The Influence of Viscosity on the Static and Dynamic Properties of PS

processes

Article The Inﬂuence of Viscosity on the Static and Dynamic Properties of PS-PEO Covered Emulsion Drops

Damith P. Rozairo 1 and Andrew B. Croll 2,*

1 Materials and Nanotechnology Program, North Dakota State University, Fargo, ND 58102, USA; [email protected] 2 Department of Physics and Materials and Nanotechnology Program, North Dakota State University, Fargo, ND 58102, USA * Correspondence: [email protected]; Tel.: +1-413-320-3810

Academic Editor: Andreas Håkansson Received: 25 October 2016; Accepted: 25 November 2016; Published: 29 November 2016

Abstract: Polymer stabilized emulsions are commonplace in industries ranging from cosmetics and foods to pharmaceuticals. Understanding the physical properties of emulsions is of critical importance to the rapid advancement of industrial applications. In this work, we use a sessile drop geometry to examine the effects of viscosity changes of the surrounding glycerine/water solution on polystyrene-b-polyethylene oxide (PS-PEO) covered toluene droplets. In the experiment, emulsion drops are driven by the buoyant force into a smooth mica surface. The drops buckle as they approach the mica, trapping some of the outer ﬂuid which slowly drains out over time. The characteristic time of the drainage process as well as the surface tension was measured as a function of glycerine/water concentration. The surface tension is found to have a minimum at a glycerine concentration of approximately 50% (by weight to water) and the drainage rate is shown to be well described by a recent model. The simple experiment not only shows how critical features of emulsion stability can be easily and reliably measured, but also identiﬁes important new features of the drainage process.

Keywords: emulsion; PS-PEO; sessile; static; dynamics; surface tension; slip; coalescence

1. Introduction Emulsification is the process in which two immiscible fluids (say A and B) are mixed together to create an ensemble of small droplets of fluid A in a matrix of fluid B. When mixing ceases, droplets begin coarsening and coalescing, returning the mixture to its lowest energy state in which only one A rich and one B rich domain remains. As coarsening is driven by the interfacial tension between A and B, surfactants are often used to slow the demixing. Emulsions are used in a range of industries including food, cosmetic, and pharmaceutical. Applications can be as simple as making mayonnaise by emulsification [1,2] and stabilizing oil with particles [3–5], or as complicated as encapsulating and delivering a specific drug to a specific location within our bodies [6–8], and making superhydrophobic surfaces [9,10]. Many of these processes use amphiphilic polymers as they form an attractive synthetic system in which responsivity can be engineered (for example to rupture droplets under some stimuli). It is of clear importance for researchers to understand the basic physical properties of emulsions in order to advance their industrial uses. There are several existing methods for measuring static properties of emulsion droplets such as the pendant drop method [11,12] and the micropipette aspiration method [13,14]. As useful as these techniques are for measuring emulsion droplets in ideal conditions, there are also some drawbacks. For example, the micropipette aspiration method pulls a droplet into a narrow tube which can cause certain (elastic or viscoelastic) interfaces to rupture. Furthermore, the speed at which the droplet is imbibed will certainly affect the measurement. On the other hand, the pendant drop can only be used

Processes 2016, 4, 47; doi:10.3390/pr4040047 www.mdpi.com/journal/processes Processes 2016, 4, 47 2 of 9 with relatively large drops, meaning details affected by surface to volume effects cannot be easily observed. Also, if the surface of a droplet were made elastic through crosslinking, it would only be measureable with a pendent drop if the crosslinking occurs after the drop is created [12]. We find that many of the drawbacks can be overcome by using the sessile drop technique [15]. The sessile drop is a simple method which uses the geometry of the droplet itself to measure the interfacial tension. The method can also be used to measure elastic interfaces, although we focus only on fluid interfaces in this work [16]. Furthermore, the technique can be adapted in order to measure unique dynamic properties related to coalescence, which are not accessible in traditional techniques. We conduct our measurements under a confocal microscope, for the highest resolution, however the technique is easily adapted to a light microscope enabling a very low cost and easily accessible measurement scheme. The study used a model system of toluene droplets in water (mixed with glycerine to control the density and the viscosity) stabilized by a diblock copolymer, polystyrene-block-polyethylene oxide (PS-PEO). The amphiphilic nature [17] of this polymer causes the PS-PEO to self-assemble at the oil-water interface and stabilize the emulsion. Below we give a more detailed description of the sessile drop technique and present both the static properties of PS-PEO covered sessile droplets as well as the dynamic properties related to the emulsion drop’s approach to a flat wall. We focus on altering the viscosity of the surrounding fluid by changing the ratio of glycerine to water and examining its effects on the droplet dynamics. Importantly, we note that the change in outer fluid has profound effects on other macroscopic (and microscopic) features; viscosity is not an independent variable. The observation highlights the importance of measuring several properties simultaneously.

2. Materials and Methods Polystyrene-block-poly ethylene oxide (PS-PEO) with molecular weights of 32 kg/mol (PS) and 11 kg/mol (PEO) was purchased from Polymer Source (Dorval, Canada). The polymer had a polydispersity index (PDI) of 1.06. Organic solvents (glycerine and toluene) were purchased from Fisher Scientific (Pittsburg, PA, USA) and were used as received. Nile red (9-diethylamino-5H- benzo[a]phenoxazine-5-one) compound was bought from MP Biomedicals (Santa Ana, CA, USA), and used to dye the toluene. Deionized water was produced using a Mili-Q Integral 3 purifier (Millipore, Billerica, MA, USA). Ted Pella, Inc. (Redding, CA, USA) supplied the highest-grade mica sheets. Mica was cleaved before each measurement in order to reveal a fresh, atomically flat surface. All other materials were used as received. A solution of 0.05% PS-PEO in toluene by weight was prepared at least two days prior to taking the measurements, allowing the PS-PEO to be fully dissolved in the toluene. Several concentrations of glycerine to water (by weight) solutions were prepared, ranging from pure water to pure glycerine. A lab-made glass cell was filled with one of the glycerine/water solutions and was capped with a freshly cleaved mica sheet. A micropipette was used to make PS-PEO/toluene emulsion drops inside the glass cell. The micropipette drop formation method allowed us to control the drop size. The drops were imaged (in 3D) using Laser Scanning Confocal Microscopy (LSCM, Fluoview 1000; (Olympus, Tokyo, Japan). Images show interference fringes that are generated as the light reflecting from the water/mica surface interferes with light reflecting from the drop/water interface (Figure1). The interference is used to measure the droplet shape near the contact patch as we outline below. Briefly, the interference maxima means that the separation between the flat mica surface and the droplet is equal to 1/2 of the wavelength of the laser illumination (we typically use a HeNe line in this work). One must account for the fluid’s refractive index, and note that any integer multiple of 1/2 wavelength criteria will also result in a maximum. A full interference calculation can account for all intensities between the maxima and minima resulting in a complete shape measurement. Processes 2016, 4, 47 3 of 9

3. Results

ProcessesAs 201 a toluene6, 4, 47 droplet is released inside the glycerine/water cell, several processes takes place;3 of 10 (1) the drop floats up due to buoyancy and interacts with the mica surface. As it nears the mica, the dropbuckles buckles in and in andtraps traps an amount an amount of the of the glycerin glycerine/watere/water mixture mixture between between the the mica mica and and the the drop interface. (2)(2) TheThe trappedtrapped fluidfluid is is then then slowly slowly pushed pushed out out through through the the self-assembled self-assembled PEO PEO brush brush at the at thefluid/oil fluid/oil interface interface along along the the annular annular contact contact region. region (3). The(3) The drop drop ultimately ultimately reaches reaches equilibrium equilibrium and andrests rests on a circularon a circular contact contact patch. patch Figure. 1Figure shows 1 a shows typical a LSCM typical image LSCM of theimage second of the and second the third and stage the thirdof the stage process of alongthe process with a along corresponding with a corresponding schematic. The schematic. first stage, The flattening first stage, and bucklingflattening of and the bucklingdrop, is not of capturedthe drop, using is not LSCM capture asd the using drops LSCM rise too as rapidly,the drops particularly rise too rapidly, in the lower particularly concentration in the lowerglycerine concentration mixtures. Figure glycerin1a showse mixtures. the buckled Figure drop 1a show just afters the it buckled comes into drop contact just after with it the comes mica, into the contactshape clearly with the shown mica, in the its shape interference. clearly shown in its interference.

Figure 1. LaserLaser Scanning Scanning Confocal Confocal Microscopy, Microscopy, (LSCM)(LSCM) images of a PS PS-PEO-PEO covered emulsion droplet in water pressed up against a micamica sheetsheet and thethe correspondingcorresponding side view schematics.schematics. ( (aa)) S Stagetage 2, 2, where the trapped pocket of water is in the process of draining out.out. The lower figure figure shows a cross section through the drop highlightinghighlighting the buckled region and trapped fluid fluid under the center of the b drop. Arrows indicate the direction of flow flow as the buckled region drains;drains; (b) An image of a dr dropop a afterfter the drop has reached an equilibrium. At this stage there are no dynamic processes which take place, the drop has reached an equilibrium. At this stage there are no dynamic processes which take place, and the drop lies in intimate contact with the mica. and the drop lies in intimate contact with the mica.

The droplet shape is imaged over the course of the experiment and from the drop shape a drainagedrainage rate (part 2) and an equilibrium contact radius can be determined. Below, we outline the details of how this measurement leads to a measurement of surface tension and the single time constant of thethe drainage.drainage. Experiments Experiments were were conducted conducted with with several diff differenterent concentrations of glycerineglycerine and water outer fluid ﬂuid (leading to different densitiesdensities and viscosities). Ultimately, we build an understanding of the PS-PEO system and highlight the generality of the scaling argument used to model the drainage process.

3.1. Dynamic Properties

Processes 2016, 4, 47 4 of 9 an understanding of the PS-PEO system and highlight the generality of the scaling argument used to model the drainage process. Processes 2016, 4, 47 4 of 10 3.1. Dynamic Properties In this sectionsection wewe presentpresent thethe results results for for the the dynamic dynamic process process in in which which the the fluid fluid is drainedis drained out out of theof the buckled buckled region. region. Specifically, Specifically, the the effects effects of of the the viscosity viscosity change change in in the the outer outer fluidfluid onon thethe drainage rate are presented here. A modelmodel of of the the drainage drainage process process has recentlyhas recently been described been described and validated and validated in an earlier in publicationan earlier andpublication the reader and is the referred reader there is referred for the completethere for derivationthe complete [18 derivation]. Briefly, we [18 assume]. Briefly, a Navier-Stokes we assume a flowNavier occurs-Stokes as theflow trapped occurs volumeas the trapped of fluid volume drains throughof fluid thedrains annular throug contacth the annular region. Thecontact boundaries region. assumeThe boundaries a slip length assumeb at a slip the emulsionlength at drop the interfaceemulsion anddrop a interface no slipboundary and a no slip at the boundary mica surface at the mica surface (see Figure 2). The flow is driven by the Laplace pressure created by the curvature of (see Figure2). The flow is driven by the𝑏𝑏 Laplace pressure created by the curvature of the buckled regionthe buckled and the region surface and tension the surfaceγ of the tension oil/water of interface.the oil/water Assuming interface. that Assuming the buckled that region the buckled forms a sphericalregion forms cap, athe spherical change cap, in the the heightchange of in the the center height of of the the buckled center of region the buckled as a function region ofas time,a functionh (t), ( ) 𝛾𝛾 isof expectedtime, to, is take expected on an exponentialto take on an form, exponential with a single form, governing with a single time governing constant: time constant: (1) ℎ 𝑡𝑡 ( ) = − t , τ𝑡𝑡 h (t) = e − , (1) 𝜏𝜏 where, ℎ 𝑡𝑡 𝑒𝑒 where, 3 =r η L . (2) τ = 3 . (2) h2𝑟𝑟γ𝜂𝜂 𝐿𝐿b 𝜏𝜏 f 2 � � Here, is the contact radius of the drop, andℎ 𝑓𝑓 𝛾𝛾 is𝑏𝑏 the dynamic viscosity. and characterize Here, r is the contact radius of the drop, and η is the dynamic viscosity. h f and L characterize thickness and width of the gap under the annular contact patch through which the fluid drains. thickness and𝑟𝑟 width of the gap under the annular𝜂𝜂 contact patch through whichℎ𝑓𝑓 the𝐿𝐿 fluid drains. Figure 2 shows a schematic side view of a droplet and highlights the geometric details. Figure2 shows a schematic side view of a droplet and highlights the geometric details.

Figure 2.2. A side view schematic of a buckled PS-PEOPS-PEO covered emulsion drop pushed against a ﬂatflat b L mica wall highlighting the slip length b at the emulsion boundary and the width L of the polymer brush at the inﬂection point. brush at the inflection point.

h(t) was measured measured for for each each droplet droplet by by taking taking advantage advantage of ofthe the interference interference rings rings captured captured in the in theLSCM LSCM images. images. The The fringes fringes are arecreated created through through the the interference interference of of light light reflected reﬂected from from the mica interface and thethe oil/wateroil/water interface interface of of the the droplet droplet,, and form an acc accurateurate map of the separation of the two interfaces.interfaces. InIn fact,fact, whenwhen a a dye dye was was dissolved dissolved in in the the interior interior ﬂuid fluid (toluene), (toluene), the the entire entire shape shape of the of dropthe drop can becan determined be determined through through the interference the interference (near (near the contact the contact region) region) and optical and optical sectioning sectioning (large scale(large drop scale shape). drop Theshape). large The scale large structure scale ofstructure the drop, of characterizedthe drop, characterized by its radius byR, isits important radius R, for is determiningimportant for the determining droplet’s surface the droplet tension,’s surface outlined tension in section, outlined 3.2 below. in section 3.2 below. Figure 3 shows typical measurements of the h(t) for three drops of similar size in different outer fluids. As might be expected, the drainage slows as the glycerine content of the outer fluid increases. Such a drainage dynamic might be attributed only to viscosity, however, the density of the outer fluid also changes as does its chemistry (interfacial tension). These additional quantities must also be measured in each experiment in order for a true understanding of the drainage dynamics to be

Processes 2016, 4, 47 5 of 9

Processes 2016, 4, 47 5 of 10 Figure3 shows typical measurements of the h(t) for three drops of similar size in different outer possible.fluids. As Viscosity might be and expected, density the can drainage easily slowsbe measured as the glycerine with traditional content of bulk the outertechniques, fluid increases. and we outSuchline a drainagebelow how dynamic interfacial might tension be attributed can be determined only to viscosity, from the however,drop shape. the density of the outer fluidAt also long changes times ash( doest) approaches its chemistry a constant, (interfacial small tension)., but non These-zero additionalvalue. We quantitiestake this long must time also thicknessbe measured to be in eacha measurement experiment of in the order size for of a the true PEO understanding chain, and ofrepresentative the drainage of dynamics the gap tosize, be possible.through which Viscosity the and fluid density has drained can easily (hf be) [1 measured8]. At this with stage, traditional no further bulk measurable techniques, changes and we outlinein the dropsbelow geometry how interfacial occur, tension indicating can a be clear determined end to the from approach the drop dynamics. shape.

Figure 3. Experimentally calculated height change (of similar sized drops) over time for three different Figure 3. Experimentally calculated height change (of similar sized drops) over time for three different outer ﬂuid viscosities. outer fluid viscosities.

3.2. StaticAt long Properties times h(t) approaches a constant, small, but non-zero value. We take this long time thickness to be a measurement of the size of the PEO chain, and representative of the gap size, through The surface tension of the PS-PEO covered oil-water interface was calculated using a variation which the ﬂuid has drained (hf)[18]. At this stage, no further measurable changes in the drops ofgeometry the Bashforth occur, indicatingand Adams a clearsessile end drop to the method approach [15] dynamics.. Bashforth and Adams devised a method to measure the surface tension of fluid drops using only the deformation of the drop shape under gravity3.2. Static [15] Properties. While the method requires a full 3D droplet shape, which we collect with confocal microscopy, this is not necessary if a constitutive equation is known. In a previous paper, we showed The surface tension of the PS-PEO covered oil-water interface was calculated using a variation how the measurement can be reduced to a scaling argument involving only the size of the contact of the Bashforth and Adams sessile drop method [15]. Bashforth and Adams devised a method patch (r) and the size of the droplet (R) for an ensemble of drops. The full details of the calculation to measure the surface tension of ﬂuid drops using only the deformation of the drop shape under and the derivation of the theory can be found in [16]. Below we repeat a brief overview. gravity [15]. While the method requires a full 3D droplet shape, which we collect with confocal The measurement of the surface tension relies on the drops to be deformed from their ideal microscopy, this is not necessary if a constitutive equation is known. In a previous paper, we showed spherical shape by gravity. Roughly, this is observed in drops larger than the capillary length = how the measurement can be reduced to a scaling argument involving only the size of the contact ( / ) , though this is not an exact estimate. Figure 4 shows a side view schematic of a deformed−1 patch (r) and the size of the droplet (R) for an ensemble of drops. The full details of the calculation𝜅𝜅 and drop highlighting1⁄2 the relevant geometric details. the𝛾𝛾 𝜌𝜌𝜌𝜌 derivation of the theory can be found in [16]. Below we repeat a brief overview. The measurement of the surface tension relies on the drops to be deformed from their ideal spherical shape by gravity. Roughly, this is observed in drops larger than the capillary length κ−1 = (γ/ρg)1/2, though this is not an exact estimate. Figure4 shows a side view schematic of a deformed drop highlighting the relevant geometric details.

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Figure 4.4. A schematicschematic representation of the PS-PEOPS-PEO coveredcovered toluene droplet pushed against a micamica sheet by gravity.gravity.

The hydrostatic pressure createdcreated byby thethe inﬂuenceinfluence of gravity is balanced by the Laplace pressure created byby additionaladditional curvaturecurvature ofof thethe dropdrop interfaceinterface nearnear thethe micamica wall.wall. FollowingFollowing BashforthBashforth andand Adams,Adams, thethe balancebalance cancan bebe formalizedformalized inin thethe equation:equation:

3 2 1 1 3 " 2# 2 d z 1 + dz +1 dz = (2 + ) 1 + dz 3. (3) e +2 e + e 3 = ( + ) + e2 2 2 2 βez 1 . (3) dxe 𝑑𝑑 𝑧𝑧xẽ dxe𝑑𝑑𝑧𝑧̃ xe d𝑑𝑑xe𝑧𝑧̃ 𝑑𝑑d𝑧𝑧̃xe 2 � � � � 𝛽𝛽𝑧𝑧̃ � � � � Here, and are the𝑑𝑑 𝑥𝑥scaled� 𝑥𝑥� horizontal𝑑𝑑𝑥𝑥� 𝑥𝑥� 𝑑𝑑and𝑥𝑥� the vertical coordinates𝑑𝑑𝑥𝑥� respectively ( = / ). The solutionHere, tox ethisand secondez are the order scaled differential horizontal equation and the gives vertical the coordinatesshape of the respectively deformed drop. (xe = xNote/b). Thethat 𝑥𝑥� 𝑧𝑧̃ 𝑥𝑥� 𝑥𝑥 𝑏𝑏 solutionthere is only to this one second free parameter order differential = ( equation) in givesthis equation the shape ( ofis thethe deformedgravitational drop. acceleration, Note that there is the is onlydensity one difference free parameter betweenβ = thegρ twob2/2 γfluidsin this, equationis the surface (g is tension the gravitational, and is acceleration,the radius of ρtheis 𝛽𝛽 𝑔𝑔𝑔𝑔𝑏𝑏 ⁄𝛾𝛾 𝑔𝑔 thedrop density at the differenceapex). Simply between, the shape the two of fluids,the dropγ is is the entirely surface controlled tension, andby theb is value the radius of . ofEquation the drop 3 𝜌𝜌 𝛾𝛾 𝑏𝑏 atwas the originally apex). Simply, derived the and shape numerically of the drop solved is entirely, by paper controlled and pencil, by the in 1883 value [15] of .β H. Equationere, GNU (3)Octave was 𝛽𝛽 originallywas used derivedto numerically and numerically solve the solved, differential by paper equation and pencil,. As in 1883is varied [15]., Here,theoretical GNU Octaveshapes wasare usedgenerated to numerically and compared solve to the measured differential droplet equation. cross sections As β is varied, resulting theoretical in a ‘fit’ for shapes each are drop. generated 𝛽𝛽 and comparedIn practice, to i measuredt is more dropletconvenient cross to sections use the resulting model to in predict a ‘fit’ for the each function drop. ( ) (the contact radiusIn as practice, a function it is of more the drop convenient radius) with to use a fixed the model choice toof predictsurface tension. the function The curver (R) generated(the contact in 𝑟𝑟 𝑅𝑅 radiusthis way as can a function then be of fit the to an drop ensemble radius) of with drops a fixed in which choice only of surface the con tension.tact radius The and curve drop generated size has inbeen this measured. way can thenNot beonly fit tois this an ensemble approach of quicker, drops in but which it enables only the the contact use of radiusa conventional and drop light size hasmicroscope, been measured. rather than Not requiring only is this a confocal approach microscope quicker, but to it collect enables the the full use 3D of drop a conventional shape. Figu lightre 5 microscope,shows data collected rather than in sever requiringal diffe a confocalrent concentrations microscope of to glycerin collect thee/water full 3Dsolution drop shape.fit to numerical Figure5 shows( ) curves. data collected Data is well in several fit by the different model, concentrations and it is clear that of glycerine/water the droplet surface solution tension fit tohas numerical changed ras( Rthe) curves. concentration Data is wellof the fit outer by the fluid model, has and been it isvaried. clear thatFinally, the dropletit is usef surfaceul to note tension that has the changed contact as𝑟𝑟 𝑅𝑅 the concentration of the outer fluid has been varied. Finally, it is useful to note that the contact radius/drop radius can be shown to scale as ~ 1/4 . ρg1 3 ∼𝜌𝜌𝜌𝜌 �4 3 /2 radius/drop radius can be shown to scale as R γ r�2 . 𝑅𝑅 � 𝛾𝛾 � 𝑟𝑟

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Figure 5. Experimental r (R) data for PS-PEO covered toluene droplets in a range of glycerine/water Figure 5. Experimental ( ) data for PS-PEO covered toluene droplets in a range of glycerine/water concentrations ﬁt to the numerical model described in the text. Resulting surface tensions are listed concentrations fit to the numerical model described in the text. Resulting surface tensions are listed in Table1. 𝑟𝑟 𝑅𝑅 in Table 1.

TableTable1 summarizes1 summarizes the the basic basic experimentally experimentally measured measured quantities, quantities, the PEOthe PEO brush brush thicknesses thicknesses ( h f ), and( ) the, and surface the surface tensions tensions for the range for the of glycerinrange of concentrations glycerin concentrations considered. considered The table also. The includes table also the densityincludes and the viscosity density ofand the viscosity glycerine/water of the glycerine/water solutions for convenience. solutions for Notably, convenience. the surface Notably, tension the ℎ𝑓𝑓 andsurface the brushtension thickness and the reach brush a somewhat thickness counterintuitive reach a somewhat minimum counterintuitive at 50% glycerine. minimum at 50% glycerine. Table 1. Experimentally measured PEO thickness and surface tension of PS-PEO covered toluene drops forTable a range 1. Experimentally of glycerine/water measured solutions. PEO thickness and surface tension of PS-PEO covered toluene drops for a range of glycerine/water solutions. Glycerine Density Viscosity Surface Tension 3 hf (nm) Glycerin%e (Kg/Densitym )[19] (Pa.s)[Viscosity14] (mNSurface/m) Tension ± % 0( 998) [19] 0.0010( . ) [14] 16.5( / ) 23.9 8.6 ( 𝒇𝒇 ) 25 1060 0.0024 11.5 20.9 ± 6.9 𝒉𝒉 0 998𝟑𝟑 0.0010 16.5 23.9 ± 8.6 50𝑲𝑲𝑲𝑲 1126⁄𝒎𝒎 0.0060𝑷𝑷𝑷𝑷 𝒔𝒔 7.5𝒎𝒎𝒎𝒎 𝒎𝒎 16.2 ± 2.1 𝒏𝒏𝒏𝒏 25 60 11671060 0.01080.0024 8.011.5 22.0 ± 8.520.9 ± 6.9 50 100 12611126 1.4120.0060 15.57.5 28.7 ± 8.016.2 ± 2.1 60 1167 0.0108 8.0 22.0 ± 8.5 4. Discussion100 1261 1.412 15.5 28.7 ± 8.0 That the surface tension varies with the glycerine/water ratio of the outer fluid is not surprising, as4. thereDiscussion is a difference in solubility of polyethylene oxide (PEO) in water and glycerine. PEO has a higherThat solubility the surface in water tension than varies it has with in glycerine, the glycerine/water so one would ratio expect of the fewer outer molecules fluid is not to surprising, assemble atas thethere interface is a difference as the glycerine in solubility content of polyethylene rises. As the oxide chain (PEO) density in water at the and interface glycerin is reduced,e. PEO has the a interfacialhigher solubility tension inγ iswater increased. than it has in glycerine, so one would expect fewer molecules to assemble at theIt isinterface surprising as the that glycerine the surface content tension rises. reaches As the a chain minimum density at anat intermediatethe interface is concentration, reduced, the however,interfacialthis tension also occurs is increased. because there are fewer molecules at the interface at low glycerine concentrations.It is surprising As the that concentration the surface decreases, tension reaches the PEO a moleculesminimum findat an themselves intermediate in an concentration increasingly, 𝛾𝛾 attractivehowever, solvent. this also This occurs causes because the chains there to swell, are fewer and once molecules again fewer at the can fitinterface on the oilat waterlow interface.glycerine Theconcentrations effect is evident. As the in theconcentration PEO brush decreases, thickness measurement the PEO molecules as well, find with themselves stretching in occuring an increasingly at both lowattractive and high solvent. glycerine This content. causes Competitionthe chains to between swell, and the twoonce effects, again poorfewer solvent can fit driving on the chainsoil water off theinterface. interface, Th ande effect good is solventevident swelling in the PEO chains brush so fewer thickness can fit measurement on the interface, as well result, with in a minimumstretching tensionoccuring at aat concentration both low and of high approximately glycerine content 50%. Without. Competition direct measurement,between the two this effects, effect may poor be solvent easily overlooked,driving chains hilighting off the theinterface utility, ofand measuring good solvent material swelling properties chains in so situ. fewer can fit on the interface, result in a minimum tension at a concentration of approximately 50%. Without direct measurement, this effect may be easily overlooked, hilighting the utility of measuring material properties in situ.

Processes 2016, 4, 47 8 of 9 Processes 2016, 4, 47 8 of 10

TheThe drainage drainage of of the the fluid fluid trapped trapped during durin theg droplet’s the droplet’s approach approach to the wall to the also wall clearly also depended clearly ondepended the concentration on the concentration of the outer of fluidthe outer (Figure fluid3). (Figure The accurate 3). The surfaceaccurate tension surface measured tension measured at each concentrationat each concentration now allows now theallows drainage the drainage model model to be moreto be deeplymore deeply evaluated. evaluated. Figure Figure6 shows 6 shows the drainagethe drainag timee time constant, constant,τ, plotted , plotted as a function as a function of radius of radius cubed, cubed, scaled byscaled viscosity, by viscosity, surface tension,surface andtension brush, and thickness brush thickness (h f ). The ( data). The for alldata concentrations for all concentrations now collapses now collapses onto a single onto lineara single curve linear as 𝜏𝜏 predictedcurve as bypredicted Equation by (2). Equation Plotted 2. in Plotted this manner, in this a linearmanner, curve a linear fit to thecurve data fit yields to the a measurementdata yields a ℎ𝑓𝑓 formeasurement the only free for parameter, the only freeL/b parameter,, which we find/ , towhich be 0.76 we ±find0.03 to. be The 0 fit.76 value ± 0.03 is. close The fit to value1, suggesting is close theto slip1, suggesting length b and the slip the widthlength of theand draining the width region of the ( drainingL) are similar region in ( length) are similar scale. It in is length remarkable scale. 𝐿𝐿 𝑏𝑏 thatIt is neitherremarkable quantity that neither depends quantity on the depends concentration on the of concentration the outer fluid of the directly outer (or fluid at leastdirectly depends (or at 𝑏𝑏 𝐿𝐿 onleast concentration depends on in concentration an identical way).in an Suchidentical an observation way). Such may an observation indicate a more may universal indicate relationa more betweenuniversal the relation two variables. between the two variables.

FigureFigure 6. 6Experimentally. Experimentally extracted extracted time time constants constants of draining of draining drops indrops a range in ofa range outer ﬂuidof outer viscosities. fluid Aviscosities. linear least A squares linear least ﬁt yields squares a value fit yields of 0.76 a ±value0.03 offor 0L.76/b±. The0.03 viscositiesfor / . The used viscosities for 0, 25, used 50, 60, for and 0, 10025, percent50, 60, glycerineand 100 percent solutions glycerin were 0.00101e solutions, 0.0024 were, 0.006 0.00101, 0.0108, 0,.00241.412, Pa0..006s, respectively., 0.0108, 1.412 Error bars. , 𝐿𝐿 𝑏𝑏 arerespectively. estimated fromError measuredbars are estimated quantities. from measured quantities. 𝑃𝑃𝑃𝑃 𝑠𝑠

5.5. ConclusionsConclusions EmulsionEmulsion drops drops of of 0.05%0.05% PS-PEOPS-PEO inin toluenetoluene solutionsolution werewere createdcreated inin a glass cell filled ﬁlled with water. TheThe glass glass cellcellwas was cappedcapped withwith aa freshlyfreshly cleavedcleaved micamica sheetsheet andand dropsdrops were observed as buoyancy pushedpushed themthem againstagainst the mica surface. LSCM LSCM was was used used to to image image the the dynamic dynamic process processeses occurring occurring as asthe the drops drops buckle buckle in in an andd trap trap a asmall small amount amount of of the the outer outer fluid ﬂuid as as the theyy approach approach the the mica mica surface. surface. BothBoth the the drainage drainage process process and and the the equilibrium equilibrium shape shape eventually eventually reached reached by by the the emulsion emulsion drop drop can can be analyzedbe analyzed to yield to yield a surface a surface tension tension and and a drainage a drainage time time constant. constant. In In this this work, work, the the concentration concentration of of glycerine/water glycerine/water waswas variedvaried inin orderorder toto examineexamine viscosity changeschanges ofof fourfourorders orders ofof magnitude.magnitude. ItIt waswas foundfound thatthat thethe surfacesurface tensiontension was also correlated with glycerineglycerine concentration,concentration, havinghaving aa nonlinearnonlinear relationrelation andand aa minimumminimum aroundaround 50%.50%. Time constants werewere foundfound toto bebe accuratelyaccurately predictedpredicted byby aa recentrecent modelmodel ofof thethe drainagedrainage process, with data for all concentrationsconcentrations collapsingcollapsing ontoonto aa mastermaster curve.curve. TheThe datadata collapsecollapse lead to the conclusion that the ratio ofof thethe hydrodynamichydrodynamic slipslip lengthlength toto thethe widthwidth ofof thethe annularannular contactcontact region was constant over all conditionsconditions tested,tested, andand nearlynearly equalequal toto one.one. TheThe stabilitystability of the ratio of the slip length to the annulus widthwidth hints hints at at a a deeper deeper relation relation between between thethe twotwo quantities.quantities. WeWe conclude conclude by by noting noting that that the the relative relative simplicity simplicity of the of experimental the experimental approach approach used hereused allows here allows its easy adoption by the broader community of emulsion researchers, and may help address its easy adoption by the broader community of emulsion researchers, and may help address interesting interesting and longstanding physical questions related to emulsion stability. and longstanding physical questions related to emulsion stability.

Processes 2016, 4, 47 9 of 9

Acknowledgments: D.P.R. and A.B.C. gratefully acknowledge the donors of the Petroleum Research Fund, administered by the American Chemical Society, for funding this work (52062-DNI7). Author Contributions: D.P.R. and A.B.C. conceived and designed the experiments; D.P.R. performed the experiments. D.P.R. and A.B.C. analyzed the data; D.P.R. and A.B.C. wrote the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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