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Journal of Chromatography A, 1216 (2009) 7840–7845

Contents lists available at ScienceDirect

Journal of Chromatography A

journa l homepage: www.e lsev ier .com/ locate /chroma

xpansion and hydrodynamic properties of �-cyclodextrin polymer/tungstenarbide composite matrix in an expanded bed

un Zhaoa, Dong-Qiang Lina,b, Shan-Jing Yaoa,∗

Department of Chemical and Biochemical Engineering, Zhejiang University, 38# Zheda Road, Hangzhou 310027, Zhejiang Province, ChinaState Key Laboratory of Chemical Engineering, Zhejiang University, 38# Zheda Road, Hangzhou 310027, Zhejiang Province, China

r t i c l e i n f o

rticle history:eceived 21 July 2009eceived in revised form5 September 2009ccepted 23 September 2009vailable online 26 September 2009

eywords:omposite matrix

a b s t r a c t

The expansion and hydrodynamic properties of matrix are significant for expanded bed adsorption (EBA)processes. A series of new composite matrices CroCD-TuC are studied and estimated in an expanded bed. Itis found that the heavier matrix is better suited for high operation fluid velocity than the lighters. Althoughthe Richardson–Zaki equation can well correlate the bed voidage with fluid velocity for all CroCD-TuCmatrices tested, the modifications are proposed to improve the accuracy of theoretical predictions ofcorrelation parameters, including terminal settling velocity (Ut) and expansion index (n). Residence timedistributions (RTDs) are determined, and the Bodenstein number (Bo) and axial dispersion coefficient(Dax) are employed to analyze the liquid mixing in the expanded bed. It is found for CroCD-TuC matrices,

yclodextrin polymerungsten carbidexpanded bedxpansionydrodynamic property

both parameters notably changed with the variation of fluid velocity and viscosity. Furthermore, Dax isan intuitive parameter estimating the bed stability on various operating conditions, and also a restrictionon developing the matrix for high operation fluid velocity. The comparison of the hydrodynamic prop-erties on different matrices reveals that CroCD-TuC 3 and CroCD-TuC 4 seem superior to other matricesin hydrodynamic properties, making them promising matrices for further use. The correlations as thefunctions of fluid velocity and viscosity have been established which may provide beneficial informationfor practical applications of CroCD-TuC matrices in EBA processes.

. Introduction

Downstream process is a bottleneck of the biotechnology indus-ries. Currently new integrated separating methods have beeneveloped to enhance the efficiency and to reduce the cost ofio-production. Expanded bed adsorption (EBA) is a promisingechnique for bioseparations [1,2]. It integrates clarification, con-entration, and primary purification into a single step, allowinghe capture of bio-molecules from unclarified feedstock withoutrior removal of particulates [3,4]. Expanded bed performs as atably classified fluidized bed with plug flow upward through theolumn, thus it requires specially designed adsorbents particu-arly different from that for packed bed [2,5]. Generally, the matrixor EBA desires regular spherical shape, proper size and size dis-ribution, relatively high density, good mechanical strength and

hemical durability [6,7]. Until recently, a number of pellicular6,8], macro-porous [9,10], high-density [11], and polymer-coated

atrices [12] have been developed and applied in EBA. Morexcellent supporting matrices have been produced and further

∗ Corresponding author. Tel.: +86 571 87951982; fax: +86 571 87951982.E-mail address: yaosj@zju.edu.cn (S.-J. Yao).

021-9673/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2009.09.054

© 2009 Elsevier B.V. All rights reserved.

modified with various ligands to fabricate functionalized adsor-bents [13].

The properties, especially the expansion and hydrodynamicproperties in an expanded bed, are quite significant for the matrix.These characteristics may provide beneficial information for prac-tical applications for EBA processes. The terminal settling velocityand the expansion index are the two objective parameters to char-acterize expansion properties and to provide reference for thecomparison with other existing EBA matrices. The residence timedistribution (RTD) measurement is a classical method commonlyused to examine the liquid mixing in an expanded bed [14,15].The theoretical analysis for fluidized or packed bed is employedin expanded bed operation to describe the flowing and dispers-ing characteristics in the column, and large amounts of empiricalor semi-empirical correlations have also been introduced to fit theexperimental data. Nowadays, there have been many reports aboutthe test of commercialized adsorbents, including StreamlineTM

DEAE [14,16,17], Fastline SP [18], Q HyperZ and CM HyperZ

[19], DEAE-Spherodex LS [20], etc. Besides that, lots of home-made matrices have also been assessed, such as cellulose/stainlesssteel [21], agarose/Nd-Fe-B alloy [22], and agarose/silica–zirconiabeads [12]. However, the conclusions are discrepant from differentresearches due to the difference of the matrix and expanded bed

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J. Zhao et al. / J. Chromato

ystem used. Therefore, each novel matrix should be assessed inerms of the expansion and hydrodynamic properties to ensure itsurther application.

In our previous work, a series of cyclodextrin-based sup-orting matrices named CroCD-TuC have been prepared by theeversed phase suspension crosslinking technique. Tungsten car-ide (TuC) powder is selected as a densifier embedded in the-cyclodextrin (�-CD) polymer skeleton. The matrices have reg-lar spherical shape, suitable pore structure and high mechanicaltrength. Although the application of CD polymer beads in thexpanded bed has been reported [23], more systematic characteri-ation of CD-based matrix in the column is still necessary for betternderstanding and rational process design. In the present work, thexpansion and hydrodynamic properties of CroCD-TuC beads wille investigated. Some important parameters will be examined tovaluate the mixing and dispersing characteristics in an expandeded. The influences of matrix density, fluid velocity and viscosityn the expansion and hydrodynamic properties will be discusseds well.

. Experimental

.1. Materials

�-Cyclodextrin (�-CD, DRAMAX®W7 Pharma) was provided byaxdragon BioChem. Ltd. (Guangzhou, China). Tungsten carbide

TuC) with the density of 15.1 g cm−3 and mean particle diameterf 2–5 �m was obtained from Ganzhou TEJING Tungsten & Molyb-enum Co., Ltd. (Ganzhou, China). Acetone (≥99%) and glycerol≥99%) were both obtained from Hangzhou SHUANGLIN Chemicalngineering Reagent Industry Co., Ltd. (Hangzhou, China). Deion-zed water was purchased from Hangzhou WAHAHA Group Co., Ltd.Hangzhou, China). Other chemicals used were of reagent grade origher quality.

.2. Preparation of composite matrices

The �-CD polymer/TuC composite beads were prepared by theeversed phase suspension crosslinking technique in our previousork (unpublished results). The mass ratio of TuC/CD is 0, 1.0, 1.75,

.5, 3.25, 4.0 and 5.0, and the corresponding matrices are named asroCD-TuC 1–CroCD-TuC 7 respectively.

.3. Determination of expansion properties and liquid mixing inxpanded bed

A home-made expanded bed (20 mm diameter, 1.0 m long) issed to determine expansion characteristics. A small amount oflass beads (0.3 mm diameter, <5% total sedimented bed height) isdded at the column inlet to improve flow distribution, and a mov-ble adapter is used to adjust the position of liquid outlet to the topf expanded bed. The fluid (deionized water or glycerol solution)s transported using a peristaltic pump (Longer Precision Pump,aoding, China). Proper column vertical alignment is assured in allxperiments. The bed height is measured three times for each fluidelocity after the expansion equilibrium, and the average value isdopted.

As published previously [19,21], the Bodenstein number (Bo)nd the axial dispersion coefficient (Dax) are often used to evaluatehe liquid mixing in the expanded bed. Both parameters are cal-ulated based on the response curve in the outlet of the column

y RTD measurement. In the present work, 0.5 ml acetone solution10%, w/w) is injected at the bottom inlet of the column in each test,nd the response signal is detected by a UV detector (WellChromast scanning spectrophotometer K-2600, Knauer, Berlin, Germany)t 265 nm.

1216 (2009) 7840–7845 7841

3. Theoretical descriptions

3.1. Expansion characteristics

The relationship between the superficial fluid velocity (U)and the voidage of expanded bed (ε) can be correlated by theRichardson–Zaki equation [24]:

U = Ut · εn (1)

where Ut is the terminal settling velocity of particles, and n is theexpansion index. The theoretical value of Ut can be calculated bythe Stokes’ law as

Ut,St = (�p − �l)gd2p

18��l(2)

where dp is the diameter of a particle, � is fluid kinematic vis-cosity, and �p and �l represent the density of a particle and fluidrespectively.

The bed voidage (ε) can be calculated as

ε = 1 − 1 − ε0

E(3)

where the voidage of sedimented bed (ε0) is usually assumed as 0.4[25], and the expansion factor E is defined as

E = H

H0(4)

When the terminal Reynolds number (Ret) is less than 0.2,corresponding to the conditions under which the inertia force isnegligible, the expansion index (n) can be expressed as a functionof the mean particle diameter (dm) and the column diameter (dc)as described by Richardson and Zaki [24]:

n = 4.65 + 19.5dm

dc(5)

According to Martin et al. [26], the Gallileo number (Ga) andthe terminal Reynolds number (Ret) are introduced to describe thefluidization behavior of particles as

Ret =[

23Ga

+ 0.6Ga0.5

]−1 1

1 + 2.35(

dp/dc

) (6)

Ga = (�p − �l)gd3p

�2�l(7)

Ret = dpUt,Ga

�(8)

5.1 − n

n − 2.4= 0.016Ga0.67 (9)

Hence Ut and n can be calculated with Eqs. (6)–(9).

3.2. Liquid mixing in expanded bed

According to the response curve of RTD measurement, the the-oretical plate number (N) of the column is calculated as

N = 5.54

(tR

W1/2

)2

(10)

where tR and W1/2 represent the retention time and the half-peakwidth respectively.

Bodenstein number (Bo) that relates convective transport of liq-

uid to dispersion and describes a possible influence of axial mixingon the performance of the EBA step is defined as [5]:

Bo = UH

εDax(11)

7842 J. Zhao et al. / J. Chromatogr. A 1216 (2009) 7840–7845

Table 1Main physical properties of CroCD-TuC beads.

Matrices TuC/CD (g/g) dm (�m) �p (g cm−3) ω P S (m2 g−1) dpore (nm)

CroCD-TuC 1 0.00 164 1.11 0.68 0.76 23.3 117CroCD-TuC 2 1.00 160 1.34 0.56 0.75 28.1 80CroCD-TuC 3 1.75 144 1.50 0.49 0.73 27.8 70

0.45 0.74 24.8 720.40 0.72 24.5 650.36 0.72 19.8 730.32 0.71 17.4 73

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CroCD-TuC 4 2.50 163 1.64CroCD-TuC 5 3.25 157 1.79CroCD-TuC 6 4.00 152 2.00CroCD-TuC 7 5.00 168 2.09

here Dax is the axial dispersion coefficient in the liquid phase. Boan be calculated from theoretical plate number (N) as follows [21]:

1N

= 2Bo

+ 8Bo2

(12)

ence, the Bo and Dax can be obtained from Eqs. (10)–(12).Krishnaswamy and Shemilt [27] recommend a correlation

etween Dax and U as

Dax

D0= A1

(U

Ut

)B1(13)

here A1 and B1 are constants, and D0 is axial dispersion coefficientor empty bed. Substituting Eq. (1) into Eq. (13) gives the correlationetween Dax and ε as

ax = A′ · ε(nB1) (14)

here A′ = A1·D0 is an undetermined coefficient.

. Results and discussion

Based on the previous work, the CroCD-TuC beads have beenrepared with regular spherical shape and suitable pore structure.he particle size range is 80–320 �m. The main physical proper-ies of the matrices, including density, water content, mean particleiameter and pore properties, are summarized in Table 1.

.1. Expansion characteristics and correlations

Similar to the results published before [9,12,21], the expansionactor decreases significantly as the matrix density increases at

he same fluid velocity, as shown by expansion curves in Fig. 1.t demonstrates the matrix with high density is suitable for highperation fluid velocity. The fluid viscosity is another key factornfluencing the bed expansion properties. It is found that the matrixxpands more easily in higher viscous fluid, because viscous fluid

ig. 1. Bed expansion factor as the function of fluid velocity for CroCD-TuCeads in water at 20 ◦C: (�) CroCD-TuC 1; (�) CroCD-TuC 2; (�) CroCD-TuC 3;�) CroCD-TuC 4; (�) CroCD-TuC 5; (�) CroCD-TuC 6; (♦) CroCD-TuC 7; alsoor CroCD-TuC 4 in water and in glycerol solutions at 25 ◦C: (�) in water,= 0.90 × 10−6 m2 s−1; (©) in 10%(w/w) glycerol, � = 1.13 × 10−6 m2 s−1; (�) in0%(w/w) glycerol, � = 1.48 × 10−6 m2 s−1.

Fig. 2. Comparison of fluid velocity at expansion factor of 2.5 with matrix density.(�) CroCD-TuC (solid line); (©) Cell-TuC-DEAE (dashed line), data from Ref. [9]; (�)Cell-SSP-L (dot line), data from Ref. [21]; (�) StreamlineTM SP, data from Ref. [22];(�) StreamlineTM DEAE, data from Ref. [28].

causes relative high drag force on the particle surface, and the influ-ence of gravity is weakened. Therefore, it requires high-densitymatrices to keep the same expansion factor at the correspondingfluid velocity in viscous fluid.

Fig. 2 gives a comparison on CroCD-TuC and other reportedmatrices of density vs. fluid velocity at E = 2.5. It follows an approx-imately linear relation between matrix density and fluid velocityat E = 2.5 for CroCD-TuC beads, the same as to Cell-TuC-DEAE [9]and Cell-SSP-L [21]. Most of these matrices have the size range of130–180 �m, hence they perform similar expansion property fromeach other. However, the commercialized matrices StreamlineTM

SP and DEAE show a little higher fluid velocity at E = 2.5 althoughtheir density is lower, for they have larger mean particle diameter(ca. 200 �m) than others.

The expansion factor and bed voidage of expanded bed are wellcorrelated by Richardson–Zaki equation (Eq. (1)) for CroCD-TuCmatrices, as shown in Fig. 3. The bed voidage increases linearlywith the increase of fluid velocity in double-logarithmic coordi-

Fig. 3. Richardson–Zaki correlation between fluid velocity and bed voidage forCroCD-TuC beads in water at 20 ◦C (solid line) and in glycerol solutions at 25 ◦C(dashed line, symbols as same as Fig. 1).

J. Zhao et al. / J. Chromatogr. A 1216 (2009) 7840–7845 7843

Table 2Parameters of Ut and n correlated with Richardson–Zaki equation and the some predications.

Matrices Liquid phase Ut (×10−3 m s−1)c n

Ut,exp Ut,St Ut,Ga Experimental Eq. (5) Eq. (9)

CroCD-TuC 1 Watera 1.17 1.63 1.18 5.45 4.81 4.99CroCD-TuC 2 Watera 4.56 4.74 3.32 5.28 4.81 4.83CroCD-TuC 3 Watera 5.07 5.62 3.93 5.15 4.79 4.80CroCD-TuC 4 Watera 7.47 9.22 6.24 4.96 4.81 4.67CroCD-TuC 5 Watera 9.19 10.57 7.11 4.92 4.80 4.62CroCD-TuC 6 Watera 10.09 12.59 8.40 4.73 4.80 4.55CroCD-TuC 7 Watera 14.78 16.79 10.87 4.63 4.81 4.41CroCD-TuC 4 Waterb 9.06 9.14 6.20 5.30 4.81 4.64CroCD-TuC 4 10% glycerolb 6.62 6.86 4.78 5.15 4.81 4.76CroCD-TuC 4 20% glycerolb 4.60 4.94 3.53 4.98 4.81 4.87

le diameter (dm).

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It reveals in Fig. 5 that Bo seems somewhat steady and evenslight increase with the further increase of fluid velocity. This isinsufficient to provide the evidence that the column performanceis better at high fluid velocity. In fact, the motion of suspendedparticles in the bed appears much disturbed at high fluid veloc-

a The experiments are carried out at 20 ◦C.b The experiments are carried out at 25 ◦C.c The values of Ut calculated by Eqs. (2) and (6)–(8) are based on the mean partic

ates, and it also increases as the fluid viscosity or matrix densityncreases at the same fluid velocity. The correlation parameters areegressed and listed in Table 2. The theoretical values of Ut pre-icted by Stokes’ law (Eq. (2)), by Martin’s method (Eqs. (6)–(8)),nd n calculated with Eqs. (5) and (9) are also listed in Table 2 foromparison. It is found that Ut predicted by Stokes’ law is somewhatlose to the experimental data, but an obvious deviation occurs ashe matrix density increase. As we know, the Stokes’ law is a sim-lified model for the infinitely dilute solution by neglecting theollision or agglomeration between particles. It concerns of theettling behavior of a single particle, as a result the particle sizend density distributions are neglected. Although Ut predicted bytokes’ law only provides approximation of the expansion param-ters, it is fairly accurate and convenient for the prediction of thexpansion characteristics in comparison with other empirical mod-ls such as Martin’s method (Eqs. (6)–(8)). However, in order tourther improve the accuracy of Ut predicted, a modification of Eq.15) is proposed with a good agreement between Ut obtained inxperiments and predicted:

t,mod = (Ut,St)1.03 (15)

The expansion index (n) decreases with the increase of matrixensity and fluid viscosity as listed in Table 2. It is a failure in fittinghe data with Eqs. (5) or (9) for the reason that the values of Ret ora are beyond the applicable range.

In the present work, it is suggested to describe the correlationetween Ga and n in the form similar to Martin et al. [26] as

5.7 − n

n − 2.4= 0.022Ga0.8 (16)

Fig. 4 gives a comparison of the results calculated with differ-nt empirical equations. It is obvious that Eq. (16) gives a betterescription of the correlation between Ga and n for all CroCD-TuCatrices tested than other existing equations [21,26].

.2. Liquid mixing in expanded bed

.2.1. Bo analysisRTD measurement is used to evaluate the liquid mixing in an

xpanded bed. The Bo number is calculated from the theoreticallate number with Eq. (12) for CroCD-TuC matrices. Here Bo/H0

s used to eliminate the influence of different sedimented bedeight. As shown in Fig. 5, at the same fluid velocity, Bo/H0 gen-rally decreases with the increase of matrix density, also with the

ncrease of fluid viscosity. As we know, Bo relating the convectiveransport of liquid to dispersion describes the possible influence ofxial mixing on the performance of the EBA operation. It is con-idered that the flow pattern is inclined to plug flow when Bo > 20,.e., the expanded bed will behave similarly to a packed bed [16].

Fig. 4. Expansion index as the function of Ga for CroCD-TuC beads in water at 20 ◦C.(�) CroCD-TuC beads. Solid line: calculated with Eq. (16); dashed line: calculatedwith Eq. (9) according to Martin et al. [26]; dot line: calculated according to Lin etal. [21].

For all CroCD-TuC matrices examined, the values of Bo are higherthan 20 (data not shown), verifying the stable plug flow in the bed.However, as fluid velocity increases, Bo decreases rather acutely,indicating that the bed is less stable at high fluid velocity due to theintensifying disturbance.

4.2.2. Dax analysis

Fig. 5. Bo/H0 as the function of fluid velocity for CroCD-TuC beads in water at 20 ◦Cand in glycerol solutions at 25 ◦C (symbols as same as Fig. 1).

7844 J. Zhao et al. / J. Chromatogr. A 1216 (2009) 7840–7845

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wdn

A

n

Fs

Fig. 8. Dax as the function of bed voidage for CroCD-TuC 4 in water and in glycerolsolutions at 25 ◦C (symbols as same as Fig. 1).

Table 3Comparison of the hydrodynamic results for CroCD-TuC with other matrices for EBA.

Matrix U (×10−3 m s−1) E Bo/H0 (cm−1) Dax

(×10−6 m2 s−1)

CroCD-TuC 3 1.12 2.32 9.49 3.68CroCD-TuC 4 1.16 1.88 6.64 4.84Cell-TuC-DEAE 2 [9] 1.11 2.03 5.50 5.74Cell-SSP-L4 [21] 1.04 1.95 3.89 7.39Ti-Cell-CL [28] 1.11 2.28 5.85 4.29

ig. 6. Dax as the function of fluid velocity for CroCD-TuC beads in water at 20 ◦Csymbols as same as Fig. 1).

ty, which indicates notable disturbance in the flowing field. It is aailure for Bo analysis to estimate the liquid mixing on this condi-ion. Therefore, Dax analysis is introduced to deal with the problemnd the results are shown in Fig. 6. It is found that the data fromach matrix tested are extremely close at the same fluid velocity, inpite of the great discrimination in matrix density. The correlationetween Dax and U can be conveniently represented as

ax = 0.28U1.63 (17)

ith a decision coefficient (R2) of 0.98. The form of Eq. (17) is sim-lar to Eq. (13), and the power index 1.63 in Eq. (17) is very closeo the value 1.69 given by Krishnaswamy and Shemilt [27]. Dax iskey parameter estimating the bed stability of expanded bed on

arious operating conditions. It reveals that the increase of fluidelocity is restricted during the operation due to the rapid increasef Dax in the exponential form according to Eq. (17). Though higheruid velocity is desired for the expansion of heavier matrices, itay result in intensified axial dispersion and therefore unwanted

isturbance in the stable flow field in the liquid phase. Dax is alsonfluenced by the fluid viscosity, as shown in Fig. 7, for CroCD-TuC 4,ax increases as fluid viscosity increases at the same fluid velocity.

The correlation of Dax and ε (shown in Fig. 8) is given by Eq. (14),hose parameters A′ and nB1 are obtained by linear regression inouble-logarithmic coordinates. A further study reveals both A′ andB1 can be described approximately as the functions of �:

′ −6

(2.40 × 10−6

)

= 8.61 × 10 exp

�(18)

B1 = 4.02 + 3.89 × 10−6

�(19)

ig. 7. Dax as the function of fluid velocity for CroCD-TuC 4 in water and in glycerololutions at 25 ◦C (symbols as same as Fig. 1).

Streamline DEAE [28] 1.05 2.64 4.90 5.63Streamline SP [29] NAa 2.00 3.70 6.35Streamline SP XL [29] NA 2.55 2.38 88.30

a NA = not available.

with the decision coefficient (R2) both above 0.98. However, Eq. (14)can be used only in a restricted range, which is clearly revealed bythe intersection of extending lines shown in Fig. 8. It is a criticalpoint, and thus the applicable range of ε is given by

∂Dax

∂�< 0 (20)

Substituting Eqs. (14), (18) and (19) into Eq. (20) giving the solutionas ε > 0.54, i.e., E > 1.3 referring to Eq. (3). It means Eq. (14) is inap-plicable in the region of low fluid velocity, since the bed is not fullyexpanded and the particles agglomerate on this condition, resultingin a failure in expanded bed operation.

4.3. Comparison of expansion and hydrodynamic properties

The expansion and hydrodynamic properties of CroCD-TuCtogether with other matrices for EBA are listed in Table 3 for com-parison at similar fluid velocity (ca. 1.1 × 10−3 m s−1). It is foundthat CroCD-TuC 3 shows the best column performance among thematrices listed. The Bo/H0 value of CroCD-TuC 3 is 2.5 times higherand Dax is only about one-half compared with that of StreamlineTM

SP. It also seems superior to StreamlineTM DEAE, StreamlineTM SP XLand other home-made matrices in hydrodynamic properties. Theheavier matrix CroCD-TuC 4 performs not so well as CroCD-TuC 3in hydrodynamic properties, however, it can be subjected to higherfluid velocity. The favorable hydrodynamic properties will makeCroCD-TuC 3 and CroCD-TuC 4 be competent for the separationprocesses in expanded bed.

5. Conclusions

The expansion and hydrodynamic properties of CroCD-TuCmatrices are examined in the expanded bed. Some correlations areestablished, which may provide beneficial information to practicalapplication for CroCD-TuC matrices in EBA processes. It is found forall CroCD-TuC matrices tested, the expansion characteristics can

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J. Zhao et al. / J. Chromato

e well correlated by the Richardson–Zaki equation. However, theheoretical predictions of parameters (Ut and n) with Stokes’ law orther models are somewhat deviated from that correlated, need-ng improvement with empirical modifications. In summary, fluidelocity and viscosity are the crucial factors influencing the expan-ion and hydrodynamic properties. It reveals that high fluid velocityauses high expansion factor, but results in the decrease of Bo andhe increases of Dax. So fluid velocity is a key parameter reflectinghe bed stability of an expanded bed, and also it is a restriction oneveloping the matrix for high operation fluid velocity. The furthernalysis shows that Dax is rather sensitive to high fluid velocity,hile Bo seems better sensitivity to the fluid velocity in the low-

o-middle region. Additionally, the liquid mixing in expanded beds also greatly dependent on the fluid viscosity. As fluid viscosityncreases, Dax notably increase at the same fluid velocity, which isot favorable to the stable operation in an expanded bed.

Comprehensively considering of the expansion and hydrody-amic properties of CroCD-TuC matrices assessed, CroCD-TuC 3nd CroCD-TuC 4 are the promising matrices for further EBA use.hey are superior to StreamlineTM DEAE, StreamlineTM SP and otherome-made matrices in hydrodynamic properties. It is expectablehat they will play good performance on the separation processesn expanded bed.

omenclature

1 undetermined coefficient′ undetermined coefficient (m2 s−1)1 undetermined coefficiento Bodenstein number0 axial dispersion coefficient for empty bed (m2 s−1)ax axial dispersion coefficient (m2 s−1)c diameter of the column (mm)m mean diameter of particles (�m)p diameter of a particle (�m)pore mean pore diameter (nm)

bed expansion factora Gallileo number of a particle

acceleration of gravity (m s−2)height of expanded bed (cm)

0 height of sedimented bed (cm)theoretical plate numberexpansion indexparticle porositydecision coefficient (with the square form)

et terminal Reynolds number of a particlespecific surface area (m2 g−1)

R retention time (min)superficial fluid velocity (m s−1)

−1

t terminal settling velocity (m s )t,exp terminal settling velocity calculated from experimental

data (m s−1)t,Ga terminal settling velocity calculated with the Gallileo

number (m s−1)

[[

[

1216 (2009) 7840–7845 7845

Ut,mod modified experimental terminal settling velocity (m s−1)Ut,St terminal settling velocity calculated with the Stokes’ law

(m s−1)V pore volume (cm3 g−1)W1/2 half-peak width (min)

Greek lettersε voidage of expanded bedε0 voidage of sedimented bed� kinematic viscosity of fluid (m2 s−1)�l liquid density (g cm−3)�p particle density (g cm−3)ω water content

Acknowledgments

This work was supported by a grant from the Ministry of Scienceand Technology of China (National Basic Research Program of China,2007CB707805) and the National Natural Science Foundation ofChina.

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