initial concentra-tions ðCb0Þ on the intraparticle diffusion. One single
Langmuir equation can be used to satisfactorily describe the whole adsorption range on the excuse of rather high determination coefficients. The surface diffusion and the pore diffusion coefficients increase and decrease in the limited level with increase of Cb0; respectively. The
increasing mobility of PEG on F-400 surface may be due to the occupation of weak energetic sites at high concentrations resulting in faster mass transfer rate. However, the decrease of pore diffusion coefficients can only be attributed to the thicker intraparticle diffusion
0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time, hrs 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time, hrs 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time, hrs 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time, hrs 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Cb / C b0 , -0.0 0.2 0.4 0.6 0.8 1.0 1.2 Cb / C b0 , -Cb / C b0 , -0.0 0.2 0.4 0.6 0.8 1.0 1.2 Cb / C b0 ,
-Fig. 4. Comparison of Cb=Cb0predicted by pore (- -), surface (— -) and branch pore kinetics models (—) with experimental data for
PEG adsorption on F-400 at same Cb0of 50 g/m3in CSTR. (&), (}), and (J): Experimental data at 298 K in SPEG;6:5; SPEG;0:25; and
layer at higher PEG concentrations. For further discus-sion of the predominant mass transfer resistance for the transport of PEG fromthe aqueous to the solid phase, the Biot number for the surface diffusion, Bisð¼
kLdpCb0=2DsrpqoÞ; is examined to judge the relative
influence of the external and internal mass transfer resistances. Filmdiffusion is considered to be the rate-determining step for Biso1; while the surface diffusion
primarily controls the adsorption kinetics for Bis>
502100[3]. Thus, both external and intraparticle mass transfers have significant effects for Bisin the range of
1–50. According to the values of Bis; the
rate-determin-ing steps of the PEG adsorption fromaqueous systems in this study can be divided into two groups: both film and surface diffusion control (e.g., Cases I and VI with Bis values of 6 and 2, respectively), and sole surface
diffusion control (e.g., Cases II, III, IV and V with Bis
values of 246, 396, 147 and 51, respectively). The results interpret that the film diffusion becomes important with the increasing Cb0in SPEG;0:25and the interaction of the
adsorbed/nonadsorbed PEG in SPEG;e: In addition, the
rough external surface of the adsorbent may also significantly cause the external mass transfer resistance even under intense stirring speed[18].
4. Conclusions
The adsorption behaviors of PEG on F-400 at low coverages seemsimilar in three solutions of SPEG;6:5;
SPEG;0:25and SPEG;e: However, the properties of solution
(e.g., high ionic strength and lower pH value) have significantly negative effects on the adsorption of PEG in SPEG;eand SPEG;0:25 when the adsorption approaches
the plateau, due to the electrostatic repulsion and the strong steric repulsion between adsorbed PEG.
The liquid diffusivity can be obtained fromthe short plateau of the PEG adsorption breakthrough curve onto F-400 in SPEG;e in SFBR by means of the Gnielinski
correlations. The internal mass transfer for the adsorption
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Pore diffusion model
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Surface diffusion model
0 7 Time, hrs 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Cb / Cb0 , -0.0 0.2 0.4 0.6 0.8 1.0 1.2 Cb / Cb0 , -Cb / Cb0 ,
-Branch pore kinetics model
1 2 3 4 5 6 0 7 Time, hrs 1 2 3 4 5 6 0 7 Time, hrs 1 2 3 4 5 6
Fig. 5. Comparison of Cb=Cb0predicted by pore, surface and branch pore kinetics model (—) with experimental data for PEG
adsorption on F-400 in CSTR. (}), (n), (J) and (X): Experimental data of PEG adsorption in SPEG;0:25with Cb0¼ 50; 100, 200, and
450 g/m3, respectively.
C.-F. Chang et al. / Water Research 38 (2004) 2559–2570 2568
of PEG onto F-400 encountered in CSTR can be successfully interpreted by the surface, pore, and branched pore kinetics models. However, the pore diffusion coefficients obtained fromthe pore diffusion model should be regarded as the effective diffusion coefficients when compared with the non-hindered pore diffusion coeffi-cients calculated fromthe liquid diffusivity.
The surface diffusion and the pore diffusion coeffi-cients are increasing and decreasing in the limited level with increasing Cb0; respectively. The increasing
mobi-lity of PEG on F-400 surface may be due to the occupation of weak energetic sites at high concentra-tions resulting in faster mass transfer rate. However, the decreasing pore diffusion coefficients can only be attributed to the thicker intraparticle diffusion layer at higher PEG concentrations. The filmdiffusion becomes important with the increasing Cb0 in SPEG;0:25 and the
interaction of the adsorbed/nonadsorbed PEG in SPEG;e:
Therefore, both filmand surface diffusion resistances, i.e., film-surface diffusion model, should be taken into account.
Acknowledgements
The authors would like to thank the sandwich programof NSC/DAAD (National Science Council of Taiwan/Deutscher Akademischer Austauschdienst) for Ph.D. candidates, and the Powder Technology Labora-tory of the Chemical Engineering Department of National Taiwan University for the assistance in the powder characterization.
Appendix
The corresponding initial and boundary equations of the surface, pore, and branch pore kinetics models are described as follows:
For the surface diffusion model, qðr; 0Þ ¼ 0; Cpðr; 0Þ ¼ 0; qq qr¼ 0 at r ¼ 0 and NL¼ Dsrp @q @rr¼dp=2 ¼ dprp 6 d%q dt; qðdp=2; tÞ ¼ qs; Cpðdp=2; tÞ ¼ Cs; qðdp=2; tÞ ¼ f ðCsÞ; VLðCb0 CbÞ ¼ m%q; %q ¼ 3 ðdp=2Þ3 Z dp=2 0 qr2dr:
For the pore diffusion model, Cpðr; 0Þ ¼ 0; qðr; 0Þ ¼ 0; qCp qr r¼0¼ 0; and NL¼ Dp qCp qr r¼d p=2 ; q ¼ f ðCpÞ; VLðCb0 CbÞ ¼ m%q; %q ¼ 3 ðdp=2Þ3 Z dp=2 0 qr2dr: For the branch pore kinetics model,
qMaðr; 0Þ ¼ 0; qmiðr; 0Þ ¼ 0; Cbð0Þ ¼ Cb0; qMaðdp=2; tÞ ¼ qsðtÞ; qs¼ f ðCsÞ; qqMa qr ð0; tÞ ¼ 0; NL¼ fMaDSMarp qqMa qr r¼dp=2 ; VLðCb0 CbÞ ¼ m%q; %q ¼ 3 ðdp=2Þ3 Z dp=2 0 qr2dr; q ¼ fMaqMaþ ð1 fMaÞqmi: References
[1] Fang CL. General concepts of additives in the electroplat-ing solution. Taipei, Taiwan: Finishelectroplat-ing Science Publishers; 1996.
[2] Chang CF, Chang CY, Tsai WT. Adsorption equilibriumof polyethylene glycol in the copper electroplating solution on activated carbon. J Colloid Interface Sci 2000;232:207–9. [3] Sontheimer H, Crittenden JC, Summers RS. Activated
carbon for water treatment. Karlsruhe, Germany: DVGW-Forschungsstelle; 1988.
[4] Isabel R. Temperature dependence of the kinetics of activated carbon adsorption. Internship work performed at Heinrich-Sontheimer-Laboratory. Karlsruhe, Germany: DVGW-TechnologiezentrumWasser; 1998.
[5] Standen A, Executive Editor. Kirk–Othmer encyclopedia of chemical technology, 2nd ed. New York: Wiley; 1969. [6] Cornel PK, Sontheimer H, Summers RS, Roberts PV.
Sorption of dissolved organics fromaqueous solution by polydtyrene resins-II. External and internal mass transfer. ChemEng Sci 1986;41(7):1801–10.
[7] Gnielinski V. Gleichungen zur berechnung des waerme-und stoffaustausches in durchstroemten ruhenden kugel-schuettungen bei mittleren und grossen pecletzahlen. Verf Tech 1978;12(6):363–6.
[8] Streeter VL. Fluid mechanics, 8th ed. Singapore: McGraw-Hill; 1987.
[9] Chang CF, Chang CY, H.oll H. Adsorption behavior of 2-naphthalenesulfonate on activated carbon fromaqueous systems. Ind Eng Chem Res 2003;42:6904–10.
[10] Cussler EL. Diffusion: mass transfer in fluid systems. Cambridge, UK: Cambridge University Press; 1984. [11] Polverari M, van de Ven TGM. Dilute aqueous poly
(ethylene oxide) solutions: clusters and single molecules in thermodynamics equilibrium. J Phys Chem 1996;100: 13687–95.
[12] Wilke CR, Chang P. Correlation of diffusion coefficients in dilute solutions. AIChE J 1955;1(2):264–70.
[13] Carberry JJ. A boundary-layer model of fluid-particle mass transfer in fixed beds. AIChE J 1960;6(3):460–3. [14] Kataoka T, Yoshida H, Ueyama K. Mass transfer in
laminar region between liquid and packing material surface in the packed bed. J ChemEng Japan 1972;5(2): 132–6.
[15] Kataoka T, Yoshida H, Ueyama K. Liquid phase mass transfer in ion exchange based on the hydraulic radius model. J Chem Eng Japan 1973;6(2):172–7.
[16] Peel RG, Benedek A. Dual rate kinetic model of fixed bed adsorber. J Environ Eng ASCE 1980;106(4): 797–813.
[17] Peel RG, Benedek A, Crowe CM. A branched pore kinetic model for activated carbon adsorption. AIChE J 1981; 27(1):26–32.
[18] Chatzopoulos D, Varma A, Irvine R. Activated carbon adsorption and desorption of toluene in the aqueous phase. AIChE J 1993;39(12;):2027–41.
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