A model provides insight into electric field-induced rupture mechanism of water-in-toluene emulsion films
Desislava Dimova, Stoyan Pisov, Nikolay Panchev, Miroslava Nedyalkova, Sergio Madurga, Ana Proykova
aa r X i v : . [ phy s i c s . c h e m - ph ] J a n A model provides insight into electric field-inducedrupture mechanism of water-in-toluene emulsionfilms
Desislava Dimova, † Stoyan Pisov, ∗ , † Nikolay Panchev, ∗ , ‡ Miroslava Nedyalkova, ¶ Sergio Madurga, ∗ , § and Ana Proykova ∗ , † Department of Atomic Physics, University of Sofia, Institute of Physical Chemistry, Departmentof General and Inorganic Chemistry, University of Sofia, and Material Science and PhysicalChemistry Department and IQTCUB
E-mail: [email protected]fia.bg; [email protected]; [email protected];[email protected]fia.bg ∗ To whom correspondence should be addressed † University of Sofia ‡ Bulgarian Academy of Sciences ¶ University of Sofia § University of Barcelona bstract This paper presents the first MD simulations of a model, which we have designed forunderstanding the development of electro-induced instability of a thin toluene emulsion filmin contact with saline aqueous phase. This study demonstrates the charge accumulation rolein toluene film rupture when a DC electric field is applied. The critical value of the externalfield at which film ruptures, thin film charge distribution, capacitance, number densities andfilm structure have been obtained in simulating the system within
NV T and
NPT ensembles.A mechanism of thin film rupture driven by the electric discharge is suggested.We show that
NPT ensemble with a constant surface tension is a better choice for further modeling of thesystems that resemble more close the real films. ntroduction Water-in-oil emulsions are commonly formed during petroleum production and pose serious threatsto installations and quality of the final product. The electrical phase separation has been used inthe petroleum industry for separating water-in-crude oil dispersion’s by applying a high electricfield onto the flowing emulsion to affect flocculate and coalescence of dispersed water droplets.
It has been realized that the emulsion is stabilized by a thin film formed between two drops whenapproaching each other. Thus demulsification requires rupturing of this thin liquid film. Generally,the main purpose of an applied electrical field is to promote contact between the drops and to helpin drop–drop coalescence. Pulsed DC (direct current) and AC (alternative current) electric fieldsare preferred over constant DC fields for efficient coalescence. Recent studies have helped to clar-ify important aspects of the process such as partial coalescence and drop–drop non-coalescencebut key phenomena such as thin film breakup and chain formation are still unclear. Despite ofthe tremendous practical importance of enhanced coalescence, the mechanism of separation is notfully understood beyond the perception that the electrical force facilitates the coalescence be-tween small drops.To help in understanding the inherent processes, computational models were designed to simulatecoalescense of droplets under realistic experimental conditions. Molecular dynamics (MD) methodis an useful tool for the purpose. Koplik and Banavar did a pioneer work in modeling the coa-lescence of two Lennard-Jones liquid droplets in a second immiscible fluid using MD simulations.The authors found that coalescence of liquid droplets was completely driven by van der Waals andelectrostatic interactions when the velocities of the droplets were small. The coalescence beganwhen the molecules on the boundary of one droplet thermally drifted to the range of attraction ofthe other droplet and formed a string to attract both sides of the molecules.Zhao et al. reported a MD study of the coalescence of two nanometer-sized water droplets inn-heptane, a system that is commonly encountered in the oil sands industry. Similarly, the coa-lescence process was initiated by the molecules at the edge of the clusters, which interacted witheach other and formed a bridge between two clusters. Eventually, these molecules attracted and3ulled out other molecules from their own respective cluster to interact with those from the othercluster. Authors made an important conclusion that the coalescence in n-heptane would occurredonly if the two droplets were very close to each other ( ∼ . nm ). If they were far apart (e.g., 1 nm ),external driving forces should be applied.However, experimental results for electrical properties and electric field-induced rupture ofsingle thin films are scarce, which limits the comparison with computations to several measurablequantities - pore formation, and the critical voltage for film rupture.Anklam et al. experimentally demonstrated that the electric-filed induced pore formation was thereason for break-up of emulsion films. Panchev et al. developed a method allowing simultane-ous investigation of a single water-in-oil emulsion film by both microinterferometry and electricalmeasurements. This method allows in a single experiment to measure the critical voltage of filmrupture, the film thickness, the drainage rate, and the disjoining pressure laying the groundworkfor computational studies.In this paper we present computational results for pore formation and film rupture obtainedwith a model, which we have designed to imitate the rupture of the film under a step-wise increaseof the electric field as it has been applied in the experiment. The film is immersed in a sodiumchloride solution. In the model and also in the experiment, the electric field is applied perpendicu-larly to the film, which separates two water droplets.The model of the thin film developed for the present study can be considered as a useful startingbasis for a further study of the stability and the structure of thick emulsion films that are stabilizedby indigenous crude oil surfactants, namely asphaltenes, resins and naphthenic acids. It is worthmentioning that so far there is almost complete lack of understanding of the intimate structuraldetails of the crude petroleum-like films. Therefore, current industrial practice of utilization ofchemical additives in combination with electric field applications has for long time been widelyviewed as a “work of art”. 4 he model and simulation procedure
To accurately simulate the interfacial phenomena, we have applied the classical MD method forthe case of two canonical ensembles -
NV T and
NPT . The choice of ensembles in MD simula-tions of finite-size systems has already been shown to play an important role in coexisting phases. MD Simulations provide detailed information on the molecular structure of the interface when theintermolecular potential is available.
The model system is a 5 nm thick toluene film located perpendicularly to the z -axis of thesimulation box. The size of the box 24 . × . × . nm ensures that no artifacts will appearwhen 3 D periodic boundary conditions are implemented to diminish finite-size effects. The boxcontains also water molecules and Na + and Cl − ions at a concentration of 1 M . The force fieldparameters of the ions Na + and Cl − included in the model are taken from Gromos96 . Parametersfor toluene molecules are derived from benzyl side chain of phenylalanine molecule. Three-site
SPC (simple point charge) water model is used. Large-scale molecular dynamics simulations of the model system are performed with the helpof the
GROMACS package, designed to simulate the Newtonian equations of motion for systemswith hundreds to millions of particles. The simulations are performed in canonical
NV T and
NPT ensembles which keep the total number of atoms constant; the temperature is T = K . Inthe NV T ensemble the constant volume equals to the size of the simulation box, 24 . × . × . nm . In the case of the NPT ensemble the system is equilibrated at the constant pressureof 1 bar . After the equilibration, the simulation is performed at a constant surface tension g = . mN / m between toluene and water. In preliminary MD runs the simulation time of 5 ns was determined to be sufficient for thermodynamic equilibration of the total energy, pressure, andtemperature of the model system.An external electric field is applied in the z direction of the simulation box. In the NV T ensemblethe electric field strength is changed from 0 to 120 mV / nm in steps of 20 mV / nm , while in the NPT ensemble the strength is changed from 0 to 75 mV / nm in steps of 25 mV / nm .5 esults and discussion NV T simulation - build-up of interfacial charge
The interaction between the toluene film and the surrounding water molecules and ions resultsin a dynamic charge distribution. The Figure 1 illustrates the ion (sodium and chlorine) chargedensity distribution in the z -direction. The distribution is computed within the last 2 . ns of therun (total run time 5 ns ). The three curves correspond to 0, 60 and 100 mV / nm strengths of theexternal electric field. At 0 mV / nm (red curve), which calibrates the results, the charge fluctuatesaround zero at the film interfaces. A non-zero external field induces charge accumulation at filminterfaces. The accumulated charge is drawn as peaks in the charge distribution. The curves for60 mV / nm (green) and 100 mV / nm (blue) electric field strengths show that the accumulated chargeincreases with the field increase: one interface of the toluene film is charged positively due to Na + accumulation, while the other interface is charged negatively due to Cl − ion accumulation. Thus,the emulsion film, subjugated to the external electric field, resembles charging of a parallel-platecapacitor. At all applied fields the ion charge fluctuates around zero away from the film.Averaging over time was performed over the last 2.5 ns of the production run. An externalelectric field with strengths up to 100 mV / nm does not rupture the toluene film for the durationof the NV T simulation - 5 ns . It should be noted that the charge distribution NV T obtained at the120 mV / nm field within time intervals less than 500 ps shown in the Figure 2a feature on averagethe same patterns as the distribution computed 100 mV / nm field shown with a blue line in theFigure 1.Electric discharge is initiated after the pore formation as it is seen in the Figure 2d. After 2 ns , theaccumulated interfacial charge is drained - no peaks in the charge distribution of the ruptured film. NV T simulation - film rupture mechanism
When the electric field is set to 120 mV / nm a pore is formed in the film after 500 ps . It is observedthat the pore expands along the simulation box over time. The time evolution of the pore formation6 C h a r g e d e n s i t y [ q n m - ] z [nm] 0 mV/nm60 mV/nm100 mV/nm Figure 1: Calculated free ion charge distribution in the z -direction demonstrates the build up ofinterfacial charge with the applied field increase - 0, 60 and 100 mV / nm is shown in Figure 3 for the time between 500 ps and 2000 ps . The pore is seen as a light spot inFigure 3a at 500 ps . When the pore is wide enough water molecules fill in the pore area, seen as abluish background in the Figure 3b at 700 ps . By observing the pore evolution in the toluene film,the time of the complete film rupture (formation of toluene drop) can be determined.Inspection of the thickness profile at 120 mV / nm reveals existence of a dimple inside the toluenefilm (Figure 4a) prior to the film rupture.The role of the non-homogeneity has been widely reportedin thin liquid film literature since 1941. Our simulations demonstrate that a non-homogeneous film ruptures at its thinnest place be-cause the electric field strength is the highest there. In other words, the biconcave region of thefilm interface is subjected to a higher–than–average electrostatic pressure and therefore is a pre-ferred site for the film rupture and nano–pore formation.7 C h a r g e d e n s i t y [ q n m - ] z [nm]120 mV/nm0-0.5 ns (a) Free ions charge distribution at 120 mV / nm between 0 − . ns -0.04-0.020.000.020.04 0 5 10 15 20 C h a r g e d e n s i t y [ q n m - ] z [nm]120 mV/nm0.5-1 ns (b) Free ions charge distribution at 120 mV / nm between 0 . − ns -0.04-0.020.000.020.04 0 5 10 15 20 C h a r g e d e n s i t y [ q n m - ] z [nm]120 mV/nm1-2 ns (c) Free ions charge distribution at 120 mV / nm between 1 − ns -0.04-0.020.000.020.04 0 5 10 15 20 C h a r g e d e n s i t y [ q n m - ] z [nm]120 mV/nm2-5 ns (d) Free ions charge distribution at 120 mV / nm between 2 − ns Figure 2: Free ions charge distribution at 120 mV / nm NV T simulation - the film structure
The charge density of free ions, water, and toluene molecules in the z -direction can be observedin the Figure 5. The figure illustrates the structure of the toluene film surrounded by aqueouselectrolyte solution at 0, 60, 100 and 120 mV / nm electric field strengths. For the latter case thedensity was averaged over the first 0 . ns of simulation, i.e. before the startup of the rupturingprocess. The part of the film that contains only toluene molecules is called toluene core , bulk waterphase is that part of the film, where the density of water molecules is maximal.The core thickness was estimated using a double–sigmoid function (Equation ?? ) at 99% of theplateau height h , where x , x being the left and the right half-height respectively, a is the steepness8 a) 500 ps (b) 700 ps (c) 1500 ps (d) 2000 ps Figure 3: Top view snapshot of time evolution of film area at applied external electric field of120 mV / nm of the sigmoid: f ( x ; x , x , a , h ) = h (cid:18) − + exp − a ( x − x ) (cid:19) + exp − a ( x − x ) (1)At no applied field, Figure 5a there exists a pure toluene core of 2 . nm thickness, which issurrounded by two interfacial layers formed by mixing toluene and water interfacial layers. In thetoluene interfacial layer, the concentration of toluene molecules decreases in the direction from thepure toluene core towards the bulk water phases, eventually reaching zero concentration. Respec-tively, in the aqueous interfacial layer, the concentration of water molecules decreases towards the9 a) 100 ps (b) 500 ps (c) 2000 ps Figure 4: Side view snapshots for the 120 mV / nm external electric field applied perpendicularlyto the toluene film: (a) the film profile after 100 ps ; (b) startup of rupturing of the thinnest part ofthe film - between 400 ps and 500 ps ; (c) breakdown of the film and formation of a toluene drop atabout 2000 ps .toluene core. Toluene–water mixed layer is 1 . nm thick, which is estimated as the distance wherethe toluene density in z -direction drops from 99 % to 1 % from the plateau height h . The bulkaqueous phases contain Na + and Cl − ions. The density profiles show that ions penetrate the mixedinterfacial layers that border the toluene core. Thicknesses of the film core and the interfacial layerare shown in the Table 1.Table 1: Film thickness at different strength of the applied electric field in NVT ensembleapplied field 0 mV / nm mV / nm mV / nm mV / nm toluene core [nm] 2 . . . . . . . . . . . . mV / nm field leads to build-up of accumulatedpositive charges on one side of the toluene film and negative charges on the other side. The peaksof accumulated charges are situated at the boundary between bulk water and interfacial aqueouslayer. In the direction towards toluene core, the concentration of ions decreases and reaches zeroat the toluene core. Ions penetrate only the mixed interfacial region, which is due to the formation10f hydration shells. The Figure 5c reveals that field increase up to 100 mV / nm is followed byaccumulation of more charges, bringing enough attractive force that leads to thinning of the puretoluene core by 0 . nm down to 2 . nm , while the thickness of the interfacial layers of tolueneand water increases by 0 . nm . A possible hypothesis is that the increased electrical compressionreshapes the film topography making it a high amplitude rugged surface and the interfacial layerbecomes thicker. The Figure 5d depicts the film structure (profile) at 120 mV / nm and data areaveraged over the time interval of 500 ps . This is the moment (500 ps ) just before the rupturingprocess takes place. -0.04-0.03-0.02-0.010.000.010.020.030.04 6 8 10 12 14 16 18 20 0 20 40 60 80100120 C h a r g e d e n s i t y [ q n m - ] D e n s i t y [ n m - ] z [nm]0 mV/nm Charge density free ionsToluene densityWater density (a) Density distribution at external electric field0 mV / nm -0.04-0.03-0.02-0.010.000.010.020.030.04 6 8 10 12 14 16 18 20 0 20 40 60 80100120 C h a r g e d e n s i t y [ q n m - ] D e n s i t y [ n m - ] z [nm]60 mV/nm Charge density free ionsToluene densityWater density (b) Density distribution at external electric field60 mV / nm -0.04-0.03-0.02-0.010.000.010.020.030.04 6 8 10 12 14 16 18 20 0 20 40 60 80100120 C h a r g e d e n s i t y [ q n m - ] D e n s i t y [ n m - ] z [nm]100 mV/nm Charge density free ionsToluene densityWater density (c) Density distribution at external electric field100 mV / nm -0.04-0.03-0.02-0.010.000.010.020.030.04 6 8 10 12 14 16 18 20 0 20 40 60 80100120 C h a r g e d e n s i t y [ q n m - ] D e n s i t y [ n m - ] z [nm]120 mV/nm Charge density free ionsToluene densityWater density (d) Density distribution at external electric field120 mV / nm Figure 5: Density distribution of free ions (red), toluene (green) and water molecules (blue) atdifferent external electric fields in NVT ensembleThe increase of potential from 100 to 120 mV / nm leads to additional thinning of the toluenecore down to 1 . nm . The thickness of interfacial layers of toluene and water increases by 0 . nm .11 PT simulation - the film structure In this section, the results from
NPT canonical ensemble simulation are presented. The chargebuild–up is plotted in the Figure 6. The Figure 7 depicts the charge build-up at 0, 25 mV / nm , and50 mV / nm . As in the NVT case, at zero external field no peak formation is observed on both sidesof ionic line that exhibits zero-charge density. At 25 mV / nm such formation already takes placeand becomes much pronounced at 50 and 75 mV / nm (Figure 7c). Film rupture occurs at a muchlower electric field strength (75 mV / nm ) compared to the NVT simulation (120 mV / nm ). Filmrupture occurs at a much lower electric field strength (75 mV / nm ) compared to the NVT simulation(120 mV / nm ). The information regarding the thickness of the toluene core, boundary layers andthe total film are summarized in Table 2. The thickness of different layers were again determinedby using the double–sigmoid formula in Equation ?? . At no applied field, the toluene core hasthe same thickness as in the NVT case. However, the difference between the two simulations isrevealed in the size of the mixed boundary zone, being larger for the NPT ensemble. Increase ofthe electric field, as in the NVT case, again leads to the thinning of the toluene core and to theexpansion of the boundary layers. However, at 50 mV / nm (NPT) there is a bit higher thinningof the core, compared to 60 mV / nm (NVT), despite of the lower applied field. This observation,together with the obtained lower critical field could suggest enhanced development of instabilityin the NPT simulation. It should be noted that in both simulations at the critical field the core hasthe same thickness instants before the film rupture. Moreover, at that critical field the thickness ofthe boundary layers and of the total layer are almost identical in both NV T and
NPT ensembles.Table 2: Film thickness at different strength of the applied electric field in NPT ensembleapplied field 0 mV / nm mV / nm mV / nm toluene core [nm] 2 . . . . . . . . . C h a r g e d e n s i t y [ q n m - ] z [nm] 0 mV/nm25 mV/nm50 mV/nm Figure 6: Calculated charge of free ions density in z -direction for three different external appliedelectric fields 0, 25 and 50 mV / nm in case of NPT ensemble with constant surface tension. -0.03-0.02-0.010.000.010.020.03 6 8 10 12 14 16 18 20 0 20 40 60 80100120 C h a r g e d e n s i t y [ q n m - ] D e n s i t y [ n m - ] z [nm]0 mV/nmCharge density free ionsToluene densityWater density (a) Density distribution at externalelectric field 0 mV / nm -0.03-0.02-0.010.000.010.020.03 6 8 10 12 14 16 18 20 0 20 40 60 80100120 C h a r g e d e n s i t y [ q n m - ] D e n s i t y [ n m - ] z [nm]50 mV/nmCharge density free ionsToluene densityWater density (b) Density distribution at externalelectric field 50 mV / nm -0.03-0.02-0.010.000.010.020.03 6 8 10 12 14 16 18 20 0 20 40 60 80100120 C h a r g e d e n s i t y [ q n m - ] D e n s i t y [ n m - ] z [nm]75 mV/nmCharge density free ionsToluene densityWater density (c) Density distribution at externalelectric field 75 mV / nm Figure 7: Density distribution of free ions (red), toluene (green) and water molecules (blue) atdifferent external electric fields in NPT ensemble.13 onclusions
The results of MD simulations and their analysis offer insight into the intimate structure of the film,namely the presence of a toluene core, neighboring a mixed boundary zone that contains altogethertoluene and water molecules. Application of external DC electric field leads to redistribution ofelectrical charges and to the accumulation of oppositely charged ions ( Na + and Cl − ) on both sidesof the film. Thus, the behavior of the system resembles a liquid capacitor, which charge increaseswith the rise of the external potential. In both NV T and
NPT ensembles, condenser plates , wherethe charge density is maximal, are situated at the very border between the bulk aqueous (water)phase and the mixed layer. No ion penetration is observed within the toluene core, thus leaving allthe distribution of charges within the mixed zone and the bulk phase that could be attributed to theformation of hydration shells. When critical electric field is reached, within a certain time after thefield application electric discharge occurs, indicating the beginning of the rupturing process. Visualsnapshots of the evolution of the film area confirm the formation of a hole within the thinnest partof the initially non–homogeneously thin film.Results clearly show that in
NPT simulations the critical instability is developed at much lowerfields (75 mV / nm ) than in NVT simulations (120 mV / nm ). First experimental investigation onelectro-induced rupture of real toluene-diluted bitumen emulsion films shows that critical fieldsrange between 4 and 11 mV / nm , depending on the bitumen concentration. Thus, NPT simulationwith a constant surface tension appears to be a better choice for further modeling of the systemsthat resemble more close the real films. In the
NPT ensemble we can expect that even lower valuesof the external electric field could rupture the toluene film if we prolong the simulation time. Thecompressive action of the built–up charges on both sides of the film is illustrated in the decreaseof the thickness of the toluene core with the electric field. The behavior of the system resembles acapacitor with increasing charge with an increase of the external potential. However, in both typeof simulations (
NV T and
NPT ), the width of the mixed zone and hence of the total film increaseswith the field increase. Moreover, the clarification of the detailed mechanism of the hole formation(wave–like or pore–like) and the role of thickness fluctuations on the rupturing process could be14rogressed through undertaking an extensive “subbox” thickness investigation, when the entiresimulation box is divided into boxes along the xy–plane, as each one of them being analyzed.In conclusion, we may argue that the model, we have developed for thin films, provides aground for implementing a further complication of the investigated system, introducing surfaceactive molecules, as well as a verification of our expectances for a decrease of the critical electricfield when longer simulations are performed. 15 cknowledgements
S.Pisov and D. Dimova acknowledge the access to the HPC cluster in Sofia Tech Park, used forthe heavy computations. S. Madurga acknowledges financial support from the Generalitat deCatalunya (grant 2014-SGR-1251). The support of H2020 program of the European Union (projectMaterials Networking) is gratefully acknowledged by S. Madurga and M. Nedyalkova.16 eferences (1) Gardner, C. F.; Buckner, S. J.(2) Eow, J. S.; Ghadiri, M.
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