Enhanced displacement of phase separating liquid mixtures in 2D confined spaces
EEnhanced displacement of phase separating liquidmixtures in 2D confined spaces
Gilmar F. Arends, Jae Bem You, John M. Shaw, and Xuehua Zhang ∗ Department of Chemical and Materials Engineering, University of Alberta, Alberta T6G1H9, Canada
E-mail: [email protected]
Abstract
Displacing liquid in a confined space is important for technological processes, rang-ing from porous membrane separation to CO sequestration. The liquid to be displacedusually consists of multiple components with different solubilities in the displacing liq-uid. Phase separation and chemical composition gradients in the liquids can influencethe displacement rate. In this work, we investigate the effects of liquid composition onthe displacement process of ternary liquid mixtures in a quasi-2D microchannel whereliquid-liquid phase separation occurs concurrently. We focused on model ternary mix-tures containing 1-octanol (a model oil), ethanol (a good solvent) and water (a poorsolvent). These mixtures are displaced with water or with ethanol aqueous solution.As a comparison, for some experiments, water was displaced by ternary mixtures. Thebright field and fluorescence imaging measurements reveal distinct phase separation be-haviours. The spatial distribution of subphases arising from phase separation and thedisplacement rates of the solution are impacted by the initial ternary solution composi-tion. The boundary between the solution and displacing liquid changes from a definedinterface to a diffusive interface as the initial 1-octanol composition in the solutionis reduced. The displacement rate also varies non-linearly with the initial 1-octanol a r X i v : . [ c ond - m a t . s o f t ] F e b omposition. The slowest displacement rate arises in the intermediate 1-octanol con-centration, where a stable three-zone configuration forms at the boundary. At very low1-octanol concentration, the displacement rate is fast, associated with droplet forma-tion and motion driven by the chemical concentration gradients formed during phaseseparation. The excessive energy provided from phase separation may contribute tothe enhanced displacement at intermediate to high 1-octanol concentrations, but not atthe low 1-octanol concentration with enhancement from induced flow in confinement.The knowledge gained from this study highlights the importance of manipulating phaseseparation to enhance mass transport in confinement for a wide range of separationprocesses. Introduction
Enhanced flow transport in confined spaces is important in many processes, from catalytic-based chemical conversion, porous membrane separation, nanomedicine, and watertreatment, to enhanced oil recovery and CO sequestration. In confined spaces, liquidmixing is dominated by slow mutual diffusion, influenced by the physical properties ofliquids. Extensive studies have been performed to understand the effects of wettability ofthe wall surface, fluid viscosity, or interfacial tension of immiscible phases. On anindustrial scale, the liquid displaced from confined spaces usually consists of multiple chem-ical constituents that can interact with the displacing liquid.
For example, in enhancedoil recovery, chemical flooding processes use a displacing liquid to recover the entrapped oilphase from porous rocks by altering the interfacial tension or by reducing the viscosity of thepore fluid.
It is important for both fundamental understanding and practical applicationsto achieve fast fluid movement in confined spaces.Enhanced fluid transport and autonomous motion of droplets and colloidal particlesdriven by chemical concentration gradients in multicomponent liquid mixtures are topicsof current research interest. Microparticles or microdroplets move as a result of diffusio-2horetic or solutal driven Marangoni phenomena. Concentration gradients are often cre-ated and sustained by chemical reaction, dissolution of surfactants and surface chemistryinteractions. Manipulating the electrolyte concentration in the displacing fluid has beendemonstrated to drive colloid transport into and out of microchannels dead-ends.
In addition to chemical concentration gradients present in multicomponent single-phaseliquid mixtures, subphase formation from phase separation in multicomponent systems isalso advantageous in displacing liquid in confined spaces. Even from a practical applica-tion perspective, several studies have indicated improvements in oil recovery efficiency fromporous media when microdroplet emulsions are formed during displacement compared tocases without emulsion formation. In these cases, the enhancement effect is attributed tothe desired rheological properties and seepage characteristics of surfactant-stabilized emul-sions. More fundamentally, microdroplets form spontaneously from the simple additionof a poor solvent into a ternary solution via the Ouzo effect. When the ternary solution isdiluted by a poor solvent that is miscible with the solvent but immiscible with droplet liquid,the mixture becomes oversaturated, leading to the formation of many micro-sized dropletsdispersed over the entire continuous liquid phase without the use of mechanical agitationor surfactant.
In confinement, the spontaneous formation of microdroplets leads to en-hanced transport of the penetrating fluid. While the effect has been demonstrated, it hasnot been explored in detail. It remains unclear how the displacement rate is influenced bythe relative and absolute compositions of phases formed during phase separation - even fora single mixture.In this work, we use a simple ternary liquid mixture as a model system to explore thedisplacement process in quasi-2D confined spaces. More specifically, the confined liquidcomprises a ternary solution of 1-octanol, ethanol, and water. The displacing liquid is water.The displacement process is shown to be strongly dependent on the composition of theconfined liquid. We demonstrate that over one range of compositions, the confined liquid isdisplaced. Over another range of compositions, we demonstrate the selective separation and3isplacement of 1-octanol. As the composition trajectories and hence the intersection pointswith the one-phase to two-phase boundary in the phase diagram are known, our findingssuggest that an effective approach to enhance mass transport in confined spaces is to usedisplacement liquid composition as a design variable.
Experimental Section
Chemicals and solution preparation
Chemicals were used as received without further purification. Solution A consisted of 1-octanol (ACS grade > H SO (ACS Plus grade, FischerScientific) and 30%-volume H O (30% ACS grade, Fischer Scientific) at 85 ◦ C for 20 min-utes (caution: piranha solution is highly caustic). They were further cleaned and sonicatedwith water and ethanol each for 15 minutes. To render the silicon wafers hydrophobic, theywere coated with octadecyltrichlorosilane (OTS-Si), as has been previously documented. In brief, 0.5%-volume of OTS in hexane mixture was used to soak the wafers for 12 hours atroom temperature. The OTS-Si substrates were then sonicated with hexane, acetone, andethanol for 10 minutes each to remove any excessive OTS on the surface.For fluorescence experiments, Nile Red (Fischer Scientific) was used due to its high sol-ubility in hydrocarbon-rich phases where the oil-rich domains become fluorescent, which isuseful for identifying liquid regions rich in 1-octanol.4 able 1.
Evaluated experimental compositions of solution A (displaced liquid) by mass percentage.
Composition 1-Octanol Ethanol WaterMass % Mass % Mass %1 50 40 102 40 45 153 35 48 174 30 48 225 25 48 276 20 48 327 15 48 378 10 48 429 8 47 4510 5 48 4711 2 48 50
Table 2.
Compositions of solution A (displaced liquid) and solution B (confined liquid) by masspercentage in additional experiments.
Solution A Solution BComposition 1-octanol Ethanol Water 1-octanol Ethanol WaterE1 50 40 10 0 25 75E4 10 48 42 0 25 75R1 0 0 100 50 40 10R4 0 0 100 10 48 42
Dimensions and setup of the microchamber
The flow chamber, as sketched in Figure 1, consisted of a polycarbonate base (8.5 × × µm was kept. The cover glass was then held inposition by a spacer and was clamped to the base of the chamber with large binder clips.5 igure 1. Sketch of the fluid microchamber with top view and cross-section of the mainand side channels.
Process of the liquid displacement
Solution B was pumped using a syringe pump (Fisherbrand Single Syringe Pump) to thechannel. The displacement process as water diffused transversely into the narrow channelwas captured in-situ using a camera (Nikon DS-Fi3) connected to an optical microscope(Nikon Eclipse Ni-U). The magnification under normal conditions was 10 × with a F.O.V.of 22 mm , and videos were captured using an auto-exposure setting leading to capturedfootage with framerates ranging from 10-15 frames per second (FPS) at a fixed resolution of2880 × Analysis of the displacement rates
The videos were processed through ImageJ by converting them to image sequences. Ifrequired, the contrast and brightness levels were adjusted, and a bleach correction was6pplied. The tracking of the boundaries was achieved by the manual tracking plugin withinthe program. The calibration used for the captured footage at 10x magnification was 0.24px/ µ m. The tracked data were saved as a raw CSV file, including the number of frames, xand y positions in pixels. The displacement rate was calculated using the x and y positionusing the first entry in the data set as the initial position. Results and Discussion
The phase diagram for the model ternary mixture 1-octanol (oil), ethanol (good solvent) andwater (poor solvent) is illustrated in Figure 2A. Confined liquid compositions labelled from1 to 11 (Table 1), are shown in the phase diagram. The phase boundary was adapted fromthe literature, tie lines not shown were computed using the UNIFAC model and informthe discussion. The Dortmund UNIFAC model was implemented using the parameter valuesnoted in the Supporting Information (Tables S1 ∼ S4).The mixing between solution A and water as water diffused into the narrow channelinduced liquid-liquid phase separation. Below we show the displacement process along withphase separation for the wide range of solution A compositions listed in Table 1. The1-octanol-rich liquid is revealed using a hydrophobic dye in fluorescence images. The dis-placement dynamics are categorized into four regimes, as shown in Figure 2B-E.7 igure 2.
Overview of different dynamic regimes. (A) Ternary phase diagram of 1-octanol,ethanol, and water system in terms of mass fractions with evaluated experimental com-positions annotated. The phase diagram is adapted from ref. Displacement regimes areindicated by colors: Regime 1 (yellow), Regime 2 (orange), Regime 3 (green), and Regime4 (blue). (B-E) Representative optical images of the phase separation regimes are shown incolour-coded rectangles as in (A).
Regime 1: Receding interface
Regime 1 corresponds to a high 1-octanol concentration, above 50% by mass in solution A.The composition is labelled in the phase diagram in Figure 3A. As water diffused from theside channel, the resulting images in Figure 3B show a clear interface separating solution Afrom water in the narrow channel.A few 1-octanol microdomains pinched off from the receding phase boundary at severallocations and remained attached to the hydrophobic wall on the water side of the boundary.Their composition was confirmed using fluorescence imaging (Figure 3C). This fluorescenceimage of a representative domain formed from solution A doped with an oil-soluble fluores-cent dye (Nile red). The high fluorescence intensity from the microdomain indicates the high8oncentration of the dye in the microdomain, in contrast to the absence of a fluorescencesignal from the surrounding liquid. The spatial distribution of the dye is consistent with thechemical composition of the 1-octanol-rich microdomains surrounded by water-rich liquid.In this regime, water diffusing into the narrow channel did not lead to liquid-liquid phaseseparation along the boundary - a behaviour consistent with that of an immiscible displacingliquid. However, liquid-liquid phase separation did occur within the stranded microdomains.Many nanodroplets (with a diameter of approximately 4 µm ) formed, as shown in Figure 3D.The formation of these water-rich nanodroplets is attributed to subphase formation arisingfrom diffusion of water into the microdomains followed by liquid-liquid phase separation.As water diffuses into a microdomain and 1-octanol and ethanol diffuse out, the globalcomposition of the microdomain changes. To a first approximation, the dilution path thatis followed is indicated by the dashed line in the phase diagram in Figure 3A. The mix-ture becomes unstable as the composition intersects the solubility curve and spontaneouslyforms water-rich and 1-octanol-rich subphases. Although the global composition of themicrodomain at separation is unknown, the compositions of the 1-octanol-rich and water-rich subphases created are approximately 80 and 19% 1-octanol by mass. It is interestingthat phase separation occurred in the microdomains of stranded solution A, but not at theboundary between water and solution A. The large surface to volume ratio of the small mi-crodomains permits them to become supersaturated with water quickly. By contrast, at theboundary, water diffuses into the bulk 1-octanol-rich phase, and 1-octanol and ethanol dif-fuse into the bulk water-rich phase. Consequently, the liquids on both sides of the boundarydo not supersaturate within the time frame of measurements. At longer times, one wouldcertainly expect the microdomains to dissolve into the water-rich phase.While the shape and size of stranded solution A microdomains varied between experi-ments (Figure 3D), possibly due to the nature of the interface instability - subphase formationwithin them over time was common.If we now focus on the displacement of the boundary between solution A and water, in9he absence of microdomain formation, we can see that the x-location displacement rate isessentially time-invariant with an average value of 10.7 ± µm/s (Figure 3E). Figure 3Fshows the fluctuating x-location displacement rate where microdomains form and detach overtime. The interface progressively displaced solution A in the positive x-direction. During theformation of a microdomain, the interface remains stationary or moves backward. When amicrodomain detaches from the interface, the interface accelerates in the positive x-direction.Such cycles were observed at multiple locations on the surface.The blue and red dashed curves in Figure 3F are 1D diffusion-based displacement curves, l = (2 Dt ) / , fitted to the interface displacement data before microdomain detachmentto obtain an effective diffusion constant. The effective diffusivity varies as the boundaryprogresses. The values range from 5.3 × − m /s for a part of the boundary withoutmicrodomain formation (Figure 3E) and 2.8 × − to 7.9 × − m /s for a location wherethere is microdomain formation. The mutual diffusivities of water and ethanol, and waterand octanol range from 1.08 × − to 1.23 × − m /s and 2.0 × − to 7.3 × − m /s ,respectively. So the diffusion rates are consistent with expectations. In locations withmicrodomain formation, the boundary displacement rate was variable and ranged from 4.3to 14.0 µm/s .The influence of solution A microdomains on the local motion of the boundary may beattributed to the pinning effect and mass transfer to microdomains. Imperfections on thewall surface pin the boundary, leading to microdomain formation once the boundary becomesunstable. As the microdomain is formed, the water-rich phase close to the microdomainexperiences interfacial tension opposite to its flow direction. The acceleration experiencedafter the detachment of the microdomain may be attributed to the release of built-up tensionthat comes from the stretched interface of the microdomain.In Regime 1, water largely displaces solution A (with a high initial concentration of 1-octanol) in a confined space with one hydrophobic wall. The large scale stability of theboundary between solution A and water contributes to the effective displacement. In con-10rast, local instability of the boundary and microdomain formation leads to lower and fluctu-ating displacement rates indicated in Figure 3F, as well as less efficient 1-octanol-rich liquiddisplacement.
Figure 3.
Overview of Regime 1. (A) Ternary phase diagram indicating the dilution pathwith the two macroscopic subphases formed. P is the plait point of the ternary mixture.Red regions within the phase envelope are the Ouzo and reverse Ouzo regions. Adaptedfrom ref. The initial solution A composition is given by a red diamond. An illustrativeunstable mixture composition during dilution is given as a blue diamond. The red starsrepresent the 1-octanol-rich and water-rich compositions formed along the green tie line.(B) Time-based optical images of early film and domain development. (C) Side by sidefluorescence and bright-field images of representative microdomains. (D) Time-based imagesof a deformed domain narrowing with time. (E) Plot showing local boundary displacementwithout microdomain formation. (F) Plot showing local boundary displacement at a locationwhere microdomains form. Blue data set was taken along the x-direction indicated by whitedashed line in (B) with the same reference position of the side channel. Time window 1 is fora period without a microdomain present. During time period 2, a microdomain forms at theboundary. Time period 3 starts as soon as the microdomain detaches from the boundary.The formation of microdomains slows boundary displacement. Their detachment acceleratesboundary displacement. 11 egime 2: Moving microdroplet zone
Regime 2 corresponds to intermediate 1-octanol concentrations, about 40% by mass in so-lution A. The overall behaviour in Regime 2 differs markedly from Regime 1, despite thesimilarity of the solution A compositions. Starting from this composition, the subphaseformed by mixing with water is well approximated by the trajectory shown in Figure 4A.From the tie line shown in the phase diagram, much more 1-octanol-rich subphase is stillexpected than water-rich subphase following liquid-liquid phase separation. Unlike Regime1, a mobile 1-octanol-rich microdroplet zone separates solution A and water throughout thenarrow channel, as shown in the fluorescence images in Figure 4B. A dark zone containingwater, a zone rich in microdroplets and a clear zone of solution A are clearly present.Figure 4C shows the level of fluorescence intensity crossing the three zones. The highfluorescence intensity in the intermediate zone confirms that it is rich in 1-octanol. Theboundary zone appears dark in bright field images, possibly due to scattering from small1-octanol-rich drops.The time-based images in Figure 4D show oscillation of the boundary zone, but thisoscillation does not lead to the formation of stranded microdomains. Instead, the boundaryzone thickness appears to remain constant at 18-20 µm in the time interval of 12 s as theboundary moves forward, as shown in the high magnification inset (Figure 4D). The timeinvariance of the boundary zone thickness may indicate that the mass transfer occurringthrough the boundary is balanced, even though the compositions of the water-rich and 1-octanol-rich phases in the zone vary along the x-direction.Lines of stranded 1-octanol-rich droplets form behind the receding boundary zone, mir-roring the shape of the boundary as it progresses (Figure 4E). The interval between twolines of droplets on the surface may be related to the time required for phase separation tooccur in the boundary zone or the time required for the droplets inside the boundary zoneto accumulate on the contact line with water.The rate of the boundary displacement is quantified in Figure 4F along a fixed-line in the12-direction. The rate of displacement fluctuates with time due to the oscillatory advancementof the boundary zone. Again, the data can be fitted with a diffusion model. Comparedto the displacement of the boundary in Regime 1 (for a case where microdomain formationdoes not occur), the displacement versus square root of time is slower in Regime 2. Thisis evidenced by the lower effective diffusivity obtained from the fit, which ranged from 5.8 × − to 6.7 × − m /s , and a lower displacement rate of 5.8 µm/s . Figure 4.
Overview of Regime 2. (A) Ternary phase diagram indicating the approximatedilution path and the compositions of the subphases formed. P is the plait point of theternary mixture. Red regions within the phase envelope are the Ouzo and reverse Ouzoregions. Adapted from ref. The initial solution composition is given by a red diamond.The unstable mixture composition after dilution is approximated by a blue diamond. Thered stars represent the 1-octanol-rich and water-rich subphases that are formed based onthe green tie line. (B) Time-based fluorescence imagery at 40% 1-octanol within Regime 2.(C) Normalized fluorescence intensity as a function of x-location within the frame of (B) att = 15 s. The red area in the graph indicates a boundary zone. (D) Time-based opticalimages of moving boundary within Regime 2 with an initial solution A composition of 40% 1-octanol. Inset contains magnified images of the moving boundary indicating zone thickness.(E) Time-based optical images of droplet formation in the boundary zone. (F) Boundarydisplacement as a function of the square root of time assuming diffusion-based dynamics.Regime 1 smooth interface displacement (black) and Regime 2 (blue) comparison.13 egime 3: Moving three-zone configuration
Regime 3 arises for the 1-octanol concentration range 20% to 30% by mass in solution A.Data for the 30% case are presented in detail and are representative of this regime. Figure5A illustrates the dilution process within the phase diagram. On separation, approximatelyequal amounts of water-rich and 1-octanol-rich subphases form because the dilution lineintersects the phase envelope close to the plait point.Fluorescence images in Figure 5B reveal three distinct zones along the x-direction aslabelled in Figure 5B at t = 30 s. The normalized fluorescence intensity plotted in Figure5C shows that zone 1 consists of a 1-octanol-rich phase revealed by partition of a dye, that zone 2 consists of a water-rich subphase, and that zone 3 contains numerous immisciblewater-rich droplets (dark features in fluorescence images within a 1-octanol-rich phase).Figure 5D illustrates the early development of the three-zone configuration as water entersfrom the side to the narrow channel. A 1-octanol-rich phase forms from phase separation, andwater droplets appear simultaneously within the 1-octanol-rich subphase and later coalesceand merge into a water-rich zone 2.The displacement of solution A proceeds as the entire zone 2 moves into the narrowchannel. The width of zone 2 appears to increase slightly with time at a fixed y-position, asshown in Figure 5E. The most noticeable aspect of the entire zone 2 is its stability in spaceover minute long time scales. We suspect that this stability is related to the near-constantwidth of zone 2, which we in turn attribute to the near equivalence of the influx and outfluxof liquid to zone 2 over time. Liquid may enter zone 2 in the form of water-rich dropletsfrom zone 3 or by water entering from the side channel, as evidenced in the Figure S2.Concurrently the 1-octanol-rich liquid leaves zone 2 to zone 3. The balancing of mass fluxesin and out of zone 2 accounts for its stability.The displacement of the zone 1 to zone 2 and zone 2 to zone 3 boundaries versus thesquare root of time are shown in Figure 5F. These boundaries move with an oscillatorybehaviour in the positive x-direction with a slower overall rate than the previous regime 2 at14.71 µm/s . The fluctuations were found to be related to the water-rich droplets entering zone2. At locations were droplets merged with the boundary between zone 2 and 3, the boundaryretracted in the negative x-direction. The boundary successively becomes deformed, leadingto the acceleration of the boundary in the positive x-direction as the shape of the boundarystarts to recover. The boundary displacement curves from the two locations in Figure 5Fshow similar trends in pinning and depinning transitions. Regardless of all the fluctuationsin boundary motion, the three-zone configuration remained stable with time due to waterreplenishment. 15 igure 5. Overview of Regime 3 and dynamic data for 30% 1-octanol in solution A. (A)Ternary phase diagram showing the approximate dilution path and subphases compositions.P is the plait point of the ternary mixture. (B) Illustrative time-based fluorescence imagesfor Regime 3. Zone 1 is a 1-octanol-rich phase, zone 2 is a water-rich phase, and zone 3is 1-octanol-rich liquid with dispersed water-rich phase drops. (C) Normalized fluorescenceintensity as a function of x-location within the frame of (B) at t = 0 s. (D) Time-basedfluorescence images stages as water begins to enter the narrow channel. (E) Water-rich zone2 width as a function of time (dashed line indicating slight increasing trend). (F) Bound-ary displacement as a function of the square root of time illustrating diffusion-dominatedmovement. (Blue) corresponds to the boundary between zones 1 and 2. (Red) correspondsto boundary between zones 2 and 3. (Orange) corresponds to Regime 2 displacement data.Inset depicts the slopes, from 2 < t / < egime 4: Diffusive boundary In Regime 4, the composition ranges from 2-20% 1-octanol by mass in solution A. In thisregime, a diffusive boundary forms and the dynamics differ from the other three regimes.The results depicted in Figure 6 are for 1-octanol for 10% by mass.Figure 6A shows the approximate dilution path and subphase compositions in the phasediagram for the 10% 1-octanol case. The diluting mixture intersects the phase envelopebelow the plait point, and following phase separation, the water-rich subphase fraction isexpected to an order of magnitude greater than the 1-octanol-rich subphase mass fraction.Figure 6B shows the diffusive boundary at an early transition stage consisting of numeroustriangular protrusions of solution A that extend into the water phase. Droplets formedfrom the tips of these protrusions in the water-rich phase were larger than those formed atother positions along the boundary because, at the tip of the protrusions, the concentrationgradients are sharper than at other positions.
At longer times, protrusions approach oneanother and collapse into a line-shaped boundary region, as shown in Figure 6C At longertimes, droplets are formed along the entire boundary in the water-rich phase.Fluorescence images in Figures 6(D, E) show the 1-octanol-rich protrusions with a 1-octanol concentration greater than in solution A. Ethanol transfers prefers preferentially tothe water-rich phase. After 30 seconds, the composition of the protrusions becomes consistentwith that of the 1-octanol rich droplets formed, as indicated by the fluorescence intensity.17 igure 6.
Overview of Regime 4 at low 1-octanol compositions. (A) Ternary phase diagramindicating the approximate dilution path and subphase compositions. P is the plait pointof the ternary mixture. (B) Time-based optical images showing boundary development and(C) boundary for the 10% 1-octanol solution A case. (D) Time-based fluorescence imageryof protrusion and change to (E) line-shaped boundary for the 10% 1-octanol case.Figure 7A provides an overview and dynamic data for solution A with 2% 1-octanol.Figure 7A shows the approximate dilution path and subphase compositions. The massratio of water-rich to 1-octanol-rich subphase is expected to be around 25 to 1 in this case.Fluorescence images in Figure 7C again show triangular protrusions of 1-octanol-rich liquidinto the boundary. While the outcomes are similar to those described in Figure 6, thetriangular protrusions are more stable (Figure 7B). This outcome is consistent with earlierwork showing that droplets form branches from a diffusion-limited nucleation and growthprocess in a 2D confinement at low concentration. Once formed, numerous droplets travelled toward the side channels in the negative x-direction before becoming immobilized on the wall surface or coalescing with other droplets.The lines with low fluorescent intensity indicated in the yellow boxes in Figure 7C showinduced droplet flow. The droplets appear as lines due to the exposure time of the camerawhen taking fluorescence imagery. This induced flow may explain the relatively fast boundary18isplacement rate associated with Regime 4.The optical images in Figures 7D and E indicate the qualitative similarity of dropletformation and boundary movement phenomena for 5% and 8% 1-octanol by mass in solutionA. Differences arise from the number of droplets formed and droplet size with time.The displacement of the boundary is plotted against the square root of time for the 2%,5% and 10% initial 1-octanol wt-% cases. As indicated by the slopes added to each curvein Figure 7F, a slower followed by a more rapid diffusive displacement process is clearlyevident for the 2% and 10% conditions. While qualitatively similar, the first diffusion-controlled process slows and has a longer duration as the initial 1-octanol wt-% increases.In Regime 4, boundary displacement is faster than Regime 3 compositions, and there areseldom oscillations in displacement versus time plots.19 igure 7.
Regime 4 dynamics with a focus on low 1-octanol wt%. (A) Ternary phasediagram indicating approximate the dilution path and subphases compositions for solutionA with an initial 1-octanol composition of 2% by mass. (B) Time-based optical images oftriangular shaped boundary movement using 2% by mass in solution A. (C) Time-basedfluorescence images of 2% 1-octanol by mass indicating the 1-octanol-rich and water-richregions. Yellow boxes show droplets recirculating back to the boundary region. Time-based optical images comparing the 5% 1-octanol (D) and 8% 1-octanol (E) conditions.(F) Boundary displacement as a function of the square root of time plot comparing the2% octanol (blue), 5% (green) and 10% (red) conditions. Dashed lines show anticipatedtwo-tiered diffusion-based displacement dynamics.20 omparison of the displacement rates in the four regimes
In Figure 8A, we compare the displacement rates in all four regimes presented. An effectivediffusivity was calculated for each regime, as shown in Figure 8B. The highest effectivediffusivity value was obtained in Regime 1 at 50% of 1-octanol for a smooth boundary, whichhas an enhanced effective diffusivity of 8 × − m /s . The effective diffusivity obtained isthus higher than the expected range of the mutual diffusivities between water and ethanol(1.1 × − to 1.2 × − m /s ), and water and 1-octanol (2.0 × − to 7.3 × − m /s )showing the enhanced diffusion. In both high and low 1-octanol ratios of Regimes 1 and 4,the displacement rate of the boundary was faster at ∼ µm/s and ∼ µm/s . In contrast,in the intermediate Regime 3, the rate is only ∼ µm/s as shown by the average velocitiesin Figure 8C. Boundary displacement in Regime 3 is slower than in the other regimes butremains 2 times the displacement rate expected for a purely-diffusive single-phase processobtained from the effective diffusivity.To understand the dependence of displacement rate on 1-octanol concentration, includinga shallow minimum at intermediate 1-octanol concentrations, we must consider competingeffects. Differences in the energy released during phase separation with 1-octanol concen-tration are illustrated in Figure 8D. The energy released during the transition from a non-equilibrium single-phase state to an equilibrium two-phase state increases with 1-octanolconcentration. To the extent that displacement rate depends on this thermodynamic drivingforce, one would anticipate an increase in displacement rate with 1-octanol concentration.This effect is clearly evident at high 1-octanol concentration. However, the displacementrate at low 1-octanol concentrations is somewhat higher than at intermediate 1-octanolconcentrations. We attribute this apparent enhancement in displacement at low 1-octanolconcentrations to droplet propulsion and the flow induced in the continuous phase from theself-propelling microdroplets in this concentration range, i.e., to how the energy of phasetransition is dissipated.Impacts of relative viscosity of the liquid phases, and the relative wettability of the liq-21id phases on the wall surface, which approach one at intermediate 1-octanol concentrations(near the plait point), are seen as secondary. Viewed from this perspective, the strong de-pendence of displacement rate on the initial composition is expected to be a general featurefor displacing multi-component liquids undergoing phase separation. Further, compositionstransitioning through Regimes 1 and 2 are preferred for displacing liquid, while composi-tions transitioning through Regimes 3 and 4 are preferred for promoting the separation andextraction of a component or a component category (1-octanol a model oil in this case) fromthe solution at lower overall displacement rates. Figure 8. (A) Summary of displacement versus square root of time for 1-octanol composi-tions spanning the four regimes. (B) Effective diffusivity and average velocity (C) calculatedfrom displacement versus time data in all four regimes. (D) Calculated enthalpy of transitionfrom a non-equilibrium single phase state to two equilibrium states based on the DortmundUNIFAC method. 22 sing water + ethanol binary mixtures to displace solution A
Additional experiments were performed at high and low 1-octanol composition regime con-ditions using a displacing liquid containing 25% ethanol by mass in water. Figure 9A showsthe approximate trajectory and associated tie line from the dilution process with this dis-placing liquid for a Regime 1 composition when water alone is used to displace it (see E1in Table 2). The resulting water-rich phase formed by phase separation, in this case, hasa composition corresponding to a Regime 4 solution composition, while the composition ofthe 1-octanol-rich phase remains qualitatively similar.Figure 9B shows an observed insoluble moving boundary and stranded 1-octanol-richmicrodomains similar to the Regime 1 behaviour (Figure 3B) with fewer undulations. Thesmoother boundary displacement may be attributed to the reduction in the interfacial ten-sions and the pinning effect from the substrate with ethanol in the displacing liquid. Highersolubility of 1-octanol in ethanol solution may attribute to smaller microdomains.Consistent results were also observed in Figure 9C, where solution A was 10% 1-octanolby mass, and the displacing liquid was 25% ethanol by mass solution (see E4 in Table 2).In this case, droplets formed behind the moving boundary and dissolved slowly due to thehigh solubility of 1-octanol in displacing liquid.The boundary displacement as a function of time summarized in Figure 9D shows atime-invariant displacement rate for binary displacing liquid. Conditions with water as thedisplacing liquid, the boundary displacement rate for Regime 4 is 10 times greater, and forRegime 1, the rate is 0.9 times lower. The faster displacement rate for Regime 1 may beattributed to improvements in solubility of 1-octanol in the displacing liquid.23 igure 9. (A) Ternary phase diagram indicating the approximate dilution path using25% ethanol in the displacing liquid at Regime 1 condition. (B) Optical image of Regime 1condition using 25% ethanol by mass in the displacing liquid. (C) Time-based optical imagesof Regime 4 condition using 25% ethanol by mass in the displacing liquid. (D) Boundarydisplacement as a function time for ethanol in displacing liquid comparing the 10% 1-octanol(blue) and 50% (yellow) conditions. Dashed lines indicate linear regression from data. Datafor pure water as displacing liquid in both regimes was added for comparison (triangles).
Displacing Water with Solution A
By displacing water with solution A (a 1-octanol-containing ternary mixture), we are ableto consider impacts of reverse flow arising in large scale porous media and to understandthe impacts of relative wettability of the displacing liquid. Two cases, linked to experimentsdescribed in detail above, are illustrative.Figure 9A shows the insoluble boundary arising when the confined liquid is water and thedisplacing liquid is solution A. The solution A composition corresponds to Regime 1 (see R124n Table 2) shown in Figure 3A. Droplets did not form within microdomains left behind bythe boundary. Instead, small 1-octanol droplets were confined in the boundary zone, similarto Regime 2 conditions in Figure 4. The boundary displacement rate was 9 times fastercompared to normal Regime 1 conditions.Figure 9B shows the displacement boundary when solution A composition correspondsto Regime 4 (see R4 in Table 2). In this case, 1-octanol-rich droplets and domains form atthe boundary . The overall displacement rate of the boundary (Figure 9C) is time-invariant(77 µm/s ) and 50 times faster than normal Regime 4 conditions. This dramatic difference indisplacement rate demonstrates that using displacing liquids with better wettability (lowerinterfacial tension) on the wall surface may provide an effective route to enhance fluid dis-placement rate in confinement. Such wettability manipulation is a common professionalpractice for enhanced oil recovery. Figure 10. (A) Optical image showing confined water being displaced by solution A witha 50% 1-octanol by weight composition. (B) Optical image showing confined water beingdisplaced by solution A with a 10% 1-octanol by weight composition. (C) Boundary dis-placement as a function time for reverse conditions comparing the 10% octanol (blue) and50% (yellow) conditions. Dashed lines indicate linear regression of data. Data for wateras displacing liquid and ternary solution as confined liquid in both regimes is added forcomparison (triangles). 25 onclusions
We investigate the displacement process for phase-separating ternary liquid mixtures in 2Dconfinement. The model mixtures contain 1-octanol (a model oil), water (a model poorsolvent) and ethanol (a model good solvent), where water (the poor solvent) is the dis-placing fluid. One of the confining walls is hydrophobic, and the other is hydrophilic. Fourcomposition-dependent displacement regimes are identified. While the details of the displace-ment mechanism corresponding to each regime differ, order of magnitude enhancements oversingle-phase diffusive displacement arise. The displacement rate was also shown to be furtherenhanced with the addition of ethanol (good solvent) to the displacing liquid, improving thewettability on the wall surface. Reverse flow cases where confined water is displaced withthe ternary mixture further illustrate the importance of the impact of relative wettabilityof coexisting phases on boundary displacement. The findings in this work are readily gen-eralized using phase diagrams to provide insights and guidelines for the design of solutionformulations for confined liquid displacement. Such displacement processes are important ingeological, chemical, and biological processes in enhanced oil recovery, CO sequestration,catalytic reactions and drug delivery systems. Acknowledgement
This project is supported by the Natural Science and Engineering Research Council ofCanada (NSERC) and Future Energy Systems (Canada First Research Excellence Fund).This research was undertaken, in part, thanks to funding from the Canada Research Chairsprogram. 26 eferences (1) Kortunov, P.; Vasenkov, S.; K¨arger, J.; F´e El´ıa, M.; Perez, M.; St¨ocker, M.; Papadopou-los, G.; Theodorou, D.; Drescher, B.; McElhiney, G.; Bernauer, B. Diffusion in fluidcatalytic cracking catalysts on various displacement scales and its role in catalytic per-formance.
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New sensitive micro-measurements of dynamicsurface tension and diffusion coefficients: Validated and tested for the adsorption of1-Octanol at a microscopic air-water interface and its dissolution into water. J. ColloidInterface Sci. , , 166–179.(33) Su, J.; Duncan, P.; Momaya, A.; Jutila, A.; Needham, D. The effect of hydrogenbonding on the diffusion of water in n-alkanes and n-alcohols measured with a novelsingle microdroplet method. J. Chem. Phys. , , 044506.(34) Li, M.; Bao, L.; Yu, H.; Zhang, X. Formation of Multicomponent Surface Nanodropletsby Solvent Exchange. J. Phys. Chem. C , , 8647–8654.(35) Lu, Z.; Xu, H.; Zeng, H.; Zhang, X. Solvent Effects on the Formation of Surface Nan-odroplets by Solvent Exchange. Langmuir , , 12120–12125.30 upporting Information:Enhanced displacement of phase separating liquidmixtures in 2D confined spaces Gilmar F. Arends, Jae Bem You, John M. Shaw, and Xuehua Zhang ∗ Department of Chemical and Materials Engineering, University of Alberta, Alberta T6G1H9, Canada
E-mail: [email protected]
Thermodynamic calculations of excessive free energy from phaseseparation
The calculations were performed to approximate the excess energy that was released fromthe liquid-liquid phase separation. The ternary liquid system was modelled with an activitycoefficient model to predict the phase behaviour. The modified UNIFAC model or DortmundUNIFAC model
S1,S2 was used as the main thermodynamic model. For the simulations, weutilized both Symmetry Process Simulation software (mass balances) and a MATLAB code(energy balances) based on two works by Fredenslund and Weidlich. The van der Waalsproperties of the functional groups shown in Figure S1A, such as the group volume R k , thesurface area Q k are in Table S1, and the interaction parameters ( a mn , b mn , c mn ) are to befound in Table S2, S3 and S4.The lowest 1-octanol composition achieved by simulations was the 5% wt-% condition bySymmetry. At 5% condition, we chose the water-rich phase to be around 75 times the amountS-1 a r X i v : . [ c ond - m a t . s o f t ] F e b f the created 1-octanol-rich phase. This was done to have a non-equilibrium compositionclose to the binodal curve that may approximate the true condition as phase separationoccurs in confinement. An example of two initial compositions are depicted in Figure S1B.Symmetry is a process design software, meaning every calculation is in terms of a flowrate.To simulate our conditions, we had to fix the initial solution A feed to be a specific massflowrate quantity. Only solution B was changed for the different initial conditions. Thechanges in the mass flowrates of B were all decided by a proportionality factor based onan initial optimized value. The proportions are all tabulated with the corresponding phasecompositions in Table S5. The mass balance simulations were performed using a mixer unitin the program at a temperature of 25 ◦ C and a pressure of 101.3 kPa.The compositions from the Symmetry simulations in Table S6 were then used in theMATLAB code that was created to only calculate the excess enthalpy as a function of thecomposition of each component. With this, we were thus able to calculate the excess enthalpyof each bulk phase, water-rich and 1-octanol-rich phases. The equilibrium energy states werecalculated by summation of each water and 1-octanol-rich phase with their specific fractionin the final state. The non-equilibrium energy states were calculated using the bulk-phasecomposition. The calculated excess enthalpy values are shown in Figure S1C. With thesevalues, it was possible to calculate the energy released for each initial composition, whichshould provide a positive value for every case.
Table S1: Modified UNIFAC van der Waals parameters of functional groups used in simulation for1-octanol system.
Functional Group Classification Group Volume, Surface Area, R k Q k Methyl Main group (n): 1 (- CH ), 0.6325 1.0608Sub-group (m): 1 (- CH )Methylene Main group (n): 1 (- CH ), 0.6325 0.7081Sub-group (m): 2 (- CH )Hydroxide Main group (n): 5 (-OH), 1.2302 0.8927Sub-group (m): 14 (Primary)Water Main group (n): 7 (-OH), 1.7334 2.4561Sub-group (m): 16 (Primary)S-2 able S2: UNIFAC modified interaction parameters a mn used in simulation for 1-octanol system. CH CH OH H OCH CH H O -17.253 -17.253 1460 0 Table S3: UNIFAC modified interaction parameters b mn used in simulation for 1-octanol system. CH CH OH H OCH CH H O Table S4: UNIFAC modified interaction parameters c mn used in simulation for 1-octanol system. CH CH OH H OCH CH H O Table S5: The multiplier factors were used with the initial flowrate of the 5 % 1-octanol conditionas basis, which was found to be 1.9 m /h from optimization with a fixed Solution A flowrate of 1 m /h . The optimization was based on having the set initial condition of 75 times the mass amountof water-phase to 1-octanol-rich phase. Condition Multiplier Solution A Solution B m /h m /h able S6: Compositions obtained from Symmetry for simulations described in terms of mass per-centage 1-octanol/ethanol/water. Condition Bulk Phase Water-rich Phase 1-Octanol-rich Phase W/O Fraction5/48/47 1.58/15.18/83.24 0.64/15.12/84.23 71.37/19.11/9.52 98.7/1.38/47/45 3.40/19.95/76.66 0.94/19.76/79.29 64.16/24.47/11.37 96.12/3.8810/48/42 4.78/22.95/72.27 1.19/22.64/76.16 59.72/27.63/12.65 93.87/6.1315/48/37 8.65/27.68/63.67 1.71/26.99/71.31 53.08/32.13/14.79 86.48/13.5220/48/32 12.85/30.85/56.29 2.14/17.20/80.26 48.95/34.77/16.28 77.1/22.9030/48/22 21.78/34.85/43.36 2.74/32.63/64.63 44.43/37.50/18.07 54.33/45.6740/45/15 31.10/34.99/33.91 2.54/31.73/65.73 45.84/36.67/17.49 34.03/65.9750/40/10 40.64/32.51/26.85 1.93/28.46/69.61 50.85/33.58/15.57 20.86/79.14
Supporting figures
Figure S1: (A) Chemical structure of compounds in system with color coded functionalgroups used in modified UNIFAC calculations of enthalpy of mixing. Blue (methyl), red(methylene), green (hydroxide), and purple (water). (B) Phase diagram of 1-octanol systemshowing two of the bulk compositions that were used to calculate the excess enthalpy energyof the different initial compositions one at low 1-octanol concentration (blue) and high 1-octanol concentration (red). Initial compositions (diamond shape), 1-octanol-rich and water-rich subphases (star), and bulk compositions (circles) are all shown in this figure. (C)Calculated excess enthalpy with Dortmund UNIFAC method. Blue data indicates excessenthalpy of mixture at non-equilibrium state. Red data indicates excess enthalpy of mixtureat equilibrium state obtained by summation of the enthalpy state of both 1-octanol-richsubphase and water-rich subphase in equilibrium.S-4igure S2: Optical images showing early development of the water-rich zone 2 within Regime3 conditions.
Supporting videos
Video S1: Bright-field imagery of boundary displacement at Regime 1 (50% 1-octanol bymass in Solution A) condition. Video shows boundary undulation and microdomain forma-tion.Video S2: Bright-field imagery of boundary displacement at Regime 2 (40% 1-octanol bymass in Solution A) condition. Video shows boundary undulation and stagnant droplets leftbehind by the boundary.Video S3: Boundary displacement at Regime 3 (30% 1-octanol by mass in Solution A)condition. Video from 0 to 8 seconds shows the fluorescence imagery of the three-zoneconfiguration at the boundary. From 8 to 20 seconds the fluorescence mode was changed tobright-field imaging.Video S4: Boundary displacement at Regime 4 (10% 1-octanol by mass in Solution A)condition. Video showing the transition from a triangular protrusion in the boundary to aline shaped protrusion. From 0 to 5 the video was in fluorescence mode, and from 5 to 25 itwas in bright-field mode. S-5 eferences (S1) Weidlich, U.; Gmehling, J. A modified UNIFAC model. 1. Prediction of VLE, hE, and.gamma.. infin.
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