measurements by holographic interferometry of concentration profiles in dead-end ultrafiltration of...

Journal of Membrane Science 229 (2004) 187–197

Measurements by holographic interferometry of concentration profilesin dead-end ultrafiltration of polyethylene glycol solutions

J. Fernández-Sempere∗, F. Ruiz-Beviá, R. Salcedo-Dıaz

Departamento de Ingenier´ıa Quımica, Universidad de Alicante, Apartado 99, Alicante E-03080, Spain

Received 3 October 2002; received in revised form 14 March 2003; accepted 3 October 2003

Abstract

An optical method (microscopic holographic interferometry) has been used to visualize concentration changes in the vicinity of the membranesurface while a polyethylene glycol 2000 (PEG) solution was ultrafiltered with a cellulose acetate membrane. This interferometric techniqueis based on the fact that changes of refractive index, which are associated to changes of concentration, can be visualized as interference fringes.Interferograms obtained in different experimental conditions (initial PEG 2000 concentration range from 1 to 10 kg/m3 and transmembranepressure range from 1× 105 to 3 × 105 Pa) as well as permeate flux are presented. Concentration profiles in the polarized layer near themembrane surface have been determined from these interferograms. In all cases, after about 20 min of ultrafiltration process, the profilesremained stable and a “pseudo-steady state” seemed to be reached. Moreover, solute concentration in the vicinity of the membrane did notreach much higher values than the initial concentration.© 2003 Elsevier B.V. All rights reserved.

Keywords:Ultrafiltration; Holographic interferometry; Concentration profiles; Polyethylene glycol; Concentration polarization; Modelling

1. Introduction

In a previous paper[1], the holographic interferometrytechnique was used to visualize the ultrafiltration membranesurroundings during the ultrafiltration of protein solutions.The special characteristics of the system studied (bovineserum albumine, BSA, solutions and polyethersulfone mem-brane) made it possible to visualize the solute retention andverify whether there is cake formation on the membrane sur-face during the ultrafiltration or not. From the experimentalresults, evidence was found which indicated the presenceof a gelatinous mass or a filter cake during BSA ultrafiltra-tion with the above mentioned membrane; at the same time,small concentration profiles were observed. The presenceof this filter cake and the small concentration profiles wereprobably due to the interaction of the irreversible adsorbedBSA protein and the polyethersulfone membrane. This phe-nomenon has also been described by other authors[2–7].

In the present paper, the visualization by means of holo-graphic interferometry of the concentration profiles duringthe ultrafiltration process has been continued, but applied

∗ Corresponding author. Tel.:+34-65903400; fax:+34-65903826.E-mail address:[email protected] (J. Fernandez-Sempere).

to a different system (polyethylene glycol (PEG) solutionsand cellulose acetate membrane) in which adsorption phe-nomena not as strong and irreversible as in the case of BSAand the polyethersulfone membrane occurred. In this way, abetter acknowledgement of the mechanisms and phenomenataking place during the ultrafiltration process in the vicinityof the membrane will be obtained.

According to Van den Berg and Smolders[8] when an ul-trafiltration process is taking place, a flux decline during theprocess can be observed. The causes are (i)concentration po-larization (i.e. accumulation of retained solutes, reversibilityand occurring immediately) and (ii)fouling phenomenasuchas adsorption, pore-blocking and deposition of solidified so-lutes, a long-term and more or less irreversible process. Theresult of both these phenomena is a decreasing driving forcefor the filtration or an increasing resistance against transportof the permeating solvent during the filtration.

Several models have been developed to describe the po-larization phenomena; in general, they can been subdividedinto (A) resistance models, (B) gel-polarization modelsand(C) osmotic pressure models. A large number of studiesabout theoretical models describing ultrafiltration have beenpublished, as can be seen, for instance, in a recent reviewon concentration polarization in ultrafiltration and reverseosmosis[9].

0376-7388/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.memsci.2003.10.029

188 J. Fernandez-Sempere et al. / Journal of Membrane Science 229 (2004) 187–197

This great variety of proposed models has its origin inthe numerous possible mechanisms, alone or combined, atwhich the flux decline can be attributed, as well as in thedifficulties to experimentally validate the models in orderto discriminate among them. If only the experimental dataof permeate flux are used, any of the proposed models canusually predict the flux decline using the appropriate ad-justable parameters of the model. In dead-end ultrafiltra-tion, the models can theoretically predict the evolution withtime of the solute concentration profiles in the vicinity ofthe membrane surface but, unfortunately there exists no ex-perimental technique completely acceptable which allows aprecise measurement of these profiles, which could serve tovalidate the model. The little knowledge about the polarizedlayer is mainly due to the experimental difficulties associatedwith making non-destructive concentration profile determi-nations within a very thin layer. Most of the studies carriedout to experimentally determine concentration profiles dur-ing membrane processes have been related to reverse osmo-sis [10–13]. However, few experimental studies have beenconducted to quantify concentration profiles during ultrafil-tration [14–20].

In a previous paper[1], data about the ultrafiltration ofBSA protein in a polyethersulfone membrane were obtained.Concentration profiles were determined by means of micro-scopic holographic interferometry.

In the present paper, the same microscopic holographicinterferometric method has been used to monitor in real timethe solute retention during polyethylene glycol (PEG) ultra-filtration in an unstirred cell. In this case, a cellulose acetatemembrane has been used and a reversible adsorption phe-nomenon, less strong than when using BSA, was observed.

Holographic interferometry can be defined as the interfer-ometric comparison of two or more waves, at least one ofwhich is holographically reconstructed[21]. This techniquehas previously been used to study diffusion, both in liquidand in gel systems[22–26]. Characteristics of the techniquewere presented in a previous paper[1].

In addition to extending the use of holographic interfer-ometry to the study of mass transfer processes through mem-branes, the objectives of this research are: (1) to obtain theevolution of concentration profiles during PEG ultrafiltra-tion in an unstirred cell and, (2) to try to determine whathappens during the ultrafiltration process in the vicinity ofthe membrane. Interferograms obtained and the correspond-ing concentration profiles are presented, as well as permeateflux values.

2. Materials and methods

The experimental set-up was similar to that described ina previous paper[1]. In order to adapt the ultrafiltration sys-tem to the holographic interferometry requirements, a spe-cial ultrafiltration module was designed to permit the obser-vation of the limit between membrane and solution through

transparent windows. The membrane was fixed to the bot-tom part of the module by gluing the perimeter to the raisedsupport. In order to check the membrane tightness, two testswere carried out: (1) measurement of water permeate flux,prior to the ultrafiltration experiment: the water flux was de-termined by weight and it had to be in the range given by themanufacturer and (2) measurement of the concentration ofPEG in the permeate, after the ultrafiltration experiment: thisconcentration had to be much less than the feed concentra-tion. The quantitative PEG determination was made by vac-uum drying, at 40◦C and 0.5 atm, a certain amount of PEG2000 aqueous solution, which had previously been weighed.Once all the water was evaporated, it was again weighed.What remained was the amount of PEG 2000 in the sample.

All the experiments have been carried out in batch condi-tions. Dead-end of circuit valve inFig. 1 was closed duringthe experiment and was only opened for filling the modulewith PEG 2000 solution, in order to eliminate air present inthe system.

Fig. 1shows the whole ultrafiltration system whose partsare: (1) feed tank; (2) water tank; (3) 3-way valve; (4) pump(Micropump HG0024), which is installed outside the opti-cal bank to avoid vibrations; (5) thermometer, (6) pressuregauges; (7) ultrafiltration module, which is installed in a ver-tical position to avoid bubble retention; (8) dead-end circuitvalve; (9) permeate collector vessel; (10) balance and (11)computer.

A schematic diagram of the optical set-up (joined to theultrafiltration system) was shown in a previous paper[1].

2.1. Materials

Polyethylene glycol (PEG) of molecular weight 2000(Fluka) was used in all the experiments. Aqueous solutionswere prepared several hours before the experiment, usingtwice-distilled water.

All the experiments have been performed with the sametype of membrane made of cellulose acetate (YC05, NMWL:500 from Millipore). The membrane was completely selec-tive to PEG 2000. Each piece of membrane was re-used forsome experiments. At the end of each one, the ultrafiltrationmodule was washed with distilled water, for at least 30 min,until the PEG was removed. Then, this water was eliminatedand the ultrafiltration circuit was filled with twice-distilledwater, resting for several hours. The membrane was consid-ered to be clean when the permeate flux of water was recov-ered. If not, a new membrane was placed in the module.

2.2. Experimental methodology to obtain interferograms

The experimental methodology is similar to that used pre-viously [1], but instead of BSA, PEG 2000 feed solutionswere used.

In order to carry out the holographic interferometricstudy, two states of the ultrafiltration process were com-pared: one was the reference state and the other was that

J. Fernandez-Sempere et al. / Journal of Membrane Science 229 (2004) 187–197 189

Fig. 1. Ultrafiltration system: (1) feed tank; (2) water tank; (3) three-way valve; (4) pump; (5) thermometer, (6) pressure gauges; (7) ultrafiltration module;(8) dead-end circuit valve; (9) permeate collector vessel; (10) balance; (11) computer.

corresponding to the evolution of the concentration polar-ization phenomenon. In this case, the reference state chosencorresponded to the ultrafiltration module filled with PEGsolution and allowed to rest for 1 h approximately.

Once the hologram was recorded on the holographic plate,the laser beam again passed through the holographic plate.Later, when the pump was connected (t = 0), the ultrafiltra-tion process was observed, as it took place (real-time holo-graphic interferometry), as a succession of interferometricimages (interferograms): due to the ultrafiltration process,the PEG 2000 concentration increased above the membranesurface and a concentration profile (a refractive index gradi-ent) appeared, which was able to be visualized by means ofholographic interferometry. Therefore, the layer of retainedsolute formed above the membrane was observed as an in-terferometric fringe layer. Recording of the interferogramswas carried out continuously by a lensless video camera. Asthe concentration polarization layer developed in a narrowframe, microscopic holographic interferometry was used.The magnifications used are shown in the interferograms.

2.3. Methodology to quantitatively obtain concentrationprofiles from interferograms

The methodology to quantitatively obtain concentrationprofiles was the same as in a previous paper[1]. Only point7 was different: to calculate the concentration correspondingto each refractive index (n) at the position of the fringe, a lin-ear relation between refractive index and PEG 2000 concen-tration at 25◦C, experimentally obtained in our laboratoryby means of an automatic refractometer (Leica, AR600),was used:

n = 1.3329+ 0.00013C (1)

where C is the PEG 2000 concentration in kg/m3.

In the case of boundary layers formed at solid-liquid in-terfaces, the “mirage” effect can appear[27,28]. As a con-sequence of the presence of a refraction index gradient, thelight passing through the cell is deflected and the shadowof the membrane surface can be displaced from its originalposition recorded in the hologram and can hide part of theinterference fringes. When the refraction index gradient isof a limited magnitude, the errors caused by light deflectionare not important. In our UF experiments, very moderateconcentrations were used and, as is commented in the Re-sults section, the concentration gradient obtained was alsosmall (it would be possibly different in reverse osmosis ex-periments). Clifton and Sanchez[27] developed a methodto calculate possible errors made when studying by holo-graphic interferometry the boundary layer formed duringelectrolytic deposition of copper at a copper cathode underlaminar flow conditions. The cell measurements used in allthe calculations were: length of light path within the cell,1.45 cm, thickness of transparent walls of the cell, 0.60 cm.The fringes were calculated for two different positions ofthe focal plane: at the centre of the cell (F = 1.325 cm)and at the inner face of the transparent wall facing the lightsource (F = 2.050 cm). A first conclusion from Clifton andSanchez discussion of their results is that “there is very lit-tle divergence between the undistorted fringe profile and thetwo others throughout most of their length. This divergenceis of the same order of magnitude (0.1 fringe width) as theerror in making measurements on photographs and so wouldbe scarcely noticeable in any experimental observation”. Thegeneralized results shown inFigs. 1 and 2from the paperby Clifton and Sánchez give the magnitude of the error inthe observed phase displacement (expressed as the numberof fringes in excess) at the active surface when holographicinterferometry is used. The error is shown as a function ofthe refractive index gradient at the active surface. In these


Fig. 2. Interferograms belonging to Experiment II (C0 = 2 kg/m3 and �P = 1.02× 105 Pa) at 120, 480, 840, 1200 and 1800 s. The membrane positionin each interferogram is indicated by means of an additional longer line that extends on each side of the interferogram.

figures, it can be seen that when the refractive index gra-dient at the active surface is of a limited magnitude, theerrors caused by light deflection are not important. In ourultrafiltration experiments the dimensions of the cell werevery similar to those of the electrolysis cell: length of lightpath within the cell, 2 cm and thickness of transparent wallsof the cell 2 cm. The focal plane was located inside of thecell, at 2/3 of the transparent wall facing the light source(F = 2.16 cm). When the method proposed by Cliffton andSánchez is applied to our data (boundary layer width in therange 0.02–0.04 cm, refractive index gradient estimated asaround 0.01 cm−1), the error would be lower than 1 fringe inexcess. According to the conclusions of the above mentionedpaper, we can also state that “holographic interferometry is

an extremely useful technique for observing boundary lay-ers. In fact, if refractive index gradients are kept below acertain limit, these errors may be neglected”.

3. Results and discussion

3.1. Visualization of the polarized layer

In order to characterize the polarized layer, several PEG2000 solution ultrafiltration experiments were carried outin an unstirred batch module. A continuous and real timeinterferometric recording of the experiments was made us-ing a lensless video camera fitted to a microscope tubular


Table 1Operating conditions of the PEG 2,000 ultrafiltration experiments

Experiment

I II III IV V VI VII

�P × 10−5 (Pa) 1.01 1.02 0.99 1.01 1.04 2.04 3.04C0 (kg/m3) 1 2 3 5 10 2 2Jw × 106 (m3/m2 s) 2.07 2.02 2.08 2.02 2.09 4.16 5.99J0 × 106 (m3/m2 s) 2.00 1.79 1.65 1.39 1.14 3.56 5.25Rm × 10-10 (Pa s/m) 4.88 5.05 4.76 5.00 4.98 4.90 5.08Ultrafiltration time (s) 3600 3600 3600 3600 3600 3600 3600Rest time (pump

disconnected (s)600 600 720 780 600 900 1200

Observed area(mm × mm)

1.19 × 1.62 1.48× 1.57 1.48× 1.63 1.48× 1.62 0.63× 0.71 1.19× 1.28 1.13× 1.29

Fig. 3. Interferograms belonging to Experiment IV (C0 = 5 kg/m3 and∆P = 1.01× 105 Pa) at 120, 480, 840, 1200 and 1800 s.


body. The reproducibility of the observed behaviour wasconfirmed repeating the ultrafiltration runs in the same con-ditions (initial feed concentration and transmembrane pres-sure). The experiments took place at different operationalconditions: the initial feed concentration (C0) varied be-tween 1 and 10 kg/m3 and the transmembrane pressure (�P)between 1× 105 and 3× 105 Pa. Five groups of experi-ments were carried out at the same transmembrane pressure(1 × 105 Pa) with different concentrations (1, 2, 3, 5 and10 kg/m3). Other two groups were carried out with the sameconcentration (2 kg/m3), varying the transmembrane pres-sure (2× 105 and 3× 105 Pa). Permeate flux was analyzedin order to determine PEG 2000 concentration; these valueswere very small, thus indicating that the acetate cellulosemembrane used was perfectly selective to PEG 2000.

Fig. 4. Interferograms belonging to Experiment IV (C0 = 5 kg/m3 and�P = 1.01×105 Pa) at 120, 180, 300, 420 and 600 s after the pump was switchedoff.

As an example,Table 1shows the operating conditionscorresponding to seven experiments, each one representingone of the afore-mentioned conditions. In all the cases, theultrafiltration process continued for 3600 s.Jw is the volu-metric permeate flux with pure water before the beginningof the ultrafiltration experiment.J0 is the volumetric per-meate flux at the beginning of the PEG 2000 ultrafiltrationexperiment.Rm is the membrane hydraulic resistance to theflux with pure water, which is calculated as:

Rm = �P

Jw(2)

Visual field indicates the true dimensions of the rectangu-lar zone observed by means of the optical system videocamera-microscope.


Using microscopic holographic interferometry it waspossible to follow the evolution of the interference fringes.The region visualized depended on the combinationobjective-ocular used in the microscope tubular body. Whenthe whole surface corresponding to the ultrafiltration cellwindow was visualized, 0.0049 m of membrane length wasobserved. However, to visualize the narrow interferencefringes closest to the membrane surface an appropriate com-bination of objective-ocular had to be used, with which themembrane length observed was around 0.001–0.002 m. Ob-viously, as the ultrafiltration module was placed verticallyon the optical table, the membrane surface was visualizedas a vertical line.

In an ultrafiltration run, the first interference fringesappeared a few minutes after the pump was switched on.After approximately 20 min, the number and the position ofthe interference fringes remained nearly stable.Fig. 2 cor-responds to Experiment II withC0 = 2 kg/m3 and�P =1.02 × 105 Pa and shows five interferograms at 120, 480,840, 1200 and 1800 s, respectively. As the experiment wascontinually recorded, interferograms between 0 and 3600 swere available, but only five have been selected in order toillustrate the evolution of the system. As can be seen, theinterference fringes rapidly became stable, which meansthe concentration profile was also stable. Moreover, thesmall number of interference fringes (four fringes) denoteda small change of concentration in the observed region,and therefore the slope of the concentration profile was nottoo high.

In Fig. 3, which corresponds to Experiment IV, with thesame pressure (1.01× 105 Pa) and a greater concentration(5 kg/m3), the number of fringes at the end of the experi-ment was greater (nine fringes), but the behaviour was simi-lar: the number of interference fringes slowly increased withtime and, after approximately 20 min, this number remainedstable, thus indicating that the concentration profile did notchange with time. In both cases (Figs. 2 and 3) no interfer-ograms at times higher than 1800 s are presented becausethe number and the distance of the fringes to the membranewere very similar to those for 1800 s. In order to confirmthis stability of the concentration profiles, the ultrafiltrationprocess was continued for a longer period (up to 6 h) in sev-eral experiments and it was observed that the interferencefringe pattern remained nearly unchanged.

When the pump was switched off and the pressure ceased,the releasing of the pressure caused the solute accumulatedon the membrane to relax and a greater number of nar-row interference fringes appeared. Later, the fringes becamemore and more separated and finally disappeared, as can beseen inFig. 4, which corresponds to Experiment IV (�P =1.01× 105 Pa andC0 = 5 kg/m3). The phenomenon can beexplained by the decompression effect of the PEG depositand, later, the diffusion of the solute from the membranesurface to the fluid bulk. In general, the greater the initialsolution concentration (C0), the easier the observation of thephenomenon became.

Fig. 5. Evolution of the dimensionless flux (J/Jw). Experiment I:C0 =1 kg/m3 and�P = 1.01×105 Pa. Experiment II:C0 = 2 kg/m3 and�P =1.02× 105 Pa. Experiment III:C0 = 3 kg/m3 and �P = 0.99× 105 Pa.Experiment IV:C0 = 5 kg/m3 and ∆P = 1.01× 105 Pa. Experiment V:C0 = 10 kg/m3 and∆P = 1.04× 105 Pa.

When higher pressure was used, experiments VI (C0 =2 kg/m3 and�P = 2.04× 105 Pa) and VII (C0 = 2 kg/m3

and�P = 3.04× 105 Pa), the behaviour was similar to theprevious group of experiments. The number of interferencefringes increased slowly but, after 20 min, the number re-mained stable. For the same time since the beginning of theexperiment, the greater the pressure, the greater the numberof interference fringes was. When the pump was switchedoff, the number of fringes increased, for instance, from 7 atthe end of Experiment VI to 13 fringes at 60 s, indicating

Fig. 6. Evolution of the dimensionless flux (J/Jw). Experiment VI:C0 = 2 kg/m3 and �P = 2.04× 105 Pa. Experiment VII:C0 = 2 kg/m3

and�P = 3.04× 105 Pa.


the relaxation of the mass accumulated on the membranesurface.

3.2. Permeate flux

Data of water permeate flux (Jw) and of PEG 2000 per-meate flux (J0) at the beginning of the ultrafiltration processare presented inTable 1. Figs. 5 and 6show the evolutionof the non-dimensional flux (J/Jw). The effect of initial con-centration and pressure on the permeate flux (J) was studied.As can be seen, the permeate flux at the beginning of theultrafiltration process (J0) underwent a considerable reduc-tion (between 10 and 48%) compared to the pure water flux(Jw). In all the experiments, after the initial decrease, a sec-ond and smaller reduction of permeate flux was observed;later, the permeate flux was nearly constant, although it de-creased very slowly. The shape of the permeate flux curveswas similar to that presented by Van Boxtel et al.[29] corre-sponding to ultrafiltration experiments. The initial concen-tration had a great influence on the permeate flux; however,the evolution of permeate flux with time was very similarfrom one experiment to other: the slope of the curves wasvery slight and similar in all the experiments. The effect ofpressure on the flux decrease, however, was inappreciable:Experiments II, VI and VII with the same initial concentra-tion (2 kg/m3) and transmembrane pressures 1×105, 2×105

and 3× 105 Pa, respectively, showed practically the sameinitial reduction in the permeate flux.

3.3. Measurement of concentration profiles

Interference fringes which appeared in the interferogramswere the result of a refractive index gradient in the vicinityof the membrane due to a concentration gradient. Becausein PEG 2000 aqueous solutions a relation exists between therefractive index and concentration, it was possible to obtainthe concentration profile from the interference fringes, usingthe methodology previously explained. The fringes farthestfrom the membrane surface were broader and it was moredifficult to precisely assign their position because of the dif-ficulty to exactly place where the maximum or the minimumof light intensity was.Table 2shows the number of inter-ference fringes, the distance (y) to the membrane for eachfringe and its concentration (C) for the seven experimentswhich appear inTable 1.

As an example,Fig. 7 shows the evolution of the con-centration profiles for Experiments II and IV, andFig. 8for Experiments VI and VII. As can be appreciated, afterapproximately 20 min, the concentration profiles were verysimilar. Moreover, there was not a great variation in theconcentration and, as the initial concentration increased, theconcentration profiles were more pronounced. FromFig. 8,it can be inferred that the greater the pressure, the morepronounced the concentration profile was. At the same time,the stabilization of the concentration profile was obtainedearlier as the pressure increased.

Table 2Concentration profiles during the PEG 2000 ultrafiltration process as afunction of the distance (y) to the membrane for each fringe

Fringeorder no.

Interferogram C (kg/m3)

At 480 s At 840 s At 1200 s At 1800 s

y (mm) y (mm) y (mm) y (mm)

Experiment I:C0 = 1 kg/m3, �P = 1.01 × 105 Pa1 0.23 0.31 0.35 1.242 0.09 0.14 0.17 1.473 0.03 0.06 0.08 1.704 0.01 0.03 1.94

Experiment II:C0 = 2 kg/m3, �P = 1.04 × 105 Pa1 0.16 0.20 0.22 0.25 2.242 0.07 0.11 0.12 0.15 2.473 0.02 0.06 0.07 0.08 2.704 0.02 0.03 0.03 2.94

Experiment III: C0 = 3 kg/m3, �P = 0.99 × 105 Pa1 0.35 0.33 0.33 0.34 3.242 0.21 0.23 0.24 0.25 3.473 0.15 0.18 0.18 0.18 3.704 0.10 0.13 0.13 0.14 3.945 0.07 0.10 0.10 0.11 4.176 0.03 0.08 0.08 0.09 4.417 0.03 0.05 0.06 4.64

Experiment IV:C0 = 5 kg/m3, �P = 1.01 × 105 Pa1 0.37 0.39 5.242 0.26 0.28 0.37 0.37 5.473 0.19 0.21 0.28 0.27 5.704 0.15 0.17 0.22 0.21 5.945 0.11 0.14 0.17 0.17 6.176 0.08 0.11 0.14 0.14 6.417 0.06 0.08 0.11 0.11 6.648 0.06 0.08 0.08 6.889 0.05 0.05 7.11

Experiment V:C0 = 10 kg/m3, �P =1.04 × 105 Pa1 0.36 0.42 0.45 0.48 10.242 0.30 0.34 0.35 0.36 10.473 0.25 0.29 0.29 0.30 10.704 0.21 0.24 0.25 0.25 10.945 0.19 0.21 0.22 0.21 11.176 0.16 0.19 0.19 0.18 11.417 0.13 0.16 0.17 0.17 11.648 0.11 0.14 0.14 0.14 11.889 0.10 0.12 0.12 0.12 12.1110 0.07 0.11 0.11 0.11 12.3511 0.08 0.09 0.09 12.5812 0.07 0.07 12.82

Experiment VI:C0 = 2 kg/m3, �P = 2.04 × 105 Pa1 0.32 0.34 2.242 0.15 0.19 0.28 0.29 2.473 0.09 0.13 0.18 0.18 2.704 0.05 0.08 0.12 0.12 2.945 0.02 0.06 0.08 0.08 3.176 0.02 0.06 0.06 3.417 0.02 0.02 3.64

Experiment VII: C0 = 2 kg/m3, �P = 3.04 × 105 Pa1 0.38 0.42 2.242 0.23 0.23 0.23 0.24 2.473 0.15 0.15 0.16 0.17 2.704 0.10 0.11 0.11 0.12 2.945 0.07 0.08 0.08 0.09 3.176 0.04 0.05 0.05 0.06 3.417 0.02 0.02 0.03 0.03 3.64


Fig. 7. Concentration profiles at different times. (a) Experiment II:C0 = 2 kg/m3 and �P = 1.02 × 105 Pa. (b) Experiment IV:C0 = 5 kg/m3 and�P = 1.01× 105 Pa.

Fig. 8. Concentration profiles at different times. (a) Experiment VI:C0 = 2 kg/m3 and �P = 2.04× 105 Pa. (b) Experiment VII:C0 = 2 kg/m3 and�P = 3.04× 105 Pa.


4. Conclusions

Microscopic holographic interferometry technique hasproved to be a useful tool to visualize the polarized layerduring the ultrafiltration of PEG 2000. The technique hasallowed us to observe the evolution with time of the inter-ference fringes in experiments made with the initial concen-tration in the range of 1–10 kg/m3 and the transmembranepressure in the range of(1–3) × 105 Pa. The results showthat, after approximately 20 min, the number and positionof the interference fringes remained nearly stable, even inthe case of longer ultrafiltration experiments (up to 6 h),which means concentration also remained stable.

The shape of the permeate flux curves was similar tothat presented by Van Boxtel et al.[29] corresponding toultrafiltration experiments: the initial PEG 2000 permeateflux underwent a considerable reduction compared to thepure water flux; for a few moments, a second and smallerreduction of permeate flux was observed; later, the permeateflux was nearly constant, decreasing very slowly.

Concentration profiles corresponding to PEG 2000 ultra-filtration using a cellulose acetate membrane have been de-termined. After about 20 min of ultrafiltration process theprofiles remained stable and a “pseudo-steady state” seemedto be reached. Moreover, there was not a great variation inthe concentration and the solute concentrations in the vicin-ity of the membrane did not reach much higher values thanthe initial concentration. The greater the initial concentra-tion and the pressure, the more pronounced the concentra-tion profile.

The explanation of these experimental results with the sta-bilization of the concentration profiles is difficult when theultrafiltration models available nowadays are used. A futureaim of this research is to carry out complementary exper-imental studies with other membranes and solutes, both inultrafiltration and reverse osmosis, and to increase the ex-perimental data base in order to propose a theoretical modelwhich would be able to explain the experimental results ob-tained.

Acknowledgements

This research was sponsored by the Plan Nacional de I+D + I BQU2000-0456 (Ministerio de Educación y Cultura).Holographic interferometry equipment was financed by theConsellerıa d’Educació i Ciencia (Generalitat Valenciana).

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measurements by holographic interferometry of concentration profiles in dead-end ultrafiltration of...

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