Two modes of phase inversion in a drying emulsion

Soft Matter

PAPER

aLaboratory of Physical Chemistry and C

Dreijenplein 6, 6703 HB Wageningen

[email protected]; Fax: +31 317 483777bDutch Polymer Institute, John F. Kenn

Netherlands. E-mail: [email protected]; FaxcWageningen University, Food Process Engi

Wageningen, The Netherlands. E-mail: thom

37; Tel: +33 317 4837 70

† Electronic supplementary informationpreparation and visualization, measuremabout the hydrodynamic model. See DOI:

Cite this: Soft Matter, 2013, 9, 2810

Received 3rd October 2012Accepted 16th December 2012

DOI: 10.1039/c2sm27285g

www.rsc.org/softmatter

2810 | Soft Matter, 2013, 9, 2810–28

Two modes of phase inversion in a drying emulsion†

Huanhuan Feng,*ab Joris Sprakel,a Dmitry Ershov,a Thomas Krebs,c Martien A. CohenStuarta and Jasper van der Guchta

We report two different modes of phase inversion in surfactant-stabilized oil-in-water emulsions subjected

to a unidirectional drying stress. Coalescence occurs either through a nucleation-and-growth mechanism,

where coalesced pockets form and grow randomly throughout the sample, or through a coalescence front

that propagates into the sample from the drying end. This drying-induced coalescence results from the

development of a pressure gradient from the drying front into the bulk of the sample, established by

limited water transport through the Plateau borders. Depending on the steepness of this pressure

profile, coalescence occurs throughout the sample or only at the drying front. Moreover, we find that

surfactant concentration plays a significant role through its effect on the critical disjoining pressure at

which coalescence occurs. Very stable emulsions, characterized by a high critical pressure, tend to

develop steep pressure profiles, which favours front-dominated coalescence, while unstable emulsions

with low critical pressures develop shallow pressure gradients, favouring nucleation-and-growth

dominated coalescence. These results offer new insights into the microscopic mechanisms governing the

complex and poorly understood macroscopic phenomena during phase inversion of drying emulsions.

Introduction

When a thin layer of an oil-in-water emulsion is dried on asubstrate, evaporation of water eventually leads to the forma-tion of a lm of the dispersed phase. Despite its widespreadpractical importance in the elds of paints, coatings andadhesives, a detailed understanding of the complex process ofphase inversion in concentrated emulsions is not available todate.

It is known that lm formation occurs in a sequence ofstages:1 (1) as water evaporates, the dispersed dropletsconcentrate2 until they come into contact and form a jammedpacking. (2) Further evaporation of water creates a capillarypressure that causes the droplets to deform and squeezetogether. Similar to dry foams, this ultimately leads to faceteddroplets separated by thin water lms. (3) Finally, when thepressure becomes sufficiently high, the individual dropletsbegin to coalesce and phase inversion takes place.3 In this nal

olloid Science, Wageningen University,

, The Netherlands. E-mail: Jasper.

; Tel: +31 317 483066

edylaan 2, 5612 AB Eindhoven, The

: +31 40 247 24 62; Tel: +31 40 247 56 29

neering Group, P.O. Box 8129, 6700 EV

as.krebs @ wur.nl; Fax: +33 317 4822

(ESI) available: Details of emulsionents of interfacial tension, and details10.1039/c2sm27285g

15

stage, the water lms must rupture and disappear so that ahomogeneous lm can be formed.

While a large variety of methods have been employed tostudy the details of the initial stages of drying lms,4–12 the naland crucial stage, during which phase inversion occurs and alm is formed, remains incompletely understood; this is mostlythe result of a lack of direct experimental data on the level ofindividual droplets within the drying emulsion.13

In this article we therefore visualize phase inversion indrying emulsions on the single particle level14,15 and onmacroscopic length scales. By developing a hydrodynamicmodel we bridge these length scales and arrive at a microscopicunderstanding of this complex macroscopic phenomenon.

Materials and methodsMaterials

Polydimethylsiloxane (PDMS), viscosity 100 mPa s, sodiumdodecyl sulfate (99% purity), and Nile Red (99% purity) werepurchased from Sigma.

Emulsion preparation

Monodisperse emulsions are produced in a T-junction micro-uidic device.16–18 The continuous phase is a 10 mmol L�1 SDSsolution, while the dispersed phase is silicone oil. The cross-ow at the T-junction shears the oil to pinch off droplets of awell-dened size into the continuous phase, as illustrated in theESI, Fig. s-1.† The droplet size can be adjusted by varying theow speeds of the two phases.17 Here we produce droplets of

This journal is ª The Royal Society of Chemistry 2013

Fig. 1 Scheme of the drying experiment chamber.

Fig. 2 Confocal microscopy images of drying emulsions at various stages. (a–c)‘Front’ coalescence at an initial SDS concentration of 100 mmol L�1. (d–f) ‘Bulk’coalescence at an initial SDS concentration of 10 mmol L�1.

Fig. 3 Images of drying emulsions at various stages. The light grey regionsrepresent the remaining emulsion phase and the dark grey regions below themeniscus represent the pure oil. The dark region above the emulsion is air. (a)‘Front’ coalescence occurs at an initial SDS concentration of 100 mmol L�1. (b)‘Bulk’ coalescence occurs at an initial SDS concentration of 10 mmol L�1.

Paper Soft Matter

50 mmdiameter, which can be observed readily by both confocaland bright-eld microscopy.

Confocal microscopy

The silicone oil is uorescently labeled by the solvatochromicoil-soluble dye Nile Red. The emission of this dye at wave-lengths above 560 nm is enhanced for molecules located at theoil–water interface with respect to those surrounded by oil only;this enables us to selectively highlight the interfaces of thedroplets (see ESI, Fig. s-2†).15

Drying experiments

The drying experiments are carried out in a shallow glasssample chamber formed by two parallel glass slides separatedby a spacer of 120 mm. One side is not sealed, but exposed to air;this leads to unidirectional drying, similar to that experiencedin drying lms. The conditions are xed at 26 �C and 60%relative humidity by placing the samples in a home-builtclimate control box. The drying experiments are conducted inemulsions with initial concentrations of SDS in the water phaseof 10, 30, and 100 mmol L�1. For each of these concentrationswe run 8 samples in parallel to obtain sufficient statistics. Theset-up is illustrated in Fig. 1. All emulsions were prepared atapproximately the same initial volume fraction of 60%.

Centrifugation experiments

The critical disjoining pressure, at which the lm that separatestwo emulsion droplets ruptures and coalescence takes place, ismeasured by centrifugation. The emulsion samples are centri-fuged with a xed centrifugal force equivalent to 20 000g. Thetemperature is xed at 30 �C to prevent crystallization of thesurfactant SDS.19 Aer an initial gradual ramping-up of thegravitational acceleration, we let the samples reach mechanicalequilibration at 20 000g for 8 hours. From the relative volumesof the coalesced oil phase on top and the remaining compressedemulsion, and knowing the density difference between oil andwater, we can extract the critical disjoining pressure.20,21

Results and discussionMacro- and microscopic observations

The compressed emulsions appear as a honeycomb-likehexagonal packing, due to the monodispersity of the emulsiondroplets created by microuidics; see Fig. 2. Note that almost allwater lms are at, indicative of a very dense packing of thedroplets, well above the close packing limit. During the dryingof the emulsions, we see two distinct types of behaviour,depending on the initial surfactant concentration. At high


surfactant concentrations coalescence occurs exclusively at thedrying end of the sample and propagates into the sample as awell-dened front (Fig. 2a–c and 3a). At low surfactant concen-trations, however, coalescence starts at random positionsthroughout the sample from which large liquid pockets grow;this is reminiscent of a nucleation-and-growth process (Fig. 2d–f and 3a). In the remainder of this paper we will refer to thesetwo distinct modes of coalescence as ‘front’ and ‘bulk’ coales-cence, respectively. Another interesting observation that can bemade from these images is that coalescence occurs preferen-tially between the droplets and the larger oil pockets that appearaer the initial nucleation events or between droplets and themacroscopic bulk oil phase.

To quantify the coalescence process, we calculate the frac-tion, a, of the emulsion that has coalesced as a function of time.We extract this information from the macroscopic images, asshown in Fig. 3; dark areas, in which there is no more diffusescattering, represent coalesced areas and light areas representthe not-yet coalesced emulsion. For each initial surfactantconcentration, we average 8 parallel samples to obtain reliablestatistics. The trends are very clear: coalescence proceeds moreslowly as the SDS concentration increases, as shown in Fig. 4.We can also see that the uctuations, expressed by the variance,shown as error bars in Fig. 4, decrease with increasing surfac-tant concentration. For low surfactant concentrations, of 10 and

Soft Matter, 2013, 9, 2810–2815 | 2811

Fig. 4 Percentage of coalesced emulsion as a function of time from dryingexperiments for different initial surfactant concentrations.

Fig. 5 Front and bulk contributions to the coalescence as a function of time forinitial SDS concentrations of 10 (a), 30 (b), and 100 (c) mmol L�1.

Soft Matter Paper

30 mmol L�1, there is an initial stage where coalescenceproceeds slowly. This persists until there is a sudden increase incoalescence rate, aer approximately 1000 minutes; this fastcoalescence mode then persists until the entire sample hascoalesced and the fraction a approaches 100%. For highersurfactant concentrations, i.e. 100 mmol L�1 SDS, coalescenceis very slow and halts altogether aer approximately 300minutes. A possible reason for this apparent halt of coalescencemay be the accumulation of surfactant at the front, which leadsto a very high critical disjoining pressure; the high osmoticpressure may even prevent further evaporation.

We see clear differences in the coalescence kinetics betweenlow and high surfactant concentrations, suggesting that theinitial stability of the emulsion plays an important role. Thisimmediately triggers the question, which microscopic mecha-nisms are at play causing these differences in macroscopicbehaviour?

A rst insight can be obtained by separating the contribu-tions of the front and bulk coalescence in the kinetic plots; for adescription of this data analysis we refer to the ESI (Fig. s-3†). Inall samples, irrespective of the surfactant concentration,coalescence starts at the front. At low SDS concentration, theaccelerating bulk coalescence then takes over; for example for10 mmol L�1 SDS concentration this occurs aer 2000 minutes(Fig. 5a). Aer even longer times, coalescence is so wide-spreadthat it becomes impossible to distinguish bulk and front coa-lescence from our images; this occurs aer approximately 4000minutes for 10 mmol L�1 SDS (Fig. 5a). The effect of surfactantconcentration also emerges clearly from Fig. 5: the higher theSDS concentration, the slower the process, although the overallpattern remains the same. At high SDS concentration, bulkcoalescence is even entirely suppressed up to 8000 minutes(�6 days), which is the maximum duration length in ourexperiment.

Pressure prole

To achieve an understanding of what occurs in these emulsionsto cause these two distinct modes of coalescence, we rst realizethat the stability of an emulsion is due to the disjoining pres-sure acting between the surfaces of the dispersed phase. When

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the actual disjoining pressure reaches a critical value, the lmcan rupture and coalescence can take place. It is thereforeimportant to determine the pressures and their critical values asthey occur in a drying system. To measure the actual capillarypressure proles, from the drying front into the bulk of thesample, and as a function of time, we determine the curvatureof the Plateau borders throughout the sample. Since we visu-alize the interfaces, curvatures can be measured in themicroscopy images as shown in Fig. 6. The pressure can then beevaluated from the Laplace law, P ¼ �g/r, in which g is thesurface tension and r the radius of curvature of the Plateauborder. The interfacial tension was measured separately, andwas found to decrease from 50 to 11 mN m�1 when the SDSconcentration increased from 0 to 10 mmol L�1, which is close


Fig. 6 Schematic depiction of a Plateau border. Bright field microscopy image ofa jammed emulsion, showing the Plateau borders between three droplets and itsradius of curvature.

Fig. 7 Pressure profiles as a function of position and time for initial SDSconcentrations of 10 (a), 30 (b), and 100 (c) mmol L�1. X ¼ 0 corresponds to thebottom of the sample, while the largest X-value in each curve represents thedrying front of the sample. Pressures are determined from the Plateau bordercurvatures by averaging 40–50 droplets along the width of the channel at eachposition. Error bars indicate standard deviation. The images to the right show thecorresponding state of the emulsions; their mean SDS concentrations, taking intoaccount the evaporated water, are indicated in the legend.

Paper Soft Matter

to the CMC of SDS. Then it remains constant at SDS concen-trations above the CMC (see ESI, Fig. s-4†).

The results, presented in Fig. 7, show that the pressure isinitially low, but increases with time. Moreover, the pressures atthe dry end increase faster, so that substantial pressure gradi-ents develop (Fig. 7). This can be easily understood; dryingrequires the ow of water from the bulk to the drying front.Such a water ow can only occur if a pressure gradient existsand the more the emulsion becomes concentrated, the nar-rower the Plateau borders and the steeper the pressure droprequired to drive the uid to the evaporation site.

It should be anticipated that when the pressure at a partic-ular location reaches the critical value that exceeds themaximum disjoining pressure (P*), coalescence will occur.22,23

To assess the probability of coalescence at a given location andpressure, it is necessary to determine this critical disjoiningpressure for our system. We obtain P* for the emulsion as afunction of SDS concentration by centrifugation experiments.The results are shown in Fig. 8. The critical disjoining pressureincreases dramatically at low SDS concentrations beforereaching its maximum value around 1000 mmol L�1. The crit-ical disjoining pressures that we nd are about a factor of 5lower than the values found by Bibette et al.,24 probably becausethe droplet size in our experiments is at least an order ofmagnitude larger. Furthermore, we nd that the critical pres-sure keeps on increasing far above the CMC, while the surfacetension stays constant beyond the CMC; this suggests that it isnot only the adsorbed amount of surfactant that determines thestability of the liquid lms. Probably the exchange kinetics ofsurfactants plays a key role in determining the critical disjoin-ing pressure.

Fig. 8 Critical disjoining pressures as a function of SDS concentration.

Hydrodynamic model

To understand our observations and the development of thesteep pressure gradients, we use a hydrodynamic model for theow of water in the drying emulsion in the stages prior tocoalescence. The water ow is assumed to occur predominantlythrough the Plateau borders, and to be controlled by viscousdrag and the pressure gradient. The interfaces of the Plateauborders are assumed to be immobile, generating a no-slipboundary condition, while the size of the Plateau borders (r)adjusts according to the local pressure, in order to satisfy the

This journal is ª The Royal Society of Chemistry 2013 Soft Matter, 2013, 9, 2810–2815 | 2813

Fig. 9 Pressure profiles in the drying emulsion obtained with a hydrodynamicmodel (R ¼ 25 mm, a¼ 0.094). At low critical pressure, the evolution of the profilestops when the profile is relatively flat, but for high critical pressure, largegradients can develop.

Soft Matter Paper

Laplace law.25 As shown in the ESI,† these assumptions,together with mass conservation of both water and oil,26 can beexpressed in the following differential equation:

v3

vs¼ v

vx

��31=2 � 33=2

� v3vx

�(1)

where 3 is the volume fraction of water at a certain distancefrom the bottom of the sample. Assuming that nearly all thewater is found in the Plateau borders, which is reasonable forvery low volume fractions, we can write:

3 ¼ a� r

R

�2

(2)

here R is the size of the emulsion droplets and a is a geometricconstant of order unity. The local Laplace pressure is directlyrelated to this by Laplace's law, P ¼ ga1/2/R31/2. In eqn (1), s is adimensionless time, s ¼ ktg/ahR, with k (ref. 27) a numericalpre-factor of order 10�3, and x ¼ x/R is the dimensionlessdistance from the bottom of the sample. Eqn (1) is a continuityequation expressing mass conservation of water. The right handside represents the velocity gradient, which is related to agradient in the channel size as a result of Laplace's law. Thesecond term on the right arises because the drainage of watercauses a backow in the opposite direction to ensure volumeconservation (see ESI†). The pressure gradient may have anextra contribution from osmotic gradients, of which the mobilesurfactant is an obvious one. Water moving towards the dryfront transports the surfactant, which then accumulates at thedry end, causing a concentration gradient and a concomitantosmotic pressure gradient. For our ansatz, we rst neglect thisosmotic pressure gradient, which is a reasonable assumption ifdiffusion is fast enough to level out concentration gradients.Surfactant transports towards the drying end may also lead tothe Marangoni effect causing transport in the directionperpendicular to x, we also ignore them here. A more detailedinvestigation, taking surfactant accumulation and diffusioninto account, will be presented elsewhere.

To solve eqn (1) for the water volume fraction prole, and thepressure prole that follows from that, we need boundaryconditions. At the bottom, where the sample is closed, there isno net ux, so that the gradient must vanish: d3/dx ¼ 0 at x ¼ 0.The boundary condition at the dry end of the sample is deter-mined by the rate of evaporation (see ESI† for details):

312v3

vx¼ vx2

vsat x ¼ x1 (3)

where x1 denotes the position of the emulsion–air interface. Thechange of the latter represents the overall volume change of thesample, so that dx2/ds is directly proportional to the evapora-tion rate of water. We solve eqn (1) with the appropriateboundary conditions numerically, by using a boundary immo-bilization method to map the moving boundary problem onto axed domain.

Fig. 9 shows the calculated pressure proles for varioustimes. Clearly, drying increases the pressure throughout thesystem. Initially, the pressure prole is at, but as drying goeson, the prole becomes steeper. If the critical disjoining

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pressure is low, as is the case for low surfactant concentrations(lower dashed line in Fig. 9), the pressure cannot reach veryhigh values, because coalescence occurs once the pressureexceeds the critical threshold. As a result, the Plateau bordersremain relatively wide and water transport towards the dry endcan proceed much faster. Pressure gradients are therefore lev-eled out, leading to a rather at pressure prole. This meansthat the critical pressure can be reached everywhere in thesample, so that bulk coalescence can take over quickly. Bycontrast, if the critical pressure is high, very steep pressureproles can be reached. This is caused by the fact that narrowpores can develop, which induce strong pressure drops, becausethey clog the system from the drying end to the bottom of thesample. In this case, the pressure in the bulk never reaches thecritical pressure and coalescence can occur only at the front.

Conclusions

We have observed two distinct modes of coalescence in a dryingemulsion: one that proceeds as a nucleation and growth processthroughout the sample and another where a coalescence frontpropagates into the sample from the dry end. Which modedominates is determined by a balance between the establishedpressure prole and the local critical disjoining pressure in theemulsion. For very stable emulsions, narrow Plateau borderscan develop, leading to steep pressure gradients; the actualpressure only exceeds the critical pressure in a narrow zonearound the drying front and front coalescence results. Theopposite occurs for unstable emulsions; only shallow pressureproles develop before coalescence commences throughout thebulk of the sample. We expect that the transition will alsodepend on the drying conditions; at higher relative humidity,the evaporation rate decreases and pressure gradients havemore time to even out, so that bulk coalescence becomes morelikely. Our results offer insight into the microscopic mecha-nisms that underlie the complex phenomena of coalescence inconcentrated systems. While a lot of water can get trapped inthe very stable emulsions in which only front coalescence takes


Paper Soft Matter

place, phase inversion reaches completion much more effi-ciently for unstable emulsions that display bulk coalescence.Complete removal of the continuous phase is an essentialrequirement for the formation of homogeneous lms of varioustypes of emulsion paints. This poses a contradictory constrainton those systems: while stability is important for maintainingan emulsion during storage, this same stability inhibits goodlm formation.

Acknowledgements

HF, JS and JvdG acknowledge the Dutch Polymer Institute (DPI)and the Netherlands Organisation for Scientic Research(NWO) for nancial support.

Notes and references

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Two modes of phase inversion in a drying emulsion