A

atwa©

K

1

daaay

uipsiapddamc

0d

Journal of Chromatography A, 1151 (2007) 25–30

Counter-current chromatography separation scaled upfrom an analytical column to a production column

Philip Wood a,b,∗, Svetlana Ignatova a, Lee Janaway a,b, David Keay b,David Hawes a, Ian Garrard a, Ian A. Sutherland a

a Brunel Institute for Bioengineering, Brunel University, Uxbridge UB8 3PH, UKb Dynamic Extractions Ltd., 890 Plymouth Road, Slough Trading Estate, Slough, Berkshire SL1 4LP, UK

Available online 12 February 2007

bstract

An analytical separation was performed on an analytical J-type counter-current chromatography (CCC) instrument using a 5.4 ml column, with1 ml/min mobile phase flow rate. This separation had a resolution of 0.69 and was achieved in 10 min. The same separation was performed using

wo 2300 ml columns connected in series at a flow rate of 850 ml/min using a production scale J-type centrifuge. This production scale separationas also obtained in 10 min with a resolution of 0.71. This represents an 850 times increase in productivity. This paper presents these separations

nd the underlying scale up theory.2007 Elsevier B.V. All rights reserved.

orman

gtc

msfmhef4sohp[a

eywords: Counter-current chromatography; Scale up; Mass transfer; High-perf

. Introduction

The ideal separation technology for industry is one that allowsirect scale up. Put simply, the same separation can be obtainedt any scale. A separation being defined in terms of purity, yieldnd time. Higher productivity is achieved by separating greatermounts of sample in the same time with identical purities andields producing matching chromatograms.

In HPLC (high-performance liquid chromatography) scalep is achieved by maintaining the sample concentration whilencreasing the sample volume and mobile phase flow rate inroportion to the increase in column volume. Columns of atandard length are used. Enlarging the cross-sectional areancreases the column volume. Technological developmentsllow production columns to be packed with the same stationaryhase material to a similar standard as analytical columns. Otherevelopments allow the mobile phase to be roughly evenlyistributed across the whole of the column’s cross-sectional

rea creating the same mobile phase linear flow velocity. Theseeasures ensure that the sample components elute from the

olumn in the same order with the same elution times. Hence

∗ Corresponding author. Tel.: +44 1753 698841; fax: +44 1753 969676.E-mail address: philip.wood@brunel.ac.uk (P. Wood).

w

pipsm

021-9673/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2007.02.014

ce liquid chromatography; High-performance counter-current chromatography

reater amounts of sample have been separated in the sameime with matching purities and yields producing identicalhromatograms.

CCC technology needs to perform scale up in a comparableanner to HPLC, i.e., perform identical separations at larger

cales in the same time. Scale up methodologies for CCC haveocused on increasing sample loading with little or no regard foraintaining the same separation time. Generally these studies

ave used semi-preparative and preparative scale columns. Dut al. [1] showed that the sample loading could be increased by aactor of 11 while obtaining the same resolution by connecting

identical semi-preparative columns in series. However theeparation time was 4 times longer hence productivity actuallynly increased by a factor of 2.75. Another study establishedow to improve productivity of a separation using a singlereparative scale column by controlling operating parameters2]. Neither of these studies took a separation performed in annalytical column and transferred it to a larger volume columnhere the scale-up factor was between 100 and 1000.For CCC the difficultly is in matching columns and process

arameters so that an identical separation can be obtained

n the larger column. This paper addresses these difficultiesresenting a basic theory of how to design matched columns forcale up and presents scale up results with near identical chro-atograms.

2 atog

2

viamaptmptiwsa(tttpTa

bis

X

b

t

t

was

S

t

S

w√

1

w

B

S

B

N

S

wv1

V

Nscl

A

WocflacT

A

Nt

A

N

A

A

d

d

6 P. Wood et al. / J. Chrom

. Theory

It has already been shown how in HPLC the linear flowelocity of the mobile phase is kept constant to allow the sim-lar separations to be obtained at different scales. In HPLC themount of stationary phase in the column is independent of theobile phase flow rate (F). However, in CCC this is not the case

s retention of the stationary phase is dependent on the mobilehase flow rate. Du et al. [3] were the first to show that the sta-ionary phase retention (Sf) is related to the square root of the

obile phase flow rate. In fact, the volume of mobile phase (Vm)resent in a CCC column is proportional to the square root ofhe mobile phase flow rate [4]. If the mobile phase flow rate isncreased by a factor of four, twice the volume of mobile phaseill be present in a column. This means that the mean cross-

ectional area of the column occupied by the mobile phase willlso have been doubled. Therefore the mean linear flow velocityu) of the mobile phase will also have doubled. This shows thathe mean flow speed of the mobile phase is also proportional tohe square root of the mobile phase flow rate. This demonstrateshat CCC columns will have to become longer as the mobilehase flow rate increases to maintain identical elution times.herefore a production column will be longer than its matchednalytical column.

In CCC volumetric scale up is based upon increases tooth cross-sectional area and column length. The strategy is toncrease the column volume and mobile phase flow rate by theame scale up factor X as shown below.

Volumetric scale-up

= V2

V1= F2

F1(1)

This equation can be rearranged to give:

V1

F1= V2

F2(2)

Now the elution times for two columns can be representedy [5]:

1 = V1

F1[Sf1(D − 1) + 1] (3)

2 = V2

F2[Sf2(D − 1) + 1] (4)

here t is the elution time, Sf is the stationary phase retentionnd D is the partition ratio. For these columns to be matched forcale-up the elution times must be the same, i.e., t1 = t2, hence:

V1

F1[Sf1(D − 1) + 1] = V2

F2[Sf2(D − 1) + 1] (5)

Substituting Eq. (2) into Eq. (5) and then cancelling gives:

f1 = Sf2 (6)

For solutes to emerge from a matched set of scale up columnshe conditions represented by Eqs. (1) and (6) must be met. Now

f = 1 − B√

F (7)

FV

X

r. A 1151 (2007) 25–30

here B is the gradient of the linear relationship between Sf andF , hence:

− B1√

F1 = 1 − B2√

F2

hich reduces to

1 = B2

√F2

F1

ubstituting from Eq. (1) gives:

1 = B2√

X (8)

ow

f = VS

VC= VC − Vm

VC= 1 − Vm

VC(9)

here VS is the volume of stationary phase and VC is the columnolume. Eqs. (7) and (9) can be equated to give 1 − Vm/VC =− B

√Fwhich reduces to:

m = VCB√

F (10)

ow Vm = AmL and VC = AmL where Am is the mean cross-ectional area occupied by the mobile phase, AC is theross-sectional area of the column bore and L is the columnength. Substituting these relationships into Eq. (10) gives:

m = ACB√

F (11)

ood et al. [4] showed that the volume of mobile phase in a setf identical length columns was independent of the bore of theolumn provided the same rotational speed and mobile phaseow rate were used. This shows that the mean cross-sectionalrea occupied by the mobile phase is also independent of theolumn bore hence Am3 = Am4 as the coils were the same length.herefore:

C3B3√

F3 = AC4B4√

F4 (12)

ow remembering that F3 = F4 then the above Eq. (12) reduceso AC3B3 = AC4B4 which can be rewritten for scale up as:

C1B1 = AC2B2 (13)

ow substituting for B1 from Eq. (8) into Eq. (13) gives:

C1B2√

X = AC2B2

C2 = AC1√

X (14)

πd22

4= πd2

1

4

√X

22 = d2

1

√X

2 = d1X1/4 (15)

rom Eq. (1) X = V2/V1 and substituting in the following1 = AC1L1 and V2 = AC2L2 gives:

= AC2L2

AC1L1

atog

a

X

w

L

ucm

N

0fp2eswatsabrBtnrepHtm

tiptedt

sttetm

ap

3

Jbcrme1nltcrisa

actrwtfKi7uRarpd

uMl

teoaptcdDt

P. Wood et al. / J. Chrom

nd substituting for AC2 from Eq. (14) gives:

= AC1L2√

X

AC1L1

hich reduces to:

2 = L1√

X (16)

The time taken for the mobile phase to travel through a col-mn (tm) is given by its mean linear velocity (u) divided by theolumn length (L) ie tm = u/L. For scale up and the elution timesust be equal for both columns hence tm1 = tm2 therefore:

u1

L1= u2

L2

ow substituting for L2 from Eq. (16) gives:

u1

L1= u2

L1√

Xu2 = u1

√X (17)

Take an analytical column with a 5.4 ml volume wound from.8 mm bore tubing having a length of 10.7 m. This column per-orms a separation at a flow rate of 1 ml/min with a stationaryhase retention of 50%. The solvent front (D = 0) appears after.7 min and the D = 1 peak would elute at 5.4 min. For peaklution and retention theory see [5,6]. This separation is to becaled up by a factor of 850 (X = 850). The production columnill have a volume of 4590 ml, the flow rate will be 850 ml/min

nd the retention will still need to be 50%. Eq. (16) shows thathe production column will need to be 312 m long and Eq. (15)hows that its bore will need to be 4.3 mm. These calculationsssume that the columns will be identical apart from lengths andores. Hence these columns would be wound for the same rotoradius (R) with an identical β-value range and equal helix angles.oth columns would also be rotated at the same rotational speed

o obtain equivalent stationary phase retentions. However, it isot always practical to wind such columns on the same rotoradius especially when large scale-up factors are required. Theffects of changes in rotor radius and helix angle on stationaryhase retention have not yet been accounted for in this theory.owever, results presented by Ignatova et al. [7] show that sta-

ionary phase retention, elution times and resolution could beaintained while increasing rotor radius.Another aspect not accounted for in the theory is the reduc-

ion in resolution of eluting from 2 columns connected in seriesnstead of 1 column. Two identical columns operated in seriesroduce lower resolution separations than a single column ofhe same bore and total length. This is because of peak broad-ning, during component elution, occurring twice, the first timeuring transfer between columns and again during elution fromhe second column [6].

Another factor that effects the separation times is the timepent in the chromatographic extra coil volume [6]. A separa-ion time is the addition of the elution time and the time spent

ravelling through the chromatographic extra coil volume. If thelution times in the columns are the same at 2 different scaleshen the time spent in the chromatographic extra coil volumes

ust also be identical. Hence these extra coil volumes should

psbb

r. A 1151 (2007) 25–30 27

lso be scaled in proportion to the column volumes and mobilehase flow rates.

. Experimental

The column on the mini centrifuge, previously described byanaway et al. [8], was wound from a 10.7 m length of 0.8 mmore, 1.6 mm outside diameter PTFE tubing to give a of 5.4 mlapacity with a β-value range from 0.68 to 0.79 at a 50 mmotor radius. The chromatographic extra coil volume of theini experimental set up was 0.94 ml. The maxi centrifuge was

quipped with a balanced pair of columns each wound from0 mm bore, 12 mm outside diameter PFA tubing. When con-ected in series giving a total volume of 4600 ml and a totalength of 58.6 m. The β-value range of these columns was 0.70o 0.84 at a 300 mm rotor radius. The chromatographic extraolumn volume of the maxi system was 483 ml. The volumet-ic scale-up factor between these columns on these centrifugess 850. These Maxi columns were used as funding for con-tructing a pair of 4.3 mm bore by 312 m long columns was notvailable.

A Gilson 151 UV detector at 263 nm was used for bothnalytical and production scale separations. For the analyti-al separation the entire flow from the column was passedhrough the detector, however, for the production scale sepa-ation the flow was split so that the flow through the detectoras approximately 10 ml/min. The analytical scale separa-

ion used a Dynamax SD-1 twin head constant flow pumpor the mobile phase. The production scale separation used anauer 1000 ml/min pump for the mobile phase. The analyt-

cal sample was injected into the mini coil using a Rheodyne125 injection valve. The production scale sample was injectedsing a bespoke injection loop that mimicked the action of theheodyne valve. A hydrophobic solvent system: heptane–ethylcetate–methanol–water (1.4:0.1:0.5:1.0, v/v) was used ineverse phase mode (lower aqueous mobile phase). The sam-le: benzyl alcohol (42 mg/ml) and p-cresol (20 mg/ml) wasissolved in the mobile phase.

Mini sample volume 1.07 ml (19.8% of 5.4 ml column vol-me) loading is 45 mg of benzyl alcohol and 21.4 mg of p-cresol.axi sample volume 920 ml (20% of 4600 ml column volume)

oading is 38.6 g of benzyl alcohol and 18.4 g of p-cresol.Both centrifuges were rotated in the appropriate direction so

hat the head end of each column was at the centre and the tailnd was at the outer edge (periphery) of the winding as rec-mmended in [9]. The Mini centrifuge was rotated at 2100 rpmnd the Maxi centrifuge was rotated at 600 rpm. The mobilehase for both separations was pumped from the head (cen-re) to tail (periphery). The mobile phase flow rate used on Minientrifuge for the analytical separation was 1 ml/min and the pro-uction scale separation on Maxi used a flow rate of 850 ml/min.ynamic equilibrium was achieved by filling with stationary and

hen rotating at the speeds specified while pumping the mobile

hase at the flow rates and direction described. Performing aeparation then reduced the stationary phase retention achievedy dynamic equilibrium. This was due to the injection volumeseing about 20% of column volume and the sample concentra-

28 P. Wood et al. / J. Chromatogr. A 1151 (2007) 25–30

tm

faH(7

4

4

5

ac(ci

ciass

Table 1Separation times taken directly from Fig. 1, which represent the time frominjection to detection

Separation time (min)

Mini Maxi

Bp

ebTnvvtwwoob

aEltttcp6atp1vecuc

Fig. 1. Comparison of the mini and maxi separations.

ions used. A second separation was then performed on eachachine and are those reported.Fractions from the Maxi centrifuge were collected every 30 s

rom both the detector and the main stream for subsequent HPLCnalysis. The HPLC analysis was conducted using a Waters 2695PLC system with a Waters 2996 photodiode array detection

DAD) system. A short gradient, 5% to 95% of acetonitrile inmin with a flow rate of 1 ml/min was used in a C18 column.

. Results

The stationary phase retention for the maxi separation was7.4% and was 64.3% for the mini separation.

. Discussion

Fig. 1 shows that very similar separations were producedt both the analytical and production scales in 10 min. Fig. 2onfirms the UV trace of Fig. 1 with a HPLC analysis of the Maxiproduction scale) fractions. This scale-up from an analyticalolumn to a production column presents an 850 times increasen productivity.

These elution times have been taken from Table 1 andorrected for the different extra coil volumes of the two exper-

mental set ups. For the Mini (analytical) separation the benzyllcohol peak elutes earlier than that for the Maxi (production)eparation. Also the p-cresol peak elutes earlier for the Minieparation than for Maxi separation. These differences in the

Fig. 2. HPLC analysis of the maxi separation.

ddt

TCp

BpDSPPR

enzyl alcohol 4.36 4.49-Cresol 7.28 7.00

lution times for the benzyl alcohol and p-cresol are accountedy the different stationary phase retentions of the two columns.his also causes the time between the elution of the two compo-ents to differ; however the resolutions for both separations areery similar. The Maxi separation with the smaller time inter-al between peaks produced a narrower combined peak widtho maintain resolution, which can be seen in Table 2. The peakidths given in this table are not the full peak widths. A peakidth has been measured between the elution time and crossingf the horizontal axis of the fitted straight line to the peak as rec-mmended in [6]. The peak widths shown are those that crossetween the peaks.

The 850 times scale-up does not completely follow the theorys presented. Scaling up 850 times from the Mini column usingqs. (16) and (15) predicts that the Maxi column should have a

ength of 312 m and a bore of 4.3 mm which are not the same ashose used. These discrepancies are due to differences betweenhe current theory and the practicalities of having to scale upo a much larger centrifuge. The discrepancies are caused byhanges in: rotor radius (Mini 50 mm and Maxi 300 mm), theroportion of stationary phase retained in the columns (Mini4.3% and Maxi 47.4%), the rotational speeds at which the sep-rations were performed (Mini 2100 rpm and Maxi 600 rpm) andhe chromatographic extra coil volumes not being in the sameroportions to the respective column volumes (Mini 0.94 ml,7.4% of 5.4 ml causing 56 s travelling through the extra coilolume and Maxi 483 ml, 10.5% of 4600 ml causing 34 s trav-lling through the extra coil volume). There are also differencesaused by performing the analytical separation in a single col-mn and performing the production scale separation using 2olumns connected in series. This is due to peak broadening

uring each time a component elutes from a column. The pro-uction scale separation will suffer more peak broadening dueo each component (p-cresol and benzyl alcohol) having to elute

able 2omparison of elution times, peak widths and resolutions for the separationsresented in Fig. 1

Elution time (min)

Mini Maxi

enzyl alcohol 3.42 3.93-Cresol 6.34 6.44ifference between elution times 2.92 2.51tationary phase retention 64.3% 47.4%eak width of benzyl alcohol 2.82 2.08eak width of p-cresol 1.44 1.44esolution 0.69 0.71

atog

tt

dcIbw

vtruoit

rirrlta[bttot

r

wtc

pmabfit[fcos

tain

ctIi

mpgctcatoe

r

waiTdcscdiitptActi(tflafpw3cteolpwtlt

6

l

P. Wood et al. / J. Chrom

wice [6]. The scale-up theory needs to be developed further toake into account such changes and differences.

A potential strategy for overcoming the loss in resolutionue to additional peak broadening during elution from a secondolumn connected in series is to use the two columns in parallel.f the desired scale up factor was 1000 then each column woulde designed for a 500 times scale up and the operation in parallelould delivery the target factor of a 1000.The helix angle for the wound tubing on the Mini column

aried in the range from 0.37◦ to 0.43◦ and for the Maxi columnshe helix angles varied from 0.44◦ to 0.51◦. These helix angleanges are roughly the same thus nearly meeting one of thenderpinning assumptions of the theory, i.e., that the helix anglesn coils should be held constant. Helix angles have shown to bemportant for dynamic similarity when increasing rotor radii ofhe centrifuge [7].

As mentioned earlier, the Mini and Maxi stationary phaseetentions were 64.3% and 47.4%, respectively, and the timentervals between peaks were 3.54 and 2.62 min, respectively,eflects the different stationary phase retentions. However, theesolution for these centrifuges was approximately equal. Reso-ution is basically the ratio of the time interval between peaks tohe sum of peak widths. Therefore the Maxi peak widths mustlso be smaller for this resolution to be maintained. Sutherland10] showed that peak width is related to the mass transfer rateetween mobile and stationary phases. The greater the massransfer rate the narrower the peak width. The equation for massransfer rate across an interface is very similar to that for the ratef heat transfer across a boundary [11]. An equation for massransfer across an interface is [11]:

ate of mass transfer = sA�C

here s is the mass transfer coefficient, A is the interfacial areahrough which mass transfer occurs and �C is the difference inoncentration across the interface.

The mass transfer coefficient is largely dependent upon thehysical and chemical properties of the solvent system and theolecules being separated. By definition the solvent system

nd the sample will not change during scale-up. There maye hydrodynamic influences that alter the mass transfer coef-cient during scale-up however these should be minimised if

he principles of dynamic similarity are used. Ignatova et al.7] have demonstrated that the same resolution can be obtainedrom columns of the same bore and length constructed for threeentrifuges with increasing rotor radii. The construction andperation of these columns adhered to the principles of dynamicimilarity.

The interfacial area of a J-type centrifuge will increase withhe bore and length of its coils. When scaling up to larger borend longer coils the interfacial area will also increase potentiallyncreasing the mass transfer rate. This may partly explain thearrower peaks of the Maxi separation.

In liquid-liquid partition chromatography the equilibrium

oncentrations across the interface are determined by the parti-ion ratio. The above equation needs to be adapted to reflect this.n a J-type CCC machine it can be assumed that just after a mix-ng wave has passed the concentrations of a solute in the adjacent

tp

a

r. A 1151 (2007) 25–30 29

obile and stationary phases are in equilibrium according to theartition ratio. In the time between two mixing waves passing aiven point the concentration of a solute in the stationary phasean assumed to be unchanged. However, the concentration inhe mobile phase will change because it is flowing through theoil and the concentration of a solute in the mobile phase varieslong the length of a coil. Therefore it is the change of concen-ration in the mobile phase that largely determines the amountf mass transfer during the next mixing wave. Hence the abovequation can be modified to that below:

ate of mass transfer = sA(Cmn − Cm(n+1))

here Cmn is the solute concentration in the mobile phase justfter the nth mixing wave and Cm(n+1)′ is the solute concentrationn the mobile phase just before the (n + 1), next, mixing wave.he above equation demonstrates that the rate of mass transferepends upon how much the concentration in the mobile phasehanges before the next mixing wave arrives. In the hypotheticalituation where the concentration in the mobile phase does nothange the above equation shows there will be no mass transferuring the next period of mixing. If the change in concentrations small the mass transfer rate will be small and if the changen concentration is larger the mass transfer rate will be propor-ionally larger. This shows that the mass transfer rate at a givenoint in a coil is depended upon the change of concentration inhe mobile phase in the time before the next mixing wave arrives.s stated earlier the concentration of a solute in the mobile phase

hanges along the length of a coil. Hence a method of increasinghe change in concentration between successive mixing wavess to increase the linear flow velocity of the mobile phase. Eq.17) shows the relationship between the scale-up factor X andhe linear flow velocities of the mobile phase. The mean linearow velocity of the Mini separation was 557 cm/min and thust 2100 rpm the mobile phase will move 0.265 cm in the timeor 1 rotation or the time for 2 mixing waves to pass any givenoint. The mean linear flow velocity for the Maxi separationas 2058 cm/min and at 600 rpm the mobile phase would move.43 cm in the time between two mixing waves. The change ofoncentration over a length of 3.43 cm will probably be largerhan that over 0.265 cm. Hence Maxi’s greater mobile phase lin-ar flow velocity gives rise to higher changes of concentrationsf the mobile phase in the time between mixing waves. Thiseads to greater mass transfer rates and hence narrower overalleaks as shown in Fig. 1 and Table 2. This may also explainhy the Maxi separation produced a slightly greater resolution

han the mini despite the Maxi stationary phase retention beingower and more peak broadening occurring due to eluting fromwo coils in series instead of one.

. Conclusions

To increase column volume for scale up both the bore andength need to be increased to maintain stationary phase reten-

ion and elution times thus enabling larger separations to beerformed in the same time interval.

Identical chromatograms can be achieved at both analyticalnd production scales. The separation time being 10 min for both

3 atog

sl

tra

oup

tbaf

dal

A

ap

Ca

R

Technol. 23 (2000) 2259.[10] I.A. Sutherland, J. De Folter, P.L. Wood, J. Liq. Chromatogr. Rel. Technol.

0 P. Wood et al. / J. Chrom

cales demonstrates that high-performance CCC (HPCCC) isinearly scaleable.

The scale up factor is 850 based on an 850 increase in bothhe column volume and mobile phase flow rate. As similaresolutions were obtained, both column/centrifuges must havepproximately equal overall chromatographic efficiencies.

The effects of high linear flow velocities of the mobile phasen mass transfer rates need to be researched to increase thenderstanding of its influences on resolution and the separationrocess, as this may modify the scale up theory presented.

The scale up theory presented in this paper combined withhe principles of dynamic similarity allow matched columns toe fitted to centrifuges of increasing radii. Hence analytical sep-rations can now be scaled up to the desired level of productivityor the pharmaceutical industry.

Larger bore and longer production columns need to beesigned and built that will allow real samples to be separatedchieving high purities and yields for production sized columnoadings.

cknowledgements

The authors would like to thank: the EPSRC (Engineeringnd Physical Sciences Research Council) for financial supportrovided by grant GR/S61836 from the RAIS scheme.

[

r. A 1151 (2007) 25–30

The authors would also like to thank Philip Sherring andolin Strawson of AstraZeneca for their help, encouragementnd support in progressing this research work.

eferences

[1] Q.Z. Du, C.Q. Ke, Y. Ito, J. Liq. Chromatogr. Rel. Technol. 21 (1998)203.

[2] I.A. Sutherland, L. Brown, A.S. Graham, G.G. Guillon, D. Hawes, L.Janaway, R. Whiteside, P.L. Wood, J. Chromatogr. Sci. 39 (2001) 21.

[3] Q. Du, C. Wu, G. Qian, P. Wu, Y. Ito, J. Chromatogr. A 835 (1999) 231.[4] P.L. Wood, D. Hawes, L. Janaway, I.A. Sutherland, J. Liq. Chromatogr.

Rel. Technol. 26 (2003) 1373.[5] W.D. Conway, Countercurrent Chromatography Apparatus: Theory and

Applications, VCH, New York, 1990.[6] P.L. Wood, Stationary Phase Retention versus Peak Elution in CCC, Ency-

clopedia of Chromatography, Taylor & Francis, New York, 2005.[7] S.N. Ignatova, P.L. Wood, D. Hawes, L. Janaway, D. Keay, I.A. Sutherland,

J. Chromatogr. A. 1151 (2007) 20.[8] L. Janaway, D. Hawes, I.A. Sutherland, P.L. Wood, J. Liq. Chromatogr.

Rel. Technol. 26 (2003) 1345.[9] I.A. Sutherland, J. Muytjens, M. Prins, P.L. Wood, J. Liq. Chromatogr. Rel.

26 (2003) 1449.11] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley,

New York, 1960, p. 656.