flow-visualization during macrovoid pore formation in dry-cast cellulose acetate membranes

Journal of Membrane Science 211 (2003) 71–90

Flow-visualization during macrovoid pore formation indry-cast cellulose acetate membranes

Matthew R. Peknya, Jeremiah Zartmana, William B. Krantzb,∗,Alan R. Greenbergc, Paul Toddd

a Department of Chemical Engineering, University of Colorado, Boulder, CO 80309-0424, USAb Department of Chemical Engineering, University of Cincinnati, Cincinnati, OH 45221-0171, USAc Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA

d Space Hardware Optimization Technology Inc., Greenville, IN 47124-9515, USA

Received 20 September 2001; received in revised form 25 July 2002; accepted 14 August 2002

Abstract

Video-microscopy flow-visualization (VMFV) is adapted to study the development of macrovoid (MV) pores in thedry-casting of cellulose acetate (CA)/acetone/water solutions. Particle tracer velocities provide the first direct evidence forthe presence of solutocapillary-driven convection that can enhance mass-transfer to a MV. Three phases of MV developmentare observed: fast initial growth, slow growth, and collapse. During the latter, MVs were observed on occasion to initiate farfrom the demixing front. These studies have led to a significantly modified hypothesis for MV development. Extremely rapidinitial MV growth is thought to occur owing to coalescence of dispersed phase microdroplets. To ensure net mass-transfer toa growing MV, it is postulated that a homogeneous supersaturated solution layer must exist between the demixed fluid layerand the homogeneous stable solution layer. Fast growth also involves convective mass-transfer to the MV whose surface isinitially entirely immersed in this homogeneous supersaturated solution layer. Slow growth involves net transport that resultsfrom both convective mass-transfer to the MV across the portion of its surface in contact with the homogeneous supersat-urated solution layer, and convective mass-transfer from the portion of its surface that extends into the homogeneous stablesolution layer. Active collapse is thought to occur owing to skin formation at the MV surface. Passive collapse occurs whenthe convective mass-transfer from the MV in the homogeneous stable solution layer exceeds that entering the MV in thehomogeneous supersaturated solution layer.© 2002 Elsevier Science B.V. All rights reserved.

Keywords:Membrane preparation and structure; Microporous and porous membranes; Theory; Macrovoid pores; Dry-cast membraneformation

1. Introduction

Macrovoids (MVs) are large (10–50�m) pores thatcan occur in asymmetric polymeric membranes pre-

∗ Corresponding author. Tel.:+1-513-556-4021;fax: +1-513-556-3473.E-mail address:[email protected] (W.B. Krantz).

pared via phase-inversion. They usually are consid-ered undesirable because they weaken the structuralintegrity of a membrane and make it more susceptibleto compaction and mechanical failure. Moreover, ifthe MVs are skinned, they will be relatively imper-meable and thereby result in a decrease in the effec-tive membrane area. However, MVs can be usefulin applications such as drug-delivery systems[1,2],

0376-7388/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S0376-7388(02)00381-2

72 M.R. Pekny et al. / Journal of Membrane Science 211 (2003) 71–90

ultrafiltration membranes[3], composite membranesupports[3], bioreactors[4], screen-printing media[5], and breathable fabrics[6]. MV prevention orcontrol is usually accomplished via a trial-and-errorapproach. A better understanding of MV develop-ment would permit more effective ways to controltheir occurrence. This paper presents the results ofvideo-microscopy flow-visualization (VMFV) stud-ies of macrovoid development in the dry-casting ofcellulose acetate (CA)/acetone/water solutions anduses the results to advance a new hypothesis for MVformation. This appears to be the first quantitativeVMFV study of any MV formation process.

2. Prior relevant studies

This review will cover prior studies related only toMV formation. It is generally believed that all poly-mer/solvent systems can have MVs when wet-castunder certain conditions. This observation appears tohave led to a search for a single mechanism respon-sible for the formation of MVs under all conditionsfor which they are observed. This undoubtedly is anoversimplification, since MV formation probably in-volves multiple mechanisms. Hence, we begin with abrief overview of the various mechanisms that havebeen proposed for MV formation. This is followedby a review of experimental studies of MV initiationand growth.

2.1. Mechanisms proposed for macrovoid formation

Recent reviews of the hypotheses advanced to ex-plain MV formation are given by Smolders et al.[3], Paulsen et al.[7], Van de Witte et al.[8], andPekny [9]. MV formation has been attributed to avariety of mechanisms: surface tension-induced freeconvection at the interface between the casting so-lution (CS) and precipitation bath[10–12]; solventsyneresis-induced shrinkage stress in the skin layer[13,14]; a steep concentration gradient-induced in-stability mechanism at the interface between thecasting solution and precipitation bath[15–17];spinodal decomposition[18–20]; osmotic pres-sure [21]; direct penetration of the nonsolvent intothe casting solution in wet-casting[22,23]; den-sity gradient-induced free convection[24]; instanta-

neous liquid–liquid demixing followed by diffusionalMV growth [3,25]; and solutocapillary-induced con-vection at the interface between the MV and thesurrounding casting solution[26–28].

There are problems with accepting any of thesemechanisms to explain the occurrence of MVs underall conditions. For example, Altena[22] developed hisproposed mechanism based on the observation thatMVs are formed only during the precipitation step inwet-casting. However, Allegrezza[24], Shojaie[27],and Shojaie et al.[29] demonstrated that MVs canform during dry-casting as well. Although the sur-face tension-induced free convection hypothesis wasappealing, Ray et al.[17] demonstrated that MVscould form under conditions for which this mecha-nism should not be operative. The steep concentra-tion gradient-induced instability mechanism appearedpromising and was able to explain the trends observedby Paulsen et al.[7] for MV formation in wet-casting.However, it is difficult to see how this mechanismcould explain MV formation in dry-casting. The in-stantaneous liquid–liquid demixing and diffusionalMV growth hypothesis of Reuvers[25] and Smolderset al. [3] is widely accepted. However, Shojaie[27]and Shojaie et al.[26,28]contend that diffusion alonecannot account for MVs that can emerge over veryshort time scales, i.e. nearly explosively.

These studies strongly suggest that MV formationcan involve several different mechanisms dependingon the membrane casting conditions. Definitive exper-imental studies clearly are required to further advanceour understanding of MV formation. The aforemen-tioned mechanisms are broadly divided into those thatinvolve some form of convection and those that donot involve any type of induced flow. For this reason,experimental studies that permit direct observation ofMV formation are particularly informative. These arereviewed in the next section.

2.2. Experimental studies of macrovoid formation

Optical microscopy has been used for over 25 yearsto study demixing and MV formation in polymericsolutions. The technique was first used by Matz[10]to study MV formation in wet-cast membranes. Hisprocedure involves placing a drop of casting solutionbetween a microscope slide and a cover slip. The slideis placed on a microscope stage and several drops of

M.R. Pekny et al. / Journal of Membrane Science 211 (2003) 71–90 73

nonsolvent are introduced at its edge. Capillary forcesdraw the nonsolvent to the casting solution wherean interface is established. The formation of MVsnear this interface is then observed with the aid ofan optical microscope. Owing to light scattering, thedemixed region appears translucent or opaque. Matzshowed that MVs in cellulose acetate membraneswere not necessarily caused by aqueous entrainmentas previously suggested. He showed that MVs growahead of the demixed liquid region. He observedthat MVs can be initiated extremely rapidly, but theirsubsequent growth is only moderately fast. Matz alsoobserved convection within growing MVs, althoughhe did not present any details on this aspect.

Frommer and Lancet[30] found that MV forma-tion is related to rapid liquid–liquid demixing. Sev-eral other researchers have verified this observation[13,31–35]via optical microscopy experiments. How-ever, the experiments of Kang et al.[36] suggest theopposite may be true. Frommer and Lancet also foundthat the demixing front advances proportional to thesquare-root of time, thus suggesting that demixing iscontrolled by nonsolvent diffusion from the precipita-tion bath. Koenhen et al.[34], Kang et al.[36], andYao et al.[35] obtained similar results. Frommer andMessalem[11] also reported convection within grow-ing MVs, but did not provide any details.

Cheng et al.[33] assert that solvent/nonsolvent mis-cibility (e.g. expressed via the interaction parameter)is the main parameter that dictates demixing kineticsin wet-cast membranes. They used optical microscopyto show that MVs are formed only when highly mis-cible solvent/nonsolvent pairs are utilized. They at-tribute this effect to rapid precipitation owing to fastnonsolvent penetration when it is highly miscible withthe solvent.

Strathmann et al.[13] were the first researchersto add tracer particles to the casting solution forflow-visualization in optical microscopy experiments.However, no quantitative results from these experi-ments were presented.

Ray [16] and Ray et al.[17] carried out opti-cal microscopy studies of MV growth in celluloseacetate/acetone solutions with surfactant additiveswet-cast in water using a technique similar to thatof Matz [10]. They found that adding Triton X-100(polyoxyethyleneiso-octyl phenyl ether) surfactantto the water bath increased the MV penetration rate.

This result seems surprising, since surfactants shouldcause damping of any interfacial convection thatmight accelerate MV growth[37]. However, theyused a surfactant concentration (5 wt.%) well abovethe critical micelle concentration of Triton X-100 inwater (40 ppm)[38]. Therefore, the primary effectcould have been due to the reduced surface tensionrather than damping via surface elasticity.

Wang et al.’s[39] optical microscopy experimentsof wet-cast membranes showed that the MV penetra-tion distance is proportional to the square-root of time.They argued that since MVs always grow faster thanthe demixing front, solvent diffusion from the castingsolution is the main cause of MV growth.

Konagurthu[6] and Konagurthu et al.[40,41] per-formed the first optical microscopy studies of MVgrowth in dry-cast membranes. They observed that al-though MVs initially grow rapidly, they can be over-taken by the demixing front, in which case they aremuch smaller. They also showed that decreasing therate of solvent evaporation eliminated MV formation.They suggested that this is due to a decrease in the wa-ter concentration gradient in the casting solution andcorrespondingly a decrease in the driving force for so-lutocapillary convection. Their optical microscopy ex-periments indicated that adding surfactants decreasedthe lateral spacing and size of the MVs.

Recently, Lai et al.[42] carried out optical mi-croscopy experiments similar to those of Wang et al.[39] using an 82/18 mixture of acetone and Tween-80(polyoxyethylene sorbitan monooleate) surfactant as asolvent. They found that the MV penetration distancewas proportional to the square-root of time, againsuggesting a diffusional growth mechanism. However,when they used NMP as the solvent without surfactant,they found that the MV penetration distance was largerthan implied by this proportionality at short times.They concluded that MV growth is driven by convec-tion when NMP is used as a solvent, but by diffusionwhen a surfactant is present. These results corroboratethose of Konagurthu et al.[41] discussed previously.

2.3. Critique of state-of-the-art

This brief review indicates that a variety of mecha-nisms have been proposed to explain MV formation.Considerable experimental work has been done to bothsupport and discredit these proposed mechanisms. It


seems clear that more than one mechanism is neces-sary to explain MV formation under all conditions.Video-microscopy has proven to be a very useful toolfor real-time studies of MV formation. Several investi-gators have observed convection in and around grow-ing MVs. Surprisingly, only one study has employedtracer particles to observe convection during MV for-mation, but even this study did not report any quanti-tative measurements of the tracer-particle velocities.

There is a consensus that the MV initiation mecha-nism proposed by Reuvers[25] and Smolders et al.[3]involving rapid liquid–liquid demixing is reasonable.However, there is a body of evidence that suggests thatpure diffusion of solvent to the MV may not be suffi-ciently fast to explain the explosively rapid initial MVgrowth. Moreover, there is considerable evidence thatconvection often occurs during rapid MV growth.

In view of the above considerations, this paperdiscusses experiments designed to study MV develop-ment in dry-cast CA/acetone/water solutions employ-ing quantitative video-microscopy flow-visualization.Since these experiments provide additional data insupport of rapid liquid–liquid demixing being impor-tant for MV initiation and convection being importantduring MV growth, it is of value to briefly review theMV initiation mechanism of Reuvers[25] and Smol-ders et al.[3], and the solutocapillary convection MVgrowth hypothesis of Shojaie[27] and Shojaie et al.[26,28].

3. Macrovoid initiation and growth mechanisms

3.1. Macrovoid Initiation

Based on experiments with wet-cast systems,Reuvers[25] and Smolders et al.[3] observed thatMVs appear to occur only in systems that begin phaseseparation shortly after they are cast (i.e. instanta-neous demixing). They hypothesized that MVs initiatewhen stable (i.e. outside the binodal) polymer solu-tion exists directly in front of a newly formed layerof polymer-poor nuclei. Conversely, MV initiationis presumed not to occur when the solution in frontof freshly demixed polymer-lean nuclei is within thebinodal (i.e. is supersaturated) because it will demix,thereby forming another layer of polymer-lean nu-clei that prevents the original nuclei from growing

into MVs. They also contend that growth occurs bydiffusion of primarily solvent to the MV nuclei. Al-though this hypothesis emanated from experiments onwet-cast membranes, other researchers have alludedto the diffusional growth hypothesis when explainingthe occurrence of MVs in dry-cast membranes[43].

3.2. Macrovoid growth

Although Shojaie[27] and Shojaie et al.[26,28]accept the MV initiation mechanism advanced byReuvers[25] and Smolders et al.[3], they contendthat diffusion alone cannot account for the rapid initialMV growth. They proposed an alternative mechanismfor MV growth based on their dry-cast experiments ofthe CA/acetone/water system. Fast evaporation of theacetone solvent establishes a water concentration atthe casting solution/gas (CS/G) interface higher thanthat in the bulk of the casting solution. Thus, the cast-ing solution near the downward penetrating leadingedge of the MV has a lower water concentration thanthat at the trailing edge near the CS/G interface. Thestudies of Darkovich and Kutowy[44] indicate that thesurface tension of aqueous acetone solutions increaseswith increasing water concentration. Therefore, thesurface tension at the MV interface is increased at itstrailing edge relative to its leading edge. This surfacetension gradient causes motion of the MV interfacetowards its trailing edge, a mechanism known as ‘so-lutocapillary convection.’ Solutocapillary convectionresults in a force on the growing MV that can propelit rapidly downward into the bulk solution. Down-ward motion of the MV induces convection in thesurrounding casting solution. This in turn enhancesthe solvent mass-transfer to the growing MV vialocally steepened concentration gradients and con-vective transport. Although this hypothesis was basedon studies of dry-cast CA/acetone/water membranes,Shojaie et al.[29] assert that this solutocapillary con-vection mechanism might apply to MVs observed inother dry-cast as well as wet-cast membranes.

4. Experimental

4.1. Materials and equipment

Cellulose acetate (Eastman 398-10) was dried ina vacuum oven at 90–100◦C for several hours prior


to use and stored at room temperature under vacuumto prevent rehydration. Certified ACS grade acetone(Fisher Scientific), Triton X-100 (polyoxyethyleneiso-octyl phenyl ether, J.T. Baker Co.) and FluoradFC-170C (a nominal C8F17 aliphatic fluorochemicalwith a hydrophobic group attached to a hydrophilicpolyethoxylate chain moiety, 3M Corporation) wereused as received. Deionized, distilled water was used

Fig. 1. Schematic of the dual-slide apparatus used in the video-microscopy flow-visualization (VMFV) experiments (not to scale).

to prepare all casting solutions. Solid TiO2 parti-cles (Degussa Aerosil P25, average primary particlesize = 21 nm) were added to the casting solutionto act as tracer particles for flow-visualization. TheTiO2 particles were stored under vacuum to preventhydration, but otherwise used as received.

All microscopy experiments were performed ona Nikon EFD-3 optical microscope. Images were


recorded with a JVC-TK1270 CCD camera andported to a computer (Apple Power Macintosh G3)for storage and analysis (NIH Scion Image 1.62aimage-analysis software). In several of the experi-ments a dark-field filter was used to enhance thecontrast between MVs, tracer particles, and the sur-rounding casting solution. An infrared filter was usedto avoid heating of the casting solution.

A schematic of the apparatus is shown inFig. 1.A dual slide test-cell configuration was constructedas follows. Two glass microscope slides were firsttreated with a fluoropolymer coating (Cytonix Fluoro-pel PFC-801A/coFS) to prevent wetting by the castingsolution. This was necessary to minimize the curva-ture of an opaque meniscus that obstructed the view offluid near the CS/G interface and the demixing front. ATeflon® spacer (∼800 mm thick) was placed betweenthe two slides and the assembly was held together witha specially designed Teflon® clamp. A stainless steelhypodermic needle (the ‘trigger needle’) then was in-serted across the gap between the two slides in or-der to isolate the casting solution from the gas phaseuntil the experiment was initiated. The solvent evap-oration rate was controlled by changing the distancebetween the trigger needle and the open end of thedual slide test-cell assembly. Owing to the horizontalorientation and small spacer thickness, the gas-phasemass-transfer was solely by unsteady state diffusion.

4.2. Procedure

All casting solutions were prepared as follows.First, standard aqueous solutions containing 300 ppmsurfactant (Triton X-100 or Fluorad FC-170C) wereprepared for use as nonsolvents. Then, appropriateamounts of CA, nonsolvent (water, water and TritonX-100, or water and Fluorad FC-170C), and acetonewere added to 20 ml glass scintillation vials. Thevials were then sealed with screw caps and wrappedin Parafilm® to prevent solvent evaporation. The vialswere magnetically stirred for at least 8 h and allowedto sit undisturbed for at least 30 min to remove anyentrained gas bubbles. All solutions were cast within24 h of preparation.

Experiments were performed with casting solutionshaving two slightly different compositions that hadpreviously been shown to generate MVs[29]: 10 wt.%CA, 30 wt.% H2O, 60 wt.% acetone, and 450 ppm

TiO2, and 10 wt.% CA, 29 wt.% H2O, 61 wt.% ace-tone, and 450 ppm TiO2. No significant differences indemixing or MV formation were observed for thesetwo compositions. Hence, all the results presentedbelow are from experiments done with the 10/30/60solutions. The casting solution was loaded into themicroscopy apparatus using a standard 1 cc syringe.When the trigger hypodermic needle was removed,the solution immediately behind it became exposed toair, creating a nearly planar casting solution/gas inter-face, thereby initiating the dry-cast process. Images ofthe casting solution near this interface were recordedas it demixed. Subsequent computer analysis of theimages allowed the velocity vectors to be measured atdifferent locations within the casting solution by fol-lowing the trajectories of individual tracer particles.

Note that two CS/G interfaces are observed inthese experiments: the ‘front’ and ‘rear’ interfaces(seeFig. 1). Because we wished to study events atthe front interface, it was necessary to minimize theeffects of bulk liquid movement. Capillary forces andsolvent mass loss induce motion of both CS/G inter-faces. However, placement of a small drop of acetoneat the back of the rear CS/G interface as shown inFig. 1, prevented the front interface from movinguntil it solidified. When the front interface solidified,it adhered to the two microscope slides, thereby pre-venting any further motion. In this manner we wereable to prevent any appreciable motion of the frontCS/G interface throughout the experiments.

4.3. Particle velocity measurements

The TiO2 particles were too small (21 nm) to be vis-ible via optical microscopy. However, we found thatthe TiO2 particles aggregated in the polymeric solu-tion at concentrations of∼450 ppm. The aggregated‘secondary particles’ (∼1–2�m diameter) were easilyvisible via optical microscopy at 100× magnification.These secondary TiO2 particles were much smallerthan any observed MVs (diameter∼50�m), and thusworked quite well as tracer particles for VMFV. Inthese experiments we measured the two-dimensionalvelocity vectors of tracer particles at the five locationsin the polymer solution shown inFig. 2:

Location 1: In the homogeneous casting solution nearthe demixing front far from any MVs.


Location 2: In the homogeneous casting solution ad-jacent to the side of a MV.

Location 3: In the homogeneous casting solution ad-jacent to the leading edge of a MV.

Location 4: Inside a MV.Location 5: In the homogeneous casting solution farfrom any MVs and the demixing front.

The following Cartesian coordinate system is usedthroughout this paper (seeFig. 2): the Y-axis extendsparallel to the demixing front withY = 0 at an arbi-trary location along the demixing front; theX-axis isperpendicular to the demixing front withX = 0 at theCS/G interface. Note that the demixing front movesin the negativeX-direction.

4.4. Limitations of video-microscopyflow-visualization technique

Some caution is necessary in using optical mi-croscopy to study membrane-formation processes.

Fig. 2. Schematic of the five general locations of tracer-particle velocity measurements and general characteristics of the observed particlemotion. Note the orientation of theX- and Y-axes. Location 1: in the homogeneous solution, near the demixing front, far from any MVs.Location 2: adjacent to the side of the MV/solution interface. Location 3: adjacent to the leading edge of the MV. Location 4: inside theMV. Location 5: in the homogeneous solution, far from any MVs and the demixing front.

The geometry of the optical apparatus is quite dif-ferent from that for conventional membrane casting.Membrane formation typically involves casting a thinfilm (∼100–500�m thick) with a large surface area.However, the ‘membranes’ studied in these VMFVexperiments are typically several millimeters thickwith a surface area of only a few square millime-ters. Furthermore, membranes are usually cast suchthat gravity acts perpendicular to the demixing front.However, gravity acts parallel to the demixing frontin these VMFV experiments.

Dry-casting experiments using optical microscopypresent several problems not encountered in wet-casting. First, the gas-phase mass-transfer for con-ventionally cast films is different from that in theseVMFV experiments. Whereas gas-phase mass-transferis dominated by a free or forced convection bound-ary layer in conventional membrane casting, it iscontrolled by diffusion in the VMFV experiments.Also, the heat transfer is different in the two situa-tions. Shojaie et al.[27–29] showed that the dry-cast


process is not necessarily isothermal; the castingsolution temperature can decrease by as much as20–25◦C due to evaporative cooling. However, be-cause of the small surface area of the CS/G interfaceand the presence of the glass plates that act as heatsinks, ‘membranes’ cast in the VMFV apparatus willbe much less affected by evaporative cooling.

The VMFV technique permits studying only twodimensions (X andY in Fig. 2) of a three-dimensionalsystem. TheZ-velocity of the tracer particle (i.e.normal to the plane ofFig. 2) was ignored in the mea-

Fig. 3. Complications arising from the curved meniscus in the VMFV apparatus. Note that the casting solution just ahead of the demixingfront is not visible due to the presence of opaque demixed fluid below it.

surements. However, due to the shallow depth-of-fieldof the microscope, no particle with a significantZ-velocity remained in focus very long. Only parti-cles that remained in focus for at least 15 s, and thushad a negligibleZ-velocity, were tracked.

It was not possible to maintain a strictly planar CS/Ginterface in the experiments. Since the casting solutionwets the glass microscope slides, a curved meniscusformed at the CS/G interface. Coating the slides witha hydrophobic fluoropolymer (Cytonix Fluoropel)increased the contact angle and thereby reduced the


curvature of the meniscus. The presence of the menis-cus complicated the interpretation of the imagesbecause it partially obstructed the view ahead of thedemixing front as shown schematically inFig. 3.Hence, it was not possible to determine the exactlocation of the demixing front or to track tracer par-ticles just ahead of it. Henceforth, unless noted oth-erwise, the term ‘demixing front’ refers to the actualdemixing front indicated inFig. 3.

5. Results and discussion

5.1. VMFV measurements

Table 1 summarizes the averageX-component ofthe tracer-particle velocities measured at the locations

Table 1RepresentativeX-velocity components at locations shown inFig. 2

Locationin Fig. 2

Surfactant Growth phase Average particleX-velocity (�m/s)

Comments

1 None Slow growth 0.492 None Slow growth 0.66 Typical average velocity at location 22 None Slow growth 0.64 Velocity of a single particle, relatively far from demixing front2 None Slow growth 0.76 Velocity of the same particle, very near the demixing front3 None Slow growth 0.264 None Slow growth 1.78 Just as particle emerges from demixing front4 None Slow growth 0.25 Same particle when it is near the MV leading edge5 None Slow growth 0.98

1 None Active collapse 0.45 Just prior to and during active collapse2 None Active collapse 0.40 Just prior to onset of active collapse3 None Active collapse 1.37 MV leading edge moves straight towards demixing front5 None Active collapse 1.22

1 None Passive collapse 0.312 None Passive collapse 0.464 None Passive collapse 0.42 Just as particle emerges from demixing front4 None Passive collapse 0.29 Same particle when near the MV leading edge

5 None Before demixing 50.30 Cellular convection5 None Fast growth 3.445 None Slow growth 0.50 Long (10–20 min) after onset of demixing

1 Triton X-100 Slow growth 0.662 Triton X-100 Slow growth 0.854 Triton X-100 Slow growth 2.274 Triton X-100 Slow growth 1.42 Just as particle emerges from demixing front5 Triton X-100 Slow growth 0.75 Same particle when near the MV leading edge

1 FC-170C Slow growth 0.542 FC-170C Slow growth 0.855 FC-170C Slow growth 0.93

shown inFig. 2 before MV initiation and during thethree phases of MV growth that will be discussed inthe following sections.Table 2summarizes the calcu-lated ratios of theX-velocity components at the loca-tions in Fig. 2 during the different stages of MV de-velopment. Relative velocities are quite useful in as-sessing the mechanisms that might be operative dur-ing MV growth. The data inTables 1 and 2will bediscussed in the subsequent sections.

5.2. Observations prior to MV initiation

Prior to demixing, considerable cellular motion oftracer particles near the CS/G interface was observed.The tracer particles moved in a more-or-less circularpattern at relatively high velocities (∼50�m/s). It wasdifficult to measure the width of these convection cells


Table 2Ratios of averageX-velocity components of tracer particles atlocations shown inFig. 2

Growth phase Surfactant Ratioa Valueb

Slow growth None νx2/νx1 1.36 ± 0.17Slow growth Triton X-100 νx2/νx1 1.1 ± 0.20Slow growth FC-170C νx2/νx1 1.58 ± 0.56Active collapse None νx2/νx1 0.87 ± 0.12Slow growth None ν4,max/ν2 1.95 ± 0.40Slow growth Triton X-100 ν4,max/ν2 1.81 ± 0.41Slow growth FC-170C ν4,max/ν2 2.23Slow growth None ν4,min/ν2 0.17Slow growth None ν4,max/ν5 2.01Slow growth Triton X-100 ν4,max/ν5 2.11 ± 0.94Slow growth None νx5/νx1 1.88 ± 0.39Slow growth Triton X-100 νx5/νx1 1.45 ± 0.13Slow growth FC-170C νx5/νx1 1.98Slow growth None ν3/ν2 0.3 ± 0.13Slow growth Triton X-100 ν3/ν2 0.17Passive collapsec FC-170C νx2/νx1 1.49Slow growthc FC-170C νx2/νx1 1.44Passive collapsec FC-170C ν4,max/ν2 0.6Slow growthc FC-170C ν4,max/ν2 1.1

a Here, ν4,max is X-velocity component of particles as theyjust emerge from the demixing front inside a MV;ν4,min is theX-velocity component of particles inside a MV near its leadingedge.

b Only one ratio measurement was performed if uncertainty isnot given.

c These four ratio measurements were performed on a singleMV filmed during both slow growth and passive collapse.

(∼1–2 mm) because of the limited field-of-view of themicroscope. These convection cells quickly dissipatedwhen the solution began to demix. They are probablydue to a Marangoni instability arising from surfacetension gradients in the CS/G interface induced bynonuniform solvent evaporation. Similar convectioncells were observed in SEM micrographs by Shojaieet al. [29] who indicated that they could be solidifiedin place when the polymer solution gelled.

After approximately 1 min, the polymer solutionat the CS/G interface began demixing. The demixedregion appeared opaque and was separated fromthe homogeneous polymer solution by the demixingfront. The thickness of the demixed region increasedwith time as the demixing front advanced furtherinto the casting solution (in the negativeX-directionin Fig. 2). After the convection cells dissipated,the tracer-particle motion slowed considerably (to∼3–4�m/s). However, rather than moving in cellularpatterns, the tracer particles moved directly towards

the CS/G interface. This motion is indicative of amass-average velocity in the casting solution in thepositiveX-direction. This arises because of the massloss owing to acetone and water evaporation. In con-ventional dry-casting this would cause motion of theCS/G interface in the negativeX-direction. However,since the CS/G interface is stationary in these experi-ments owing to mass addition from the acetone dropat the rear CS/G interface, the bulk liquid moved inthe positiveX-direction.

As the demixed fluid layer became thicker, the rateof solvent/nonsolvent mass-transfer to the CS/G in-terface decreased, thereby slowing mass loss from thesystem. Therefore, the velocities of particles 1 and5 in Fig. 2, denoted byνx1 and νx5, decreased withtime. For example, in one experimentνx1 ≈ νx5 ≈3.4�m/s immediately after the onset of demixing;15 min later,νx1 ≈ 1.0�m/s andνx5 ≈ 0.5�m/s.Most of this velocity decrease occurred just after theonset of demixing.

Very little particle motion could be seen after theonset of demixing if the casting fluid was observedin real-time. This is due to the slow mass-transferassociated with dry-casting in the VMFV apparatus.It was necessary to play back videos 15–20 timesfaster than real time in order to observe the fluidmotion. From these videos it became apparent thatMV growth occurs in these VMFV experiments inthree distinct phases: (1) an initiation phase involvingfast growth; (2) an intermediate slow growth phase;and (3) a final collapse phase. However, it is possiblethat the latter two phases of MV growth might notoccur in conventional membrane casting owing to thelimited time available for demixing. As mentionedpreviously, owing to the geometry of the VMFV ap-paratus, these experiments involved MV formationin very thick membranes. Hence, it was not possibleto study the effects of the solid casting substrate onMV formation. Moreover, these VMFV experimentsinvolved demixing for 20 min or more in contrast toconventional membrane casting for which demixingoccurs within a few seconds. The three phases of MVgrowth are discussed in the subsequent sections.

5.3. MV growth phase I: initiation (fast growth)

MV initiation occurs near the CS/G interface ashort time (5–30 s) after the onset of demixing. This is


approximately the same time required for theMarangoni convection cells described inSection 5.2to dissipate. As such, MV initiation does not appear tobe caused by these convection cells. We concur withMatz’s [10] observation that MVs initially grow veryrapidly, followed by a period of much slower growth.The duration of the fast growth phase varies consider-ably between MVs, typically being 5–30 s. The MVsexplosively emerge from the apparent demixing frontand advance into the casting solution far more rapidlythan does the demixing front. MV growth then slowsto the point where the MV leading edge advances intothe homogeneous casting solution at a rate equal tothat of the demixing front. This marks the transitionbetween the MV fast growth and slow growth phases.

Rapid MV initiation with a transition to slowgrowth is consistent with the solutocapillary hypoth-esis of Shojaie[27] and Shojaie et al.[26,28]. Rapidacetone evaporation creates a steep water concentra-tion gradient near the CS/G interface. As such, thedriving force for solutocapillary convection is verylarge when MVs initiate, causing rapid MV expansion.However, the water concentration gradient that drivesthe solutocapillary convection quickly diminishes forseveral reasons. Demixing increases the resistance toevaporative mass-transfer, thereby reducing the rate ofacetone mass loss that sustains the water concentra-tion gradient. Water also diffuses away from the CS/Ginterface, which decreases its gradient. The soluto-capillary convection itself helps to diminish the waterconcentration gradient by transporting acetone-richfluid from deeper within the casting solution.

The solutocapillary hypothesis for MV growthcould be tested in detail if it were possible to simulta-neously measure tracer-particle velocities at locationsboth near (location 2 inFig. 2) and far from the MVnear the demixing front (location 1 inFig. 2). If solu-tocapillary convection were active, one would expectνx2/νx1 > 1. If the MV interface were subject only toviscous drag forces, one would observeνx2/νx1 < 1.Unfortunately, we were unable to measureνx1 duringthe fast growth phase of MV development.

Although most MVs initiate near the CS/G interfaceat the onset of demixing (type I MVs), MVs were alsoobserved to initiate deeper in the casting solution upto several minutes after the onset of demixing (type IIMVs). Type II MVs initiate at or near the demixingfront and display the same three growth phases as

type I MVs with two notable differences. First, typeII MV initiation is usually accompanied by the activecollapse of a nearby MV (seeSection 5.5.1). Second,the fast growth phase of type II MVs is longer andless rapid than that of type I MVs. None of the MVgrowth mechanisms advanced to date appears capableof explaining type II MVs.

5.4. MV growth phase II: slow growth

The slow growth phase begins when theX-velocityof the leading edge of the MV is approximatelyequal to the demixing front velocity and typicallylasts 20–300 s. MVs do not grow significantly inthe Y-direction during this phase. Hence, the size ofthe MV ahead of the apparent demixing front doesnot change appreciably. Because of the highly vari-able duration of the slow growth phase, some MVscontinued to grow long after most nearby MVs hadcollapsed (seeSection 5.5). Hence, isolated MVscould be viewed in the absence of neighbors, therebypermitting observations not possible during the MVinitiation phase. In particular, the ratioνx2/νx1 de-scribed in Section 5.3 could be measured. Thetrajectories of approximately 120 particles were mea-sured in approximately 25 experiments. In all cases,1.1 ≤ νx2/νx1 ≤ 1.7, which suggests solutocapillaryconvection at the MV interface.

It was also possible to view convection currentspresentwithin growing MVs by tracking the trajecto-ries of tracer particles that penetrated into the MVs. Itis surprising that the tracer particles could penetrateinto the MVs, since their diffusion across the MV in-terface is not likely. A mechanism to explain this willbe discussed inSection 5.7. The general character-istics of particle motion inside MVs are sketched inFig. 2(location 4). RepresentativeX-component parti-cle velocities and their ratios are listed inTables 1 and2, respectively. A characteristic feature is that theseparticles travel in elliptical paths. As such, particlesnear the center of MVs travel away from the demixingfront, whereas particles outside MVs move towards thedemixing front. This type of motion is to be expected,since viscous drag at the MV interface will cause fluidadjacent to both sides of the MV interface to be swepttowards the demixing front. This in turn will cause acounterflow of fluid in the center of the MV. However,the magnitude of this counterflow velocity was consid-


erably larger than would be expected owing solely toviscous drag at the MV interface. This was confirmedby using the solution to the equations-of-motion for aviscous Newtonian liquid moving at a velocityU rela-tive to a spherical drop of another immiscible viscousNewtonian liquid that was developed for the specialcase of creeping flow in the absence of any surfacetension effects by Hadamard[45] and Rybczynski[46] as outlined in Levich[47]. Creeping flow is justi-fied for these VMFV experiments, since the Reynoldsnumber was typically 10−4. Although polymer-richcasting solutions are probably viscoelastic in nature,assuming Newtonian rheological behavior is adequatefor these estimates of the flow velocities surroundinga MV. The Hadamard–Rybczynski solution predictsthat the maximum fluid velocity occurs at the cen-terline of the MV and is equal toU/2, which impliesthat ν4/ν5 ∼= 1/2. It also predicts that the maximuminterfacial velocity occurs at an angle of 90◦ from theapex of the drop and is equal toU/2, which impliesthat ν′

4/ν2 ∼= 1. The data inTable 2 indicate thatν′

4/ν5 ∼= 2 andν′4/ν2 ∼= 2. Since the measured particle

velocities are not consistent with those expected if theinternal MV circulation were driven solely by relativemotion of the external fluid, an additional drivingforce must be present. It is likely that this force arisesfrom surface tension gradients along the surface ofthe MV. This will be discussed further inSection 5.7.

Other characteristics of the observed tracer-particlemotions also suggest that solutocapillary convectionoccurs at the MV surface during the slow growthphase. The tracer particles near the side of a MV (lo-cation 2 inFig. 2) usually accelerated, whereas thosefar from any MV (e.g. locations 5 and 1 inFig. 2)decelerated as they approached the demixing front.These observations are consistent with model pre-dictions[29,30] that indicate the water concentrationgradient increases towards the demixing front for thecasting solution compositions studied here. This inturn implies that the surface tension gradient alongthe MV surface increases towards the demixing front.Hence, the solutocapillary driving force and resultinginduced flow velocity will be larger at the trailingedge of the MV near the demixing front. Owing tosymmetry as well as smaller surface tension gradients,the tracer-particleX-component velocity at the MVleading edge (location 3 inFig. 2), ν3, was observedto be much smaller thanν2.

An interesting observation during the slow growthphase was the coalescence of two adjacent MVs. Thiswas suggested in SEM images presented by the au-thors in an earlier paper[9,48]. This is the first directevidence of MV coalescence.

5.5. MV growth phase III: collapse

The optical microscopy experiments of Konagurthu[6] suggested that MV growth ends because the demix-ing front overtakes the MVs. Indeed, this appears to behappening when MV growth is observed in real time.However, when videos of MV growth are played backat 15–20 times faster than real time, it is clear thatKonagurthu’s explanation is an oversimplification. Weobserved that MVs shrink towards the demixing frontfor a certain period of time before it overtakes them.This collapse phase is the third and final phase of MVgrowth. Interestingly, we observed that there appearto be two distinct types of MV collapse, which wewill refer to as ‘active’ and ‘passive’ collapse, shownschematically inFig. 4a and b, respectively.

5.5.1. Active collapseMost MVs underwent active collapse, via a process

lasting between 30 and 120 s that is shown schemati-cally in Fig. 4aand will be described here. Just prior tothe end of the slow growth phase, theX-velocity com-ponent ratioνx2/νx1 (i.e. the X-velocity componentadjacent to the lateral MV interface to that far froma MV) drops below unity. Shortly thereafter, the MVleading edge velocity reverses direction and moves to-wards and eventually reaches the demixing front. TheMV surface often deforms considerably as this occurs.At this point, the entire MV is within the demixingfront. Its structure is frozen into place because the vis-cous polymer-rich phase surrounding the MV behindthe demixing front does not allow any additional ex-pansion or collapse. We also often observed the initi-ation and growth of type II MVs when a nearby MVunderwent active collapse.

We postulate that active collapse is associated withskinning (i.e. the formation of a thin gelled solid layer)at the MV surface. The fact thatνx2/νx1 drops be-low unity suggests that solutocapillary convection hasceased at the MV surface and hence that the MV is nolonger mobile. Moreover, the deformation of the MVsurface indicates that it can sustain stress and hence


Fig. 4. Schematic of the two observed MV collapse mechanisms:(a) active collapse; (b) passive collapse.

that the MV surface behaves as a solid. This deforma-tion is most likely a response to densification of theMV surface due to skin formation.

In order for collapse to occur, nonsolvent-rich so-lution within the MV must be transferred to the sur-rounding polymer-rich phase. It is unlikely that thiscould occur sufficiently rapidly through the relativelyimpermeable MV skin. Therefore, we speculate thatthis occurs owing to fracture of the MV skin at a weakpoint or where a stress concentration occurs. A rupturein the MV skin would release nonsolvent-rich solu-tion locally. This in turn could explain the nucleationand growth of type II MVs that was observed duringactive MV collapse.

5.5.2. Passive collapseA significant number of MVs also underwent pas-

sive collapse as shown schematically inFig. 4b. Incontrast to active collapse, no deformation or reversemovement of the MV towards the demixing front isobserved during passive collapse. Moreover, passivecollapse occurs over a significantly longer time pe-riod of 240–360 s. During passive collapse, the MVshrinks approximately equally from all sides. The ve-locity component ratioνx2/νx1 ≈ 1.5 during passivecollapse, which is approximately the same as thatobserved during slow growth. This suggests that solu-tocapillary convection is still occurring during passivecollapse. However, the tracer-particleX-velocity com-ponent within a MV (i.e. at location 4 inFig. 2) isapproximately one-half of that observed during slowgrowth. This suggests that the transfer of nonsolventand solvent into the MV is reduced during passivecollapse.

5.6. Effect of surfactants

Preliminary experiments were performed with90 ppm solutions of Triton X-100 and FluoradFC-170C surfactants. Unfortunately it was not pos-sible to draw any definitive conclusions from theVMFV experiments using surfactants. The surfactantsnot only reduced the surface tension at the MV/CSinterface, but also affected the contact angle of thecasting solution at the glass plates. This caused anincrease in the meniscus size shown inFig. 3 fromapproximately 80–250�m. This in turn made it im-possible to observe any MVs at or near the demixingfront. Hence, it was not possible to obtain any reliableestimates of the number of MVs relative to controlexperiments without surfactants. For this reason onlyqualitative observations on the effects of surfactantswill be given here.

Both surfactants reduced the frequency of MV oc-currence relative to control experiments done underidentical conditions but without surfactants in thecasting solution. No MVs were observed in most ex-periments performed with FC-170C, whereas at leasta few MVs were present in nearly every experimentdone with Triton X-100. These results are in contrastto those of earlier dry-casting experiments done bythe authors[9,48]. We previously reported that, whileMV size is considerably reduced, the MV number


density often increases when surfactants are addedin dry-casting CA membranes. It is possible that theinability to observe smaller MVs at or near the demix-ing front owing to the thicker meniscus present whensurfactants are added results in a very conservativeestimate of the MV number density. The MVs thatwe were able to observe in the surfactant solutionsfollowed growth and collapse processes similar tothose described inSections 5.3–5.5above.

The smaller MVs observed in the presence of sur-factants is consistent with the anticipated effects ofsurface elasticity that have been described by Bergand Acrivos[37] and others. Surfactants can reducethe surface tension gradients at the MV surface andthereby reduce Marangoni convection. This in turn de-creases mass-transfer to the growing MV and therebyreduces its size. This explanation is supported bythe results of limited measurements of theX-velocityratio νx2/νx1, which is reduced in the presence ofsurfactants.

5.7. Modified hypothesis for MV growth

The results of this study support the hypothesis ofShojaie[27] and Shojaie et al.[29] that solutocapil-lary convection strongly influences MV growth. How-ever, this hypothesis needs to be revised to explainseveral features of MV growth that were revealedin the current VMFV experiments. In particular, amore complete description of MV growth must elu-cidate the mechanisms involved in the three phasesof MV growth and collapse. It must also explain howtracer particles can enter the interior of MVs sincethese particles most likely cannot diffuse across theMV/casting solution interface. It also must explainwhy the observed tracer-particle velocities within aMV are nearly double those at its surface. The initi-ation of type II MVs away from the demixing frontmust also be explained. In the following we advancea more thorough description of MV growth that ex-pands the solutocapillary convection hypothesis ofShojaie[27] and Shojaie et al.[29].

MV growth necessarily requires that nonsolventand solvent be transferred to the MV surface andthen into the interior of the MV. Smolders et al.[3]contend that these two processes occur by diffusionalone. Shojaie[27] and Shojaie et al.[29] argue thatthe mass-transfer to the MV is aided by solutocap-

illary convection induced at the MV interface. Ourstudies clearly show that solutocapillary convectionfacilitates mass-transfer of nonsolvent and solventto the MV surface. However, neither hypothesis forMV growth addresses how nonsolvent and solvententer the MV interior. Moreover, neither hypothesisis self-consistent if the membrane casting processinvolves just a demixed two-phase fluid layer sepa-rated from the homogeneous stable solution layer bythe demixing front as shown inFig. 2. The problemwith the ‘two-layer’ model shown inFig. 2 is that thechemical potential driving force for mass-transfer ofnonsolvent and solvent is in the wrong direction tofacilitate MV growth. Since the homogeneous castingsolution is assumed to have a composition outsidethe binodal, it is thermodynamically stable to phaseseparation. Hence, there is no reason why nonsolventwould transfer from this homogeneous casting solu-tion where its concentration is relatively low to theinterior of an MV where its concentration is high.

We propose a modified hypothesis for MV growththat involves three regions as shown inFig. 5: ademixed two-phase fluid layer; a homogeneous super-saturated solution layer having a composition withinthe binodal separated from the two-phase region bythe demixing front; and a homogeneous stable solu-tion layer having compositions outside the binodal.The existence of a supersaturated region during mem-brane formation via phase-inversion is reasonable andhas been suggested by Strathmann et al. and others[13]. Since we as well as several other researchershave observed that MVs grow ahead of the demix-ing front, a MV will first extend from the demixedtwo-phase fluid layer into just the supersaturated solu-tion layer but eventually into both the supersaturatedas well as the homogeneous stable solution layer asshown inFig. 5 [10,11,13,39,42].

Consider the situation shown inFig. 5 where theMV extends from the demixed fluid layer throughthe supersaturated solution layer into the stable so-lution layer. Representative compositions for thesethree layers are shown in the ternary phase diagramin Fig. 6. Although the phase-inversion process thatcreates the structure of a microporous membrane isinherently a nonequilibrium process, substantive in-sight can be gained by considering compositions andcompositional paths on the ternary phase diagram.This approach to understanding the evolution of


Fig. 5. The three-layer model for macrovoid formation. The arrows indicate the direction of net mass-transfer to or from the macrovoid.The magnitude of the mass-transfer rate is shown qualitatively by the size of the arrows.

Fig. 6. A schematic ternary phase diagram, with the critical point denoted by, showing a hypothetical composition path during membraneformation (dashed line). Also shown are typical instantaneous compositions within the three layers postulated to exist during macrovoidformation: CST within the homogenous stable solution layer,CSS within the homogeneous supersaturated fluid layer, andCDM (overallcomposition) within the demixed fluid layer.


membrane structure has considerable precedent andhas been used in prior publications by the authorsas well as others[13,14,29]. The demixed fluid layerconsists of two discrete phases with an overall aver-age compositionCDM inside the binodal in the ternaryphase diagram inFig. 6. Since the demixed fluid layershould be at or very near equilibrium, the compositionsof the polymer-lean and polymer-rich phase shouldlie at or near where the tie line throughCDM intersectsthe binodal as shown inFig. 6. The demixed fluidlayer is bounded by the supersaturated solution layerwhose compositionCSS lies inside the binodal. Thesupersaturated solution layer is bounded by the stablesolution layer whose compositionCST lies outside thebinodal. The MV will have a composition relativelyrich in nonsolvent lying near the polymer-lean branchof the binodal. Because the fluid within the MV hasa composition and corresponding chemical potentialdifferent from that in the three layers in which it is incontact, mass-transfer will occur. The mass-transferof nonsolvent and solvent will be directed into theMV across any of its area that is within the demixedfluid layer. However, this mass-transfer should not besignificant since the microdroplets of polymer-leandispersed phase present a much larger surface areathan does a large MV. Moreover, the somewhat higherpolymer concentration within the continuous phase inthe demixed fluid layer implies a lower diffusion co-efficient and thereby reduced mass-transfer to a MV.The mass-transfer will also be directed into a MValong any of its surface area that is in contact with thesupersaturated solution layer. The local supersatura-tion can be relieved by mass-transfer to a MV in con-trast to phase separation owing to the energy barrierassociated with creating the surface energy requiredfor nucleation[49]. The mass-transfer into the MVis quite high in the supersaturated solution layer be-cause there is no other polymer-lean dispersed phasepresent to relieve the supersaturation. Note however,that the mass-transfer will be directed from a MV tothe surrounding solution in the stable solution layer,since indeed it is stable to phase separation. The netrate of mass-transfer from the MV will increase as theMV penetrates further into the stable solution layer.

This three-layer model provides a mechanismwhereby a MV can grow via diffusional transfer ofnonsolvent and solvent primarily across the MV areawithin the supersaturated solution layer. However,

molecular diffusion, even aided by solutocapillaryconvection, cannot explain the initial very rapid MVgrowth and the appearance of tracer particles withinthe MVs. Indeed, it does not seem possible for thesolid tracer particles to diffuse across the interface ofa MV. We propose that the rapid initial MV growth isfacilitated by coalescence of smaller droplets of thepolymer-lean dispersed phase with a larger MV. Thisproposed coalescence growth mechanism is favoredenergetically since it represents a reduction in surfaceenergy. Unfortunately, it was not possible to observethis coalescence during the initial fast growth phaseof MV development because of the curvature of theinterface between the demixed fluid layer and thehomogeneous solution layer as was discussed earlierand is shown schematically inFig. 3. However, wedid observe coalescence of adjacent MVs during thelater stages of MV growth. Hence, it is quite reason-able to expect that coalescence is even more likely tooccur during the initial stage of MV growth when theMVs are smaller and surface energy effects dominate.This hypothesized coalescence mechanism not onlyexplains the very rapid initial MV growth, but alsoexplains how the tracer particles enter the MV; that is,coalescence involves the rupture of a MV interface,which permits the direct intrusion of tracer particlesinto the MV interior.

5.8. Interpretation of the VMFV results in light ofthe modified MV growth hypothesis

Allowing for a homogeneous supersaturated solu-tion layer between the demixed two-phase fluid layerand the homogeneous stable solution layer as well ascoalescence of dispersed phase microdroplets with thegrowing MV permits a self-consistent explanation forall the observations made during these VMFV studies.In the following, the results of this VMFV study are re-visited in light of this modified MV growth hypothesis.

Prior to the initiation of MVs, minute perturbationsin the evaporative mass-transfer can create lateral sur-face tension gradients along the CS/G interface. Thesein turn can give rise to a Marangoni instability mani-fest by convection cells having a scale on the order ofa millimeter or so as evidenced by the tracer-particlecirculation. This Marangoni instability is distinct fromthe solutocapillary convection generated along the MVinterface. However, this instability also arises from the


relatively large surface tension gradients that can begenerated in the cellulose acetate/acetone/water cast-ing system. This Marangoni convection quickly dampswhen demixing begins.

Soon after demixing begins, MVs initiate within orat the demixing front owing to the preferential growthof some nuclei of the dispersed phase as suggested byReuvers[25] and Smolders et al.[3]. However, theseinvestigators contend that MV growth cannot occur ifthe solution in front of the polymer-lean nuclei is meta-or unstable (within the binodal) because it will demixand thereby prevent any expansion of nuclei into MVs.However, as discussed previously, mass-transfer to aMV cannot occur unless it penetrates into a homo-geneous supersaturated solution layer. Hence, the un-derlying presumption of the MV growth hypothesizedhere is radically different from that advanced by priorinvestigators.

The initial MV growth occurs in the presence of alarge gradient in the nonsolvent (water) concentrationowing to evaporation of the more volatile solvent(acetone). This in turn leads to a surface tension gradi-ent along the MV surface. The larger surface tensionassociated with higher nonsolvent (water)-rich regionnear the demixing front results in a net force that‘pulls’ the surface of the MV towards the demixingfront. Although it was not possible to measure anyparticle velocities during this fast growth phase of MVdevelopment, later measurements of tracer-particlevelocities during the slow growth phase providedconvincing evidence for the presence of solutocapil-lary convection. Indeed, the tracer-particle velocitiesat or near the MV surface were directed towards thedemixing front and were typically 50% larger thanthose far removed from the MV surface. This solu-tocapillary convection induces weak convection cellswithin the non-phase-separated casting solution asevidenced by accelerating tracer-particle velocitiesdirected towards the demixing front near the MV sur-face and decelerating tracer-particle velocities fartherfrom the MV surface.

The solutocapillary convection induced at the MVsurface significantly increases the mass-transfer to theMV over that due purely to diffusion. However, it is notsufficient to account for the very large mass-transferrates that are required to explain the nearly explosiveemergence of the MVs and their subsequent rapidgrowth. The very rapid MV development during the

initial stage of the fast growth phase is the result of thecoalescence of microdroplets of the dispersed phaseand smaller MVs with a larger MV. This coalescencecauses rupture of the MV interface and permits intru-sion of tracer particles into the interior of the MV. Thisrapid growth causes the MV to quickly penetrate wellinto the homogeneous supersaturated solution layer.The absence of dispersed phase microdroplets in thislayer precludes MV growth due to coalescence, butprovides for significant mass-transfer to the MV viasolutocapillary-enhanced diffusion that constitutes thelater stage of the fast growth phase. The tracer parti-cles within the MV were observed to move at a veloc-ity somewhat greater than and in a direction counter tothat of tracer particles adjacent to the outside surfaceof the MV. These higher velocities within the MV area consequence of the large mass-transfer to the MVthat occurs across its surface within the homogeneoussupersaturated solution layer. Note that the solutocap-illary convection tends to sustain the homogeneoussupersaturated layer since it replenishes the nonsol-vent and solvent that are lost to the growing MVs.

Eventually the MV begins to penetrate into the ho-mogeneous stable solution layer. The mass-transfer isdirected away from the MV across any of the MVarea that extends into this homogeneous stable solu-tion layer. Hence, during this phase of MV develop-ment, the net mass-transfer is directed into the MVacross any of its surface that extends through the ho-mogeneous supersaturated solution layer, but directedout across the MV surface that extends into the homo-geneous stable solution layer. During this slow growthphase of MV development, the MV grows only asfast as the demixing front advances. This slow growthphase is stable to small perturbations in the amount ofMV surface area that is in contact with the homoge-neous stable solution layer. For example, if this areaincreases for some reason, the mass-transfer out of theMV will increase, which will decrease the surface areaof the MV in contact with the homogeneous stable so-lution layer. Conversely, if this MV area spontaneouslydecreases, the net mass-transfer into the MV will in-crease, which in turn will increase the MV surface areain contact with the homogeneous stable solution layer.This stability accounts for the relatively long durationof the slow growth phase of MV development. Solu-tocapillary convection remains active during the slowgrowth phase, but its intensity gradually diminishes


as the nonsolvent concentration gradient is diminishedowing to reduced solvent loss via evaporation.

At some point the MV may encounter bulk concen-trations that cause skinning to occur over a portionof its surface that is within the homogeneous stablesolution layer. Skinning is associated with a cessa-tion of solutocapillary convection along the solidifiedMV surface. Densification associated with skinninginduces stresses within the skin layer that can ulti-mately lead to rupture of the MV surface. This isevidenced by the contraction and distortion of theMV surface that was associated with active collapse.Rupture of the MV surface causes rapid release ofthe nonsolvent-rich solution from the interior of theMV. If this nonsolvent-rich solution is released intothe homogeneous supersaturated solution layer, it cangive rise to the formation of a type II MV, that is, onethat is initiated near an existing MV, but relatively farremoved from the demixing front.

Eventually the nonsolvent (water) concentrationgradient driving the solutocapillary convection thatenhances the mass-transfer to the MV in the homoge-neous supersaturated solution layer diminishes owingto decreased solvent (acetone) evaporation. The latteralso causes the thickness of the homogeneous super-saturated region to decrease, since it is the solventloss that gives rise to the supersaturation. In addition,this change in the concentration gradient causes amarked decrease in the friction (diffusion) coefficientswithin the homogeneous supersaturated region, sincenonsolvent and solvent are no longer being convectedinto this region to counteract the increase in polymerconcentration. These effects in combination cause theMV growth to progressively decrease. Hence, even-tually the mass-transfer away from the MV acrossthe surface that extends into the homogeneous stablesolution layer will exceed the mass-transfer directedinto the MV across its surface that extends throughthe homogeneous supersaturated solution layer. Thiscauses passive MV collapse distinguished by a sym-metric uniform decrease in its surface area. Soluto-capillary convection is still observed during passivecollapse, although with diminished intensity, sinceskinning does not occur. Since there is no sudden re-lease of nonsolvent-rich solution from the MV duringpassive collapse, no type II MV initiation occurs.

This description of MV initiation, growth, andcollapse is specific to the VMFV experiments

described here for the cellulose acetate/acetone/waterdry-casting system. The evaporation time in theseexperiments was much longer than that typicallyused in dry-casting studies. For this reason, the laterstages of MV growth and collapse observed in thesestudies might not be relevant for shorter evaporativecasting times. Similar studies need to be done forother casting-solution formulations to ascertain howgeneral these observations might be. It would also beof interest to use the VMFV technique in order todetermine if MV initiation and growth proceeds bya similar mechanism in wet-casting for which MVformation is more prevalent than in dry-casting.

6. Conclusions

A video-microscopy flow-visualization techniquehas been successfully adapted to elucidate theMV-growth process in the dry-casting of celluloseacetate/acetone/water solutions. Tracer-particle trajec-tories indicate the presence of solutocapillary convec-tion near the MV surface shortly after the inceptionof phase separation. This solutocapillary convectionsignificantly increases the rate of mass-transfer bycontinually bringing nonsolvent and solvent fromthe bulk of the casting solution to the MV surface.Three stages of MV development were observed:fast initial growth, slow growth, and collapse. MVsemerge from the demixing front extremely rapidly. Itis unlikely that this very rapid initial growth can beexplained solely by diffusive mass-transfer, even ifit is enhanced by solutocapillary convection. Rather,it is believed that it is due to coalescence of micro-droplets of the dispersed phase with the emergingMV. The principal evidence for this conjecture is theappearance of tracer particles within MVs. It is notclear how these tracer particles could enter the MVsin the absence of coalescence that involves ruptureof the MV surface. A radical conclusion from thisstudy is that MV growth requires a homogeneoussupersaturated solution layer separating the demixedfluid layer from a homogeneous stable solution layer.Prior researchers have contended that MV formationoccurs in the presence of just two layers: the demixedfluid layer and a homogeneous stable solution layer.However, if such were the case, the driving force fornet mass-transfer would be directed away from rather


than to a MV. Hence, we believe that a supersaturatedsolution layer is absolutely essential to provide a sig-nificant driving force for mass-transfer to a growingMV. This study revealed two forms of MV collapse.Active collapse is thought to involve skin formation atthe MV surface. The densification associated with thisskin formation induces stresses in the MV surface thatcause it to deform and in some cases to rupture. Thisrupture rapidly releases nonsolvent-rich solution thatcan cause the initiation of additional MVs. These typeII MVs are distinguished by the fact that they formnear the primary or type I MVs relatively far fromthe casting solution/gas interface well after the onsetof phase separation. Passive collapse occurs when themass-transfer from the portion of a MV that extendsinto the homogeneous stable solution layer exceedsthat across its surface in contact with the homoge-neous supersaturated solution layer. Passive collapseis characterized by uniform axisymmetric contractionof the MV. It is not clear that the later stages of MVgrowth that were observed in this study would occurfor shorter evaporation times. Moreover, the generalapplicability of these conclusions to other dry-castingsolutions or to wet-casting is yet to be ascertained.

Acknowledgements

The authors gratefully acknowledge support of thisresearch by the NASA Microgravity Research Divi-sion (NAG8-1475 and NAG3-2451), US Departmentof Education (Graduate Assistance in Areas of Na-tional Need Fellowship), 3M Corporation, NSF I/UCRC Center for Membrane Applied Science and Tech-nology (MAST) at the University of Colorado andUniversity of Cincinnati, Bioserve Space Technolo-gies at the University of Colorado, and University ofColorado Undergraduate Research Opportunities Pro-gram (UROP).

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