Structure, Thermodynamics, and Dynamics of Thin Brine Films inOil−Brine−Rock SystemsChao Fang,† Shuyu Sun,‡ and Rui Qiao*,†

†Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24061, United States‡Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, SaudiArabia

*S Supporting Information

ABSTRACT: Thin brine films are ubiquitous in oil−brine−rock systems suchas oil reservoirs and play a crucial role in applications such as enhanced oilrecovery. We report the results of molecular simulations of brine films that areconfined between model oil (n-decane) and rock (neutral or negatively chargedquartz slabs), with a focus on their structure, electrical double layers (EDLs),disjoining pressure, and dynamics. As brine films are squeezed to ∼0.7 nm (∼3water molecule layers), the structures of the water−rock and water−oilinterfaces change only marginally, except that the oil surface above the brine filmbecomes less diffuse. As the film is thinned from ∼1.0 to ∼0.7 nm, ions areenriched (depleted) near the rock (oil) surface, especially at a bath ionconcentration of 0.1 M. These changes are caused primarily by the reduceddielectric screening of water and the weakened ion hydration near water−oilinterfaces and, to a smaller extent, by the increased confinement. When the brine film is ∼1.0 nm thick, hydration and EDLforces contribute to the disjoining pressure between the charged rock and the oil. The EDL forces are reduced substantially asthe ion concentration increases from 0.1 to 1.0 M, and the magnitude of the reduction is close to that predicted by thePoisson−Boltzmann equation. When the brine film is thinned from ∼1.0 to ∼0.7 nm, the disjoining pressure increases by ∼10MPa, which is mostly due to an increase in the hydration forces. The first layer of water on the rock surface is nearly stagnant,even in 0.74 nm-thick brine films, whereas the viscosity of water beyond the first layer is bulk-like, and the slip coefficient of oil−water interfaces is close to that under unconfined conditions. The insights that are obtained here help lay a foundation for therational application of technologies such as low-salinity waterflooding.

1. INTRODUCTION

Thin liquid films that are confined between surfaces areubiquitous in nature and engineering systems, for example, incolloids, foams, nanofluidic chips, desalination membranes thatare based on layered materials, and porous electrodes ofsupercapacitors.1−4 The diverse chemistry of the confiningsurfaces and liquids, together with the confinement that isimposed by surfaces, endows thin liquid films with richstructures at molecular and mesoscopic scales. For example,water forms distinct layers with enhanced density near rigid,hydrophilic surfaces but depletion layers with reduced densitynear soft, hydrophobic surfaces.5−8 When the confiningsurfaces carry net charges, an electrical double layer (EDL)emerges in the liquid film, and the EDL’s structure dependsstrongly on the characteristics of the liquid (e.g., solvent-freeionic liquids vs dilute aqueous solutions), the concentration ofbulk ions, and the thicknesses of the films among other factors.Thin liquid films often exhibit dynamic properties that differfrom those of bulk liquids and fascinating thermodynamics.The latter can manifest as the surface forces they mediate, thephase behaviors they display, and the charges they store.Liquid films can mediate a host of surface forces with vastlydifferent ranges and strengths, for example, the steric force,

hydration force, hydrophobic force, double-layer force, and vander Waals force. The structure, dynamics, and thermodynamicsof thin liquid films play an essential role in numerousproblems, for example, the stability of colloids and foams,boundary lubrication, and throughput of desalination bygraphene-derived membranes to name just a few.9−13 Assuch, thin liquid films have been studied extensively viaexperimental, theoretical, and simulation approaches.10,14,15

In petroleum reservoirs, which are essentially oil−brine−rock (OBR) systems, thin brine films are often found betweenrocks and oil droplets.16,17 The thicknesses of these filmsdepend on the characteristics of the rock surfaces, the brinecomposition, and the properties of the oil droplets and canrange from a few angstroms to tens of nanometers.18,19 Forexample, using small-angle neutron scattering, it wasdemonstrated that water films with a thickness of ∼0.8 to1.3 nm exist on the surfaces of silica particles that are dispersedin heptane using anionic surfactants.19 Despite their smallthickness, brine films can play a fundamental role in oil

Received: May 17, 2019Revised: July 18, 2019Published: July 21, 2019

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pubs.acs.org/LangmuirCite This: Langmuir 2019, 35, 10341−10353

© 2019 American Chemical Society 10341 DOI: 10.1021/acs.langmuir.9b01477Langmuir 2019, 35, 10341−10353

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recovery from reservoirs. For example, the contact angle of oildroplets on rock surfaces, which is a primary factor thatgoverns the recovery of oil,20 depends strongly on thedisjoining pressure in these films.17,21 Indeed, some enhancedoil recovery (EOR) techniques are posited to function via themodification of thin brine films in OBR systems. For example,in low-salinity waterflooding (LSW), water with low saltconcentration is injected into reservoirs, and notable successhas been reported in many field studies.22−27 While multiplemechanisms are likely responsible for EOR, an emergingconsensus is that the expansion of EDLs in the brine films thatis caused by the decrease of brine’s ion concentration and theensuing increase of the EDL disjoining pressure in the filmsplay a key role by making the rock surface more water-wet.16,21

In addition to their structure and disjoining pressure, whichaffect the thermodynamics of EOR, the dynamics of brine filmsis expected to play a key role in determining the kinetics ofLSW.28,29

Insights into the structure, thermodynamics, and dynamicsof brine films in OBR systems may facilitate the improvementof existing EOR techniques and/or the formulation of newEOR concepts. While such insights may be derived from priorworks on thin liquid films in other systems, the uniqueproperties of OBR systems can render this approach difficult.For example, the brine films in some OBR systems can havesubnanometer thickness.19 These brine films exhibit twointeresting features: First, these brine films are confined by asolid rock with a rigid surface and an oil phase with a soft,diffusive surface. Second, the thickness of these brine films iscomparable to key intrinsic length scales of the brine solution,brine−rock interfaces, and brine−oil interfaces (e.g., the Debyelength of brine, the hydration diameter of the ions in brine, thecharacteristic length of the density oscillation of watermolecules near rock surfaces, and the width of diffuse brine−oil interfaces). The combination of these features renders thesebrine films highly unique; thus, it is difficult to extrapolate theinsights that are obtained in the studies of other thin liquidfilms to them.In principle, molecular dynamics (MD) simulations in which

the thin brine film, oil, and rock are resolved with atomisticresolution can be used to gain insights into the molecularlythin brine films in OBR systems. Indeed, molecular simulationsof OBR systems have been reported, and insights such aseffects of salinity on the wettability of oil on the rock surfacehave been obtained.30−36 However, the brine films in thesestudies, if they exist, are often bound by oil droplets or poreswith a width of several nanometers. With this type of setup, thebrine films typically extend by less than 2 nm laterally, andtheir thickness varies substantially in the lateral direction.Consequently, these studies do not address the scenario ofextended brine films that is encountered in practice. Manyquestions on the structure, thermodynamics, and dynamics ofextended brine films that are found in practical OBR systemsremain open. For example, what are the molecular structures ofthe rock−brine and brine−oil interfaces in these films, andhow do these interfaces evolve as the brine film approachesmolecular thickness? How are ions distributed in the EDLs inthe brine film, and how does the ion distribution respond tochanges in the bulk ion concentration and film thickness?What is the disjoining pressure inside these films? What is therelative contribution of the hydration and EDL forces to thetotal disjoining pressure? How do these forces change with thefilm thickness and bulk ion concentration?

In this work, we conduct extensive MD simulations to studyextended brine films that are sandwiched between rocksurfaces and thick slabs of oil. Our overarching objective isto clarify the structure, thermodynamic properties, andhydrodynamic properties of thin brine films that are relativelyideal but still relevant to practical OBR systems. In terms ofstructure, we seek to identify the molecular structures of therock−brine and brine−oil interfaces in these films and theirevolutions as the brine films approach molecular thickness. Wealso investigate the ion distribution in the EDLs in the brinefilms and their response to changes in the bulk ionconcentration and film thickness. In terms of thermodynamicproperties, we seek to determine the disjoining pressure inmolecularly thin brine films and to investigate the relativecontributions of the hydration and EDL forces to the totaldisjoining pressure. We also seek to quantify the effectivedielectric properties of the brine films and how they change asthe film thickness is reduced. In terms of hydrodynamicproperties, we seek to quantify the effective viscosity of brinefilms and the possible slip at brine−oil interfaces. Theremainder of the manuscript is organized as follows: InSection 2, the molecular systems and simulation methods arepresented. In Section 3, the structure of brine films and thedisjoining pressure in them are quantified at several filmthicknesses and brine concentrations, and the mechanisms thatunderlie the observed results are discussed. The hydrodynamicproperties of the brine films are also presented. Finally, theconclusions of this work are presented in Section 4.

2. MATERIALS AND METHODSThe molecular modeling of OBR systems is complicated by thediverse composition of oil, brine, and rock in oil reservoirs: the rockscan be sandstone or carbonate;16 the brine can contain a variety ofions, for example, Na+, Cl−, Ca2+, and Mg2+; and the oil is a mixture ofmany hydrocarbons, basic and acidic groups (e.g., naphthenic acids),and impurities. Since the molecular study of the OBR system is highlylimited at present, we focus on a simplified description of OBR here.Quartz slabs are used as the model rock because quartz is a keycomponent of sandstone. Aqueous NaCl solution is used as the brine,and pure n-decane is used as the oil. The surfaces of the quartz slabsthat face brine and oil are negatively charged in most simulations tobe consistent with experimental data at typical pH although neutralsurfaces are also considered as a reference (see below). The oil−brineinterface is neutral, which corresponds to the limit of very low densityof electroactive species at the water−oil interfaces.37

2.1. Simulation Systems. Three types of systems have beensimulated: The first type of system, namely, the “thin brine film”system, is used to study molecularly thin brine films that are confinedbetween rock and oil surfaces. As shown in Figure 1a, this type ofsystem consists of a quartz slab, an oil reservoir, a brine reservoir andbrine film, and two rigid pistons that bound the oil and brinereservoirs. The quartz slab is ∼3 nm thick. Its surface that faces thebrine film and oil has a surface charge density of −0.12 C/m2. A brinefilm is formed between the upper rock surface and the oil phase, and itis connected with the brine reservoir. Its thickness ranges from 0.7 to1.0 nm, which is within the range of brine film thicknesses that wasidentified via neutron scattering.16,19 To maintain a bulk-like behaviorat positions that are away from the rock surface, the initial brine andoil reservoirs measure ∼5 and ∼4 nm, respectively, in the z direction.The top piston is used to control the thickness of the brine film (seebelow); the bottom piston is used to prevent water molecules fromevaporating, and it can move freely in the z direction. The system isperiodic in all directions; however, two large vacuum spaces areplaced outside the pistons to effectively interrupt the periodicity in thez direction. The simulation box measures 14.00 × 3.93 × 18.00 nm3

in the x, y, and z directions, respectively.

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In addition to the setup in Figure 1a, thin brine film systemswithout an explicit brine reservoir (see Figure 1b) are also studied.After the system that is shown in Figure 1a reaches an equilibrium, itsmiddle portion (delineated using a red dashed box) is extracted tobuild the system that is shown in Figure 1b. The chemical potential ofthe brine film in the new system is the same as that in the originalsystem, which features an explicit brine reservoir; however, thedimension (and thus the computational cost) of the new system issmaller. Systems that are set up this way are used to study thehydrodynamic properties of thin brine films.The second type of system, namely, the “thin water film” system, is

similar to the thin brine film system except that the quartz surface isneutral and there are no ions in the system. This type of system isused to study the hydration force in thin water films in the absence ofany surface charge or salinity effects. The third type of system is the“reference” system. In this type of system, a thick brine slab (∼4 nmthick) is sandwiched between a thick oil slab (∼4 nm thick) and thequartz slab (see Figure 1c). Because bulk-like behavior occurs for thewater and oil away from the rock−brine and brine−oil interfaces, therock−brine and brine−oil interfaces do not affect each othersubstantially. Therefore, this type of system enables us to study thebrine/EDLs near isolated rock surfaces and unconfined oil−brine

interfaces, which are useful references for investigating the behavior ofthin brine films.

For the first type of OBR systems, four systems with two brine filmthicknesses and two brine concentrations are studied; for the secondtype, two systems with two brine film thicknesses are studied; and forthe third type, two systems with bulk ion concentrations of 0.1 and 1M are studied. The brine film thickness, brine reservoir ionconcentration, and other parameters of the three types of systemsare summarized in Table 1.

2.2. Molecular Models.Water is described using the rigid SPC/Emodel.38 n-Decane is modeled using the optimized parameter set ofthe original OPLS-AA force fields for hydrocarbons.39 The force fieldparameters for Na+ and Cl− ions are obtained from ref 40. The rock iscomposed of α-quartz. The quartz slab that is shown in Figure 1ameasures ∼11 and 3.93 nm in the x and y directions, respectively. Itsupper and lower surfaces are cleaved from the (101) plane byfollowing the recent study of the quartz−water interface,41 therebyyielding a surface silanol group density of 5.92 nm−2. This silanolgroup surface density leads to a strongly hydrophilic surface, assuggested by previous work,42,43 which facilitates the formation of abrine film on the quartz surface in OBR systems.43−45 Following priorwork,41 the zero plane of the quartz slab is defined as the z position ofthe second-outermost layer of surface silicon atoms (see Figure S1 inthe Supporting Information). The outermost silanol groups of thequartz surface that faces the oil phase are selectively deprotonated viathe method in ref 41 to produce a net surface charge density of −0.12C/m2. The force field parameters of the quartz thus prepared, whichinclude the Lennard-Jones (LJ) parameters and partial charges, areobtained from the CLAYFF force fields.41,46 To reduce thecomputational cost, the silicon and oxygen atoms of the quartz slabare fixed, and their nonelectrostatic interactions with each other areexcluded. The hydrogen atoms of the surface silanol groups areallowed to move by considering their bonded interactions with otheratoms in the quartz slab. The LJ parameters for the interactionsbetween dissimilar atoms are obtained using the Lorentz−Berthelotcombination rule. The LJ potentials, partial charges, and bondedparameters of atoms in the systems that are studied here are listed inthe Supporting Information.

2.3. Simulation Methods and Protocol. All simulations areperformed using the Gromacs code (version 4.5.6).47 The bondlengths and angles of water molecules are constrained using theSETTLE algorithm. All simulations are conducted in the NVTensemble with a temperature of 350 K, which accords with typicalreservoir conditions.48,49 The temperature is maintained using thevelocity rescale thermostat50 with a time constant of 1 ps. A globalcutoff of 1.2 nm is used to compute the LJ potentials, and the particlemesh Ewald method with a slab correction to remove the periodicityin the z direction is used to calculate the electrostatic interactions.51

The first types of systems with explicit brine reservoirs (see Figure1a) are built and equilibrated in four stages: In the first stage, an ∼3nm-thick brine slab is initially enclosed between the quartz surfaceand the oil slab. The top piston is allowed to move in the z directionwithout applying any external force to it, and the system isequilibrated for 4 ns. In the second stage, a 20 MPa pressure isexerted on the top piston to push the oil and brine downward to forma thin brine film between the oil and the quartz surface. During thisstage, the thickness of the brine film in the middle portion of the

Figure 1. Molecular systems for studying oil−brine−rock (OBR)systems. (a) Snapshot of a model OBR system featuring a thin brinefilm, a brine reservoir, and a thick oil slab. The pressure in the brinereservoir and oil is regulated using two pistons. The black dashed boxshows the simulation box. The 5.5 nm-wide red box denotes theregion in which the statistics of brine films are taken. (b) Snapshot ofthe system for investigating the dynamic properties of the brine film.(c) Snapshot of a reference system for studying the isolated rock−brine and unconfined brine−oil interfaces. The brine film is ∼4 nmthick so that the brine−rock and brine−oil interfaces do not affecteach other. Water is shown as blue (oxygen) and white (hydrogen)spheres. Oil (n-decane) is shown as cyan (carbon) and white(hydrogen) spheres. Na+ and Cl− ions are shown as orange and greenspheres, respectively. The rock is made of α-quartz and shown using abar-and-stick model.

Table 1. Parameters of the Three Types of Systems

parameters thin brine film thin water film reference

system snapshots Figure 1a,b Figure 1cbrine (water) film thickness 0.7−1.0 nm 0.7−1.0 nm ∼4.0 nmoil slab thickness ∼4.0 nm ∼4.0 nm ∼4.0 nmsalt concentration 0.1 M, 1 M 0 0, 0.1, 1 Mquartz slab’s surface chargedensity

−0.12 C/m2 0 0, −0.12 C/m2

box length in x, y, z directions 14.00 × 3.93 × 18.00 nm3

5.50 × 3.93 × 10.00 nm314.00 × 3.93 × 18.00 nm3

5.50 × 3.93 × 10.00 nm35.50 × 3.93 × 13.00 nm3

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system is recorded. Once the film thickness has reached 0.9 or 0.7 nm,the piston is fixed in space. In the third stage, the system isequilibrated further with the piston fixed. The pressure on the toppiston and the numbers of ions and water molecules in the middleportion of the brine film (denoted by the red dashed box in Figure 1a)are monitored over time. Typically, the pressure and the numbers ofwater molecules and ions in the brine film reach their equilibriumvalues within 200−500 ns (see Figures S2 and S3 in the SupportingInformation). In the final stage, the system is simulated for another100 ns to gather statistics. The equilibrium thickness of brine filmsthat are built using this protocol is not prescribed a priori andtypically differs from the film thickness at the end of the second stage.Via trial and error, the thickness of the equilibrated film has beenadjusted to be within 0.02 nm of the target values.The first type of system without explicit brine reservoirs (see Figure

1b) is built based on the brine film composition that was obtained atthe end of the third stage. Once built, it is equilibrated for 50 nsfollowed by the shearing simulations that are described in Section 3.4.The second type of system is built and equilibrated via a similarapproach to the first type of system. The third type of system is builtby stacking thick oil and brine slabs and equilibrating the system for100 ns.

3. RESULTS AND DISCUSSION3.1. Structures of Interfacial Water and Oil. We begin

with the structures of the interfacial water and oil in thin brinefilms, with a focus on how these structures differ from thosenear unconfined water−oil interfaces and isolated water−rockinterfaces. The results that are presented below are based onsystems that feature brine reservoirs with an ion concentrationof 0.1 M. Similar interfacial oil and water structures areobserved for the 1 M brine concentration cases and are notshown.3.1.1. Water−Oil Interfaces. Figure 2 shows the water and

decane density profiles in/near two brine films. The thickness

of these brine films, which is denoted as h, is difficult to defineuniquely. Here, h is defined from the perspective that a brinefilm is confined between the quartz and oil surfaces. Becausewater molecules can access the space ∼0.22 nm above thequartz slab’s zero plane, the effective surface of the quartz slabcan be assigned to z = 0.22 nm (see Figure 2a). For decane,using the convention of assigning the positions of diffusiveinterfaces, its nominal surface is taken as the position where itsdensity is 50% of the bulk density. With the above definition,the thicknesses of the brine films that are shown in Figure 2a,bare determined to be 0.74 and 0.94 nm, respectively. The

Gibbs dividing surface can also be used to define the filmthickness; however, since the above choice of film thicknessdefinition is simple and widely used and our analysis andconclusion do not depend sensitively on the definition of thefilm thickness, the above definition of the film thickness isadopted throughout the text. The space below (above) thenominal decane surface is shaded in blue (green) to reflect thatthis space is occupied predominately by brine (oil).Figure 2a shows that when the brine film is 0.94 nm thick,

the density profiles of water and decane near the water−oilinterface are almost identical to those near unconfinedinterfaces. As the film is thinned to 0.74 nm, the densityprofile of water near the water−oil interface changes little;however, that of the oil becomes slightly sharper (see Figure2b). Hence, the oil surface that bounds a brine film becomessharper (more well-defined) when the film is thinned to ∼2 to3 layers of water molecules. Sharper oil surfaces are alsoobserved in brine films with a bulk ion concentration of 1 M(see Figure S4 in the Supporting Information).

3.1.2. Structure of Interfacial Oil. The sharpening of the oilsurface above thinner brine films occurs because as a brine filmbecomes thinner, the oil molecules above it maintain a similarconformation but assume a more parallel alignment withrespect to the brine−oil interfaces. To demonstrate this, we fiteach decane molecule into an ellipsoid and determine its threeprincipal axes Sk (k = 1, 2, 3) and radius of gyration Rg (see theinset in Figure 3c and the Supporting Information). The

orientation of the decane molecule at position z with respect tothe oil−brine interface is characterized by the order parameter

λ = ⟨ · − ⟩z zS n( ) 3( ( ) ) 1 /2zk k2

(1)

where ⟨ · ⟩ denotes the ensemble average and nz is the unitnormal vector of the oil−brine interface. λk = 1 (−0.5) ifdecane’s kth principal axis is normal (parallel) to the oil−brineinterface.Figure 3a,b shows the radius of gyration of the decane

molecules near brine−oil interfaces. We observe that Rg ofdecane molecules is maintained at 0.36 nm regardless of

Figure 2. Water−oil interface in brine films. (a, b) Density profiles ofwater and oil in brine films with thicknesses of (a) 0.94 and (b) 0.74nm. The water density is calculated based on its center-of-massposition, and the oil density is calculated from the number density ofcarbon atoms. The areas that are shaded in blue and green correspondto the water and oil phases, which are separated by a plane at whichthe decane density is half of its bulk value. The dashed lines representthe reference density profiles of interfacial water (in blue) and decane(in green) near unconfined brine−oil interfaces. The reference densityprofiles are placed such that the water−oil phase boundary meets.

Figure 3. Structure of oil near brine film−oil interfaces. (a, b) Densityand radius of gyration of decane near brine films with thicknesses of(a) 0.94 and (b) 0.74 nm. Similar profiles near unconfined brine−oilinterfaces are shown as black lines. (c, d) Orientation order parameterof the decane molecule’s three principal axes near brine films withthicknesses of (c) 0.94 and (d) 0.74 nm. Data for brine film−oilinterfaces are shown as symbols, whereas those for unconfined brine−oil interfaces are shown as solid lines of the same color. The inset in(c) shows the three principal axes of a decane molecule.

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whether it is in bulk oil or at any position across water−oilinterfaces; the latter has also been reported in prior work oninterfacial hydrocarbons with similar chain lengths.52 Theseresults demonstrate that the conformation of a decanemolecule that is in contact with the brine film changes littleas the film is thinned.Figure 3c,d shows the order parameters of the principal axes

of decane molecules near the brine−oil interfaces. As a decanemolecule approaches an unconfined brine−oil interface, itslongest axis becomes more parallel to the interface; hence, ittends to “lie” on the brine surface, similar to the phenomenonthat was reported for linear alkanes near isolated water−oilinterfaces.5 When the brine film is 0.94 nm thick, theorientation ordering of the decane molecules near this film isnearly identical to that near unconfined brine−oil interfaces.As the film is thinned to 0.74 nm, λ1 of the decane moleculesthat are in contact with the brine film decreases toward −0.5,while λ3 increases toward 0.5, thereby suggesting that theinterfacial decane molecules adopt a more parallel orientationwith respect to the brine surface. Because decane moleculesthat are in contact with the brine films are better aligned withthe brine surface, these molecules tend to occupy a narrowerspace in the z direction, thereby rendering the oil surfacesharper. The more parallel orientation of interfacial decaneabove the 0.74 nm-thick brine film can be explained as follows:Many decane molecules that are directly above the 0.94 nm-thick film are in contact with water with a density that is closeto that of bulk water (see Figure 2a); many decane moleculesabove the 0.74 nm-thick film are in contact with the secondwater peak near quartz surfaces, which are packed moredensely than bulk water (see Figure 2b). Because it is moredifficult to insert a decane molecule into more densely packedwater, more decane molecules will lie on the surface of the 0.74nm-thick brine film, thereby leading to a sharper oil surface.Furthermore, the more parallel orientation of the decanemolecules near the thinner (0.74 nm-thick) brine film can alsobe explained by the solvation effects: When a decane moleculeprotrudes into a brine film, its molecular contact area withwater increases and, as a result, a free energy cost is incurred.Near the thinner brine film, for the same increase of decanemolecule−water contact area, the free energy cost is higherbecause the water molecules that solvate the protruding decanemolecule are more densely packed originally (due to thelayering of these water molecules near the quartz surface).3.1.3. Water−Rock Interfaces. Figure 4a,b shows the water

density profiles near quartz surfaces that bound brine filmswith thicknesses of 0.94 and 0.74 nm, respectively. The densityprofile of water near an isolated quartz surface, which showstwo distinct water layers that are centered at z = 0.34 and 0.60nm, as observed in previous works,41 is also included in Figure4 as a reference. The water in the brine film can be divided intothree layers according to the two valleys that are positioned atz1 = 0.47 nm and z2 = 0.71 nm (first layer: z0 < z < z1; secondlayer: z1 < z < z2; and third layer: z > z2). The water density inthe third layer closely resembles that near the unconfined oil−water interfaces (see Figure 2a,b). As brine films are thinned to0.94 nm, the first two layers of water remain intact; only whenthe brine film is thinned to 0.74 nm does the second waterlayer become disturbed by the presence of water−oil interfacesnearby. The water−rock interface is hardly disturbed in thebrine film down to approximately three water layers, which is aconsequence of the strong interactions between water and thequartz surface: the first water layer interacts strongly with the

surface silanol groups, whereas the second water layer mainlyinteracts with the densely packed water in the first layer. Thesoft, hydrophobic surface of oil impacts only the layer of watermolecules that is in direct contact with it.The strong water−water/quartz interactions in the first two

water layers near the quartz can be observed from thehydrogen bonds that are formed by the water molecules inbrine films. Geometric criteria are used for hydrogen bonds:53

a hydrogen bond exists if Loo < 0.35 nm and ∠OOH ≤ 30°(Loo, the oxygen−oxygen distance; ∠OOH, the angle that isformed between one water molecule’s OH bond and theoxygen−oxygen vector that points from the donor to theacceptor). As shown in Figure 4c,d, the number of hydrogenbonds per water molecule, which is denoted as nHB, is smallerfor water in the first layer than in the bulk due to theirfavorable interactions with surface silanol groups. nHB is closeto the bulk value in the second water layer; hence, dominantwater−water interactions occur in this layer. Similar to thedensity profiles, the profiles of nHB near the rock surface andthe oil surface closely resemble those near the isolated quartzsurface and the unconfined oil−water interface, respectively. Asa side note, in both brine films, the orientations of their twolayers of water molecules can deviate from those near isolatedquartz surfaces (see Section 3.3).The above results demonstrate that in brine films that are as

narrow as 2−3 water layers, the packing of water moleculesand the coordination between them can be reasonablyapproximated by those near isolated rock−brine interfacesand unconfined oil−brine interfaces. This differs from thewater that is confined between two rigid surfaces where thestructure of water near one surface can be modifiedsubstantially when the two surfaces approach each otherclosely.54

3.2. Structure of Electrical Double Layers. In this part,we investigate the structure of EDLs in the thin brine filmswhen the quartz slab has a surface charge density of σ = −0.12C/m2. The ion concentration in the brine reservoir is 0.1 Munless otherwise specified. We focus on the evolution of theion distribution as the brine film thickness decreases and theunderlying mechanisms.

Figure 4. Water−rock interface in brine films. (a, b) Density profilesof water near an isolated quartz surface and across brine films withthicknesses of (a) 0.94 and (b) 0.74 nm. The shaded areas denote thethree water layers, which are separated by two valleys at z1 = 0.47 nmand z2 = 0.71 nm. (c, d) Hydrogen bond number profiles of watermolecules in brine films with thicknesses of (c) 0.94 and (d) 0.74 nm.The hydrogen bond profiles near unconfined interfaces are positionedsimilarly to the water/oil density profiles in Figure 2.

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3.2.1. Ion Distribution. Figure 5 shows the density profilesof Na+ ions in two brine films and near isolated quartz surfaces.

The average concentrations of Na+ ions in the 0.74 nm-thickand 0.94 nm-thick brine films are 1.60 and 1.24 M,respectively. The density profile of Cl− ions is not shownbecause of their very small value, especially inside the brinefilms. Regardless of the brine film thickness (an isolated quartzsurface is effectively bounded by a very thick brine film), twoNa+ density peaks appear at z = 0.33 and 0.55 nm. Thelocations of these peaks are in excellent agreement with priorstudies of EDLs near the same quartz surface.41 As the brinefilm is thinned, the evolution of the Na+ density profiles showstwo features: First, the Na+ density away from the quartzsurface (e.g., at the second Na+ peak) decreases substantially.For example, in the 0.74 nm-thick film, the height of thesecond Na+ peak is reduced to 1/3 of its height near anisolated quartz surface. Second, the first Na+ peak grows by28.7 and 44.6% compared to that near isolated quartz surfacesas the film is thinned to 0.94 nm and, subsequently, to 0.74nm.The first feature and the existence of the second Na+ peak

are primarily caused by the ion hydration effect. In classic EDLtheories such as the Poisson−Boltzmann (PB) equation, theion distribution is governed by long-range ion−ion electro-static interactions, and water acts only as a dielectric medium.However, water also behaves as a molecular solvent thathydrates ions, and the related short-range ion−waterinteractions have been found to substantially affect the iondistribution in EDLs.55−60 To explore this effect, we computethe hydration number of Na+ ions (nhdr). nhdr of an ion isdefined as the number of water molecules within its firsthydration shell. The radius of an ion’s first hydration shellcorresponds to the first minimum of the ion−water radialdistribution function (RDF). For a Na+ ion, the radius of itsfirst hydration shell is approximately 0.31 nm (see the

Supporting Information). Calculation of nhdr of Na+ ionsacross the brine films revealed that nhdr of Na

+ ions attains alocal maximum at z = 0.53 nm (see Figure S7 in theSupporting Information), which is caused by the inhomoge-neous distribution (layering) of water molecules near thequartz surface. Because a Na+ ion is hydrated by more watermolecules at this location than in bulk, it is energeticallyfavorable to reside here, thereby helping explain the secondNa+ peak at z = 0.55 nm. Similar solvent-induced effects havebeen reported in prior MD and DFT simulations of EDLs nearsolid surfaces.55−60

As a brine film is thinned, the oil surface moves toward thequartz surface. Since the water density is reduced near an oilsurface, the ion hydration at a specified distance from thequartz surface is reduced. For example, in the 0.74 nm-thickbrine film, nhdr of Na+ ions in the region z > 0.5 nm issubstantially smaller than that in the 0.94 nm-thick brine films.Consequently, the Na+ density in this region is lower than inthe 0.94 nm-thick brine films.The second feature of Na+ density evolution, namely, the

increase of the first Na+ density peak as the brine films arethinned, can be caused by several factors. First, as brine filmsare thinned, Na+ ions in the region away from the quartzsurface are depleted as explained above. However, the numberof Na+ ions in the film remains almost unchanged because theymust balance the charge on the quartz surface (the number ofCl− ions in the brine film is negligible under the reservoirconcentration that is studied here). Therefore, the Na+ densityclose to the quartz surface will increase. Second, as the brinefilms are thinned, even if Na+ ions are not repelled from the oilsurface due to the hydration effect, these ions are confined in anarrower space; thus, the Na+ density near the quartz surfaceshould increase. Assessing whether the increased confinementin thinner brine films can lead to the higher first Na+ peak isdifficult because, ideally, this confinement effect should beevaluated using a model that incorporates all relevant physics(e.g., ion hydration effects) in addition to the geometricalconfinement. While such models do exist, they often requireempirical parameters as inputs.61 Here, we use the classic PBequation to obtain a qualitative understanding only.As shown in the inset of Figure 5c, in the PB model, each

brine film is represented as a slit pore that is bounded by onecharged wall (which mimics the quartz surface) and oneneutral wall (which mimics the neutral oil surface). Becausethe first Na+ density peak at z = 0.33 nm is 0.11 nm away fromthe nominal brine−quartz interface (see Figures 5a and 2a),the width of the slit pore, which is denoted as H, is taken to be0.83 (0.63 nm) for the 0.94 nm-thick (0.74 nm-thick) brinefilm. The dielectric constant inside the pore, namely, εr, is setto 56.83 ± 1.31, which is computed for bulk SPC/E water at350 K (see the Supporting Information).62,63 The ionconcentration in the bulk electrolyte is set to 0.1 M, which isthe same as that in our brine reservoir. As shown in Figure5c,d, the density of Na+ ions on the pore increases by 7.4 and12.9% as H decreases from ∞ to 0.83 and 0.74 nm,respectively. These increases are much smaller than theincreases of the first Na+ peak that are observed in Figure5a,b, thereby suggesting that the increased confinement inthinner brine films is likely not the direct reason for theincreased Na+ adsorption on the quartz surface.

3.2.2. Dielectric Effects. In the above analysis, based on thePB equation, the dielectric constant of the brine film is taken asthat of bulk water. However, the dielectric response of

Figure 5. Electrical double layers in thin brine films. (a, b) Densityprofiles of Na+ ions and water near an isolated quartz surface and inthin films with thicknesses of (a) 0.94 and (b) 0.74 nm. (c, d) Na+ iondensity that is predicted by the Poisson−Boltzmann equation in brinefilms with ion-accessible thicknesses of (c) 0.83 and (d) 0.63 nm. Theinset in (c) is the continuum model of the brine film. The ion-accessible thickness H is determined as the distance between the Na+

ion’s first peak and the nominal oil surface in (a) and (b). The brinefilm is in equilibrium with a brine reservoir with an ion concentrationof 0.1 M. The co-ion densities are not shown due to their very smallvalues.

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nanoconfined water is known to differ substantially from thatin bulk,64−66 which can modify electrostatic interactionsbetween ions and thus affect the ion distribution in the brinefilm. To appreciate the dielectric effects in molecularly thinfilms, following the work of Netz and co-workers,65 wecompute the dielectric profile of water in thin water films nearneutral quartz surfaces.The thin water film systems in Table 1 with film thicknesses

of 0.72, 0.92, and 4 nm are studied. The component of thedielectric constant in the direction perpendicular to the quartzsurface is of primary interest and is computed by followinglinear response theory.65,67,68 A perpendicular polarizationcorrelation function is defined as

= ⟨ ⟩ − ⟨ ⟩⟨ ⟩⊥ ⊥ ⊥ ⊥ ⊥c z m z M m z M( ) ( ) ( ) (2)

where ⟨ · ⟩ denotes the time average and m⊥(z) is theperpendicular polarization density at position z, which isevaluated via m⊥(z) = − ∫ 0

zρe(z ′ )dz′ (ρe is the space chargedensity). The total perpendicular polarization of the simulationbox is M⊥ = LxLy∫ 0

Lzm⊥(z)dz where Lx, Ly, and Lz are the boxlengths in the x, y, and z directions. Using the fluctuation−dissipation theorem,66,67 the inverse perpendicular dielectricprofile of a periodic system is related to c⊥(z) via

ε ε= − +⊥−

⊥ ⊥z c z k T C V( ) 1 ( )/( / )10 B (3)

where ε0 is the vacuum permittivity, kB is the Boltzmannconstant, T = 350 K is the system temperature, C⊥ =LxLy∫ 0

Lzc⊥(z)dz is the variance of the total polarization, and Vis the simulation box volume. For sufficiently thick water films,ε⊥−1(z) should approach 1/εr at positions that are away fromthe confining surfaces.Figure 6a shows the perpendicular polarization correlation

function in the studied water films. Near the quartz surface

whose zero plane is located at z = 0, the c⊥(z) profiles of thetwo thin water films are undistinguishable from each other butare generally lower than that for the case with H = 4 nm due tothe larger value of M⊥ for the much thicker water film. Thecorresponding ε⊥

−1(z) profiles are shown in Figure 6b. Near thequartz surface, ε⊥

−1(z) crosses zero several times and exhibitsnegative values in some regions; namely, ε⊥(z) can becomenegative or diverge locally. Similar phenomena have beenreported for water near many types of substrates and theycorrespond to the overscreening of surface charges at variouspositions by water.65,67−69 While it is not straightforward toevaluate how the complex ε⊥(z) affects dielectric screening inthe water film, the complex ε⊥

−1(z) profile can be used toconstruct a coarse-grained dielectric box model that approx-imates the film as a continuum with a uniform effectivedielectric constant.65 According to linear response theory, sucha dielectric box model effectively reproduces the integral overthe electrical field by

∫ ε ε− = −⊥−

⊥ ⊥z z L( ( ) 1)d (1/ 1)L

0

1 eff effz

(4)

where L⊥eff and ε⊥

eff are the effective dielectric box length in the zdirection and the effective perpendicular dielectric constantwithin the box, respectively. As practiced in the originaldielectric box model,65 one computes L⊥

eff by setting ε⊥eff to the

dielectric constant of bulk water (56.83 here). Using theobtained value of L⊥

eff, a shift δ = L⊥eff − h is obtained (h is the

water film thickness). The effects of the quartz slab, oil phase,and water film on the dielectric profile are all lumped into theshift δ. Since the quartz slab and the oil phase are the same insystems with different water films, the perpendicular dielectricprofiles are the same in them (data not shown here).Therefore, δ in systems with different water film thicknessesh provides a measurement of how the dielectric environment ischanged when h changes. Typically, δ varies monotonically as awater film becomes thicker and approaches an asymptoticvalue, namely, δ0, when h is larger than a few nanometers. Inthin films, it has been established that ε⊥

eff can be obtained viaeq 4 and using the effective dielectric box length that is basedon the asymptotic shift (L⊥

eff = h + δ0).65

Figure 6c shows the shift δ in the three water films. The shiftδ for the 4.0 nm-thick film is 0.715 nm. This value is taken asthe asymptotic shift δ0 and labeled using a dashed line. As thefilm thickness decreases to 0.92 and 0.72 nm, δ is reduced to0.709 and 0.698 nm, respectively. The magnitude of δ for ourwater films, which are confined between a rigid quartz surfaceand a soft decane slab, is similar to that of the water films thatare confined between two polar walls with similar separa-tions.65 δ decreases as a water film is thinned, whichcorresponds to a decrease of the dielectric efficiency ofnanoconfined water in the direction normal to the confiningsurfaces. Furthermore, via the method that is described above,the effective dielectric constant ε⊥

eff is found to decrease to 57and 81% of the bulk dielectric constant in films with h= 0.72and 0.92 nm, respectively (see Figure 6d). Using thesedielectric constants, the PB model that is sketched in Figure 5cis solved again to evaluate how the Na+ density in brine filmschanges as they are thinned. As shown in Figure 5c,d, the newPB model predicts that as the film thickness decreases from H= ∞ to 0.94 and subsequently to 0.74 nm, the maximal Na+

density in the film increases by ∼30 and ∼80%. The largerincreases that are observed here are in better agreement withthe increase of the first Na+ peak that is predicted by the MD

Figure 6. Perpendicular dielectric profiles in thin water films. (a)Polarization correlation function near the quartz surface. (b) Inverseperpendicular dielectric profile near the quartz surface. (c) Shift of theeffective dielectric box length with respect to the film thickness. Thedashed line denotes the shift when the water film is 4.0 nm thick. (d)Effective dielectric constant in the direction normal to the quartzsurface. The dashed line denotes the static dielectric constant of bulkwater.

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simulations than when the dielectric decrement in the thinfilms is neglected. Physically, as the effective dielectric constantin a film decreases, the Na+−Na+ and Na+−surface electrostaticinteractions become less screened, which leads to a strongeradsorption of Na+ ions on the quartz surface.3.2.3. Salinity Effects. Finally, we examine the EDL

structure in brine films in equilibrium with brine reservoirswith an ion concentration of 1.0 M. Figure S8 in theSupporting Information shows the counterion (Na+) densityprofile across the film, along with the water density profiles(the co-ion density profiles are shown in Figure S9 in theSupporting Information). The density of Na+ ions issubstantially reduced near the oil surface for the 0.90 nm-thick and 0.72 nm-thick brine films, which is again due to thereduced ion hydration near the oil surfaces, as explained above.In contrast to the scenario in which the ion concentration inthe reservoir is 0.1 M, the height of the first Na+ peak near thequartz surface increases only by ∼10% as the brine filmthickness decreases from h = ∞ to 0.90 and 0.72 nm, asexpected. At a bulk ion concentration of 1.0 M, the Debyelength is ∼0.3 nm; thus, most of the charge on the quartzsurface is screened by the Na+ ions that are adsorbed on it(within the first Na+ peak). Consequently, the height of thefirst Na+ peak near the quartz surface is controlled mainly bythe surface charge density and shows no substantial variation asthe brine film is thinned.3.3. Disjoining Pressure in Brine Films. The disjoining

pressure in thin films is measured as the pressure differencebetween the top and bottom pistons in Figure 1a. For filmsthat are in contact with charged quartz substrates (σ= −0.12C/m2), film thicknesses of 0.92 ± 0.02 and 0.72 ± 0.02 nm andbrine reservoir ion concentrations of 0.1 and 1 M are studied.Figure 7 shows the disjoining pressure of the films as functions

of the film thickness at two ion concentrations. For brine filmswith a thickness of ∼0.92 nm, the disjoining pressure increasesfrom 2.45 to 3.57 MPa as the brine concentration decreasesfrom 1 to 0.1 M. A similar increase from 11.3 to 13.1 MPa isobserved in brine films with a thickness of ∼0.72 nm. Theincreased repulsion between the oil and quartz surfaces atlower salinity is consistent with the double-layer expansionmechanism for wettability alteration in OBR systems.16,70

To interpret the above results more quantitatively, weobserve that the total disjoining pressure Π is typically dividedinto the van der Waals component Πvdw, the double-layercomponent Πedl, and the hydration component Πhdr. For thenanometer-thin films that are considered here, Πvdw is typically

much smaller than the other two components and thus is notdiscussed further. Directly measuring the individual compo-nents of Π in MD simulations is difficult. However, since Πhdrand Πvdw do not vary substantially within the salinity windowthat is studied here (0.1−1 M),71,72 we use the measuredchange of Π in response to a salinity change to gain insight intothe validity of classical theories in predicting Πedl and itschange with the salinity. Using the PB equation that is adoptedin classic DLVO theory and the model of the brine film that issketched in Figure 5c, Πedl can be obtained via the contactvalue theorem1

i

kjjjjjj

y

{zzzzzz∑ ∑ρ ρΠ = = − ∞H k T z H( ) ( )

ii

iiedl B ,

(5)

where ρi(z = H) is number density of ion i on the neutralsurface at z = H in the inset of Figure 5c, ρi, ∞ is the ion densityin the brine reservoirs, and kBT is the thermal energy. ρi(z =H) can be obtained by solving the classical PB equation.Solving eq 5 and the PB equation with a quartz surface

charge density of −0.12 C/m2, Πedl in a 0.92 ± 0.02 nm-thickbrine film is determined to be 1.26 and 0.02 MPa at brineconcentrations of 0.1 and 1 M; in a 0.72 ± 0.02 nm-thick brinefilm, Πedl is 2.21 and 0.31 MPa at brine concentrations of 0.1and 1 M. As the salinity decreases, the increase of Πedl that ispredicted by the PB equation agrees well with the MD results.This satisfactory agreement is somewhat fortuitous but not amere coincidence. Indeed, the PB equation has also beenshown to well predict Πedl in nanometer-thick brine films thatseparate moderately charged soft surfaces.61 The satisfactoryperformance of the PB equation originates from Πedl in thesefilms being dominated by the entropic effect that is associatedwith the enrichment of ions, which is captured by the PBequation.At a bulk ion concentration of 1 M, the observed value of Π

should be mostly determined by Πhdr because Πedl issubstantially suppressed according to the PB predictions. Inmany theoretical models of disjoining pressure, Πhdr and Πedlare assumed to be additive; namely, Πhdr is assumed to beindependent of Πedl (and hence the surface charge and ionconcentration). This additivity was shown to breakdown inthin films between rigid surfaces in early experiments1 and infilms between soft surfaces in recent MD simulations.61 Here,we examine the extent to which Πhdr in thin films that separatea rigid quartz slab and a soft hydrocarbon liquid is affected bythe quartz’s surface charge. We studied the disjoining pressurein two water films (thicknesses: 0.72 ± 0.02 and 0.92 ± 0.02nm) that are in contact with neutral quartz surfaces.Figure 7 shows that when the quartz surface is neutral, the

measured Π, which should be essentially Πhdr, is 1.18 and 6.23MPa in the 0.92 nm-thick and 0.72 nm-thick water films,respectively. In comparison, Π at 1 M ion concentration, whichshould also be dominated by Πhdr, is 2.45 and 11.3 MPa in 0.90nm-thick and 0.72 nm-thick brine films, respectively. Theseresults demonstrate that Πhdr increases as the quartz slab’ssurface charge density σ changes from 0 to −0.12 C/m2 andthus it is not simply additive with Πedl. The differences amongthe values of Πhdr under various surface charge densities can beattributed to several factors: First, when σ changes from 0 to−0.12 C/m2, many Na+ ions become adsorbed on the quartzsurface. The hydration of these Na+ ions is stronger than thatof the quartz surface because Na+ ions are smaller than thesilanol group. Therefore, water molecules are more difficult to

Figure 7. Disjoining pressures in thin films with various thicknesses,quartz surface charge densities, and reservoir ion concentrations.

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remove near the charged quartz surface than near the neutralsurface, thereby leading to a more repulsive Πhdr. Second, whena quartz surface is electrified, the orientation of the interfacialwater molecules and its evolution as the brine film is thinned,both of which affect the hydration force,73,74 change too. Forexample, the dipole orientation of water molecules near aneutral quartz surface changes little as a water film is thinnedfrom h = ∞ to 0.92 nm (see Figure S10a in the SupportingInformation), whereas that near a charged quartz surface (σ =− 0.12 C/m2) changes substantially as a brine film is thinnedfrom h = ∞ to 0.90 nm (see Figure S10b in the SupportingInformation). The larger change of the interfacial watermolecules’ orientation during the thinning of a brine filmnear a charged quartz surface helps explain the stronger Πhdr inthese films.Overall, in films as thin as ∼0.9 nm, the disjoining pressure is

controlled by both the double-layer forces and the hydrationforces; as films are thinned to ∼0.7 nm, the hydration forcedominates over the double layer force for ion concentrations aslow as 0.1 M. However, the hydration force is not independentof the double-layer force in that it changes as the quartz surfacebecomes electrified. When the brine salinity is lowered, theresponse of the disjoining pressure can be predicted accuratelyby the classic PB equation. Hence, the hydration force is lessdependent on the salinity than the surface charge density of thequartz surface in the films that are studied here.3.4. Dynamics of Thin Brine Films. The oil−brine−rock

interfaces are often subject to shearing in the lateral direction,for example, when an oil slug moves through a pore under theaction of a pressure gradient.75−77 In available studies of suchproblems, the dynamic properties of brine films are taken asthose of bulk brine, and a no-slip boundary condition isassumed at the oil−brine interface due to the limitedinformation on these aspects. In this section, we bridge thisgap by studying the hydrodynamic properties of thin brinefilms. Without loss of generality, we focus on brine films with areservoir concentration of 0.1 M.First, we study the shearing of a reference system that

features thick slabs of brine and oil (Figure 1c). Here, thebrine−rock and the brine−oil interfaces are isolated due totheir large separation. Shearing is imposed by pulling the toppiston in the x direction with a constant speed of Vp (Vp is 70m/s here; simulations with Vp=50 m/s showed the samehydrodynamic properties within statistical error). After asteady state has been reached, the velocities of water anddecane are collected on the fly for 50 ns. Figure 8a,b showsthat away from the quartz−water and water−oil interfaces, thevelocity profiles of water and decane are linear. The velocity ofwater is almost zero within the first water density peak (z <0.47 nm), which is consistent with the notion that watermolecules are attracted strongly to the quartz surfaces.78

Across the nominal brine−oil interface (z = 4.07 nm), there isa velocity jump, which corresponds to a slip between the brineand oil phases. A similar interfacial slip has been identified instudies on weakly interacting fluids and was found to originatefrom the poor mixing of the two fluid phases across the diffusefluid−fluid interface and/or the limited entanglement ofmolecular chains of the species from the two fluids.79−81

In light of the above observations, we use a continuummodel to describe the hydrodynamics of oil−brine−rockinterfaces (see Figure 8c). First, a no-slip plane is located at adistance δ from the brine−rock interface (the brine−rockinterface is located 0.22 nm above the zero plane of the quartz

surface; see Figure 2a). Second, a slip occurs at the brine−oilinterface with Vslip = τ/β where Vslip is the difference betweenthe brine and oil velocities that are extrapolated from theirprofiles in their respective phases to the nominal brine−oilinterface, β is the interfacial slip coefficient,80,82,83 and τ is theshear stress at the brine−oil interface. Finally, the Stokesequation with a constant effective viscosity (μe, w and μe, d forthe brine and oil) is used to describe the flow in the brine andoil slabs. μe, d is taken as the bulk value of decane because theoil slab is thick. Using this model and the velocity profiles inMD simulations, δ, β, and μe, w can be obtained (see theSupporting Information). From the data that are presented inFigure 8b, δ is determined to be 0.29 nm, and β is found to be0.39 ± 0.04 MPa·s/m. μe, w is determined to be 0.39 mPa·s,which is almost the same as that of bulk water.Next, we simulated the shearing of oil−brine−rock

interfaces in thin brine films. Figure S12a,b in the SupportingInformation shows velocity profiles in brine films withthicknesses of 0.74 and 0.94 nm, respectively. Their keyfeatures, namely, the shift of the no-slip boundary away fromthe quartz surface and the interfacial slip, are similar to those inFigure 8b. The continuum model in Figure 8c is also applied tothese brine films with μe, w and β as adjustable parameters andμe, d taken as the bulk oil viscosity (0.53 mPa·s). The no-slipplane near the quartz surface is assumed to remain at the sameposition as in the reference system (z = 0.51 nm or,equivalently, δ = 0.29 nm) since water−rock interfaces inthin brine films differ little from those in the reference system(see Figure 4). By requiring that Vslip at the brine−oil interfaceand the total water flux across the brine film that are predictedby the continuum model match those that are measured inMD simulations, μe, w and β in the brine films are extracted(see Table 2). The effective viscosities of water in the twobrine films are the same as that of bulk water within statistical

Figure 8. Shear flow near quartz−brine and brine−oil interfaces. (a)Number density profiles of water and decane’s carbon atoms near thequartz surface in a reference system (see Figure 1c). (b) Velocityprofiles of water and decane. The shear flow is induced by pulling thetop piston in Figure 1c at a constant speed of 70 m/s. (c) Schematicof the continuum model for describing the shearing flow in brinefilms.

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uncertainty. While the friction coefficient β at the brine−oilinterfaces seems to increase marginally as a brine film isthinned, the variations are within the statistical error of oursimulations. These results suggest that the hydrodynamicproperties of brine films are not strongly affected by themolecular confinement in these films, which is consistent withthe insensitivity of the structure of water in brine films andbrine−oil interfaces to the brine film thickness (see Section3.1).For oil slugs inside a pore, the brine films between the slug

and pore walls act like a slip layer, thereby facilitating thetransport of the oil slug due to their lower viscosity than oil.84

For a brine film with a thickness h and under a shear stress τ,the velocity of the oil at the brine−oil interface is V0/τ = h/μbaccording to the classic hydrodynamic models (μb is theviscosity of bulk water). In light of the continuum model that issketched in Figure 8c, the velocity of the oil at the interfacebecomes τ δ μ β′ = − +− −V h/ ( )0 e,w

1 1 or

ikjjj

y{zzz

δ μ μ μ β′ = − +−V Vh

h/ 1 /( ).0 0 b e,w1

b (6)

The first term on the right-hand side accounts for the effectsof the shifted shear plane from quartz surfaces and thedeviations of the viscosities from their bulk values. The secondterm on the right-hand side accounts for the slip at brine−oilinterfaces. For the 0.74 and 0.94 nm-thick films that areconsidered here, the first term is ∼0.75 to 0.85 based on thedata in Table 2, thereby suggesting that these effects onlychange the transport of oil slugs marginally. The second term is∼1 for the two films that are considered here; namely, due tothe interfacial slip, the oil surface can move ∼100% faster thanwhen this slip is neglected. Physically, in terms of providinglubrication for the movement of an oil slug along a pore, theslip at the brine−oil interface effectively increases the apparentthickness of the brine layer between the oil slug and pore wallsby μ β= /b . If is comparable to the physical thickness h ofthe brine film, the interfacial slip substantially affects thetransport of the oil slug. Because brine films in OBR systemsare often thinner than one or a few nanometers,18,19 theinterfacial slip should be considered in future continuumsimulations of oil droplet transport in OBR systems.

4. CONCLUSIONSIn summary, we studied molecularly thin brine films that areconfined between nonpolar oil and quartz surfaces via MDsimulations. We quantify the structures of the interfacial water,oil, and EDLs, the disjoining pressure, and the shearingproperties of the brine films and brine−oil interfaces. Thesubnanometer confinement in brine films only weakly modifiesthe molecular packing at the rock−brine and brine−oilinterfaces. However, increasing the confinement (thinningthe brine films) markedly increases the counterion density nearthe charged quartz surfaces, especially under low brine

concentration conditions. Although the increased geometricalconfinement contributes directly to the enhanced counterionadsorption, its indirect contributions are more important; thatis, as the confinement is increased, the dielectric screening inbrine films is weakened. The disjoining pressure in the films isdominated by the hydration forces. Interestingly, the disjoiningpressure increases as the brine concentration is lowered, andthe magnitude of its increase is consistent with that predictedby the PB equation. Analysis of the disjoining pressure insystems with neutral and charged quartz surfaces demonstratesthat the hydration disjoining pressure increases substantially asthe quartz surface is electrified. Hence, the hydration anddouble-layer forces are not simply additive, which is consistentwith prior experimental measurements between solid surfacesand simulations of surface forces between soft surfaces.1,61 Thefirst layer of water molecules on the quartz surface is effectivelystagnant; however, the viscosity of water beyond this layer isbulk-like in brine films that are as thin as three water moleculelayers. An interfacial slip is observed between the brine and oilphases, which contributes to an effective slip length of of ∼1nm in the systems that are investigated here.The present study is based on simulations, and a direct

validation of its results is limited by the scarce experimentalstudies on OBR systems. We hope the results that arepresented here will stimulate experimental investigations ofthin brine films in the future. Nevertheless, insights from thisstudy should help improve the fundamental understanding,numerical modeling, and application of technologies, includingLSW. The little-disturbed structure and dynamic properties ofinterfacial water and oil as the brine films are thinned highlightthat the water−rock and water−oil interfaces can be predictedreasonably well from unconfined water−rock and water−oilinterfaces. The classical PB equation well predicts theresponses of the disjoining pressure to salinity changes forthe cases that are studied here. However, hydration forces notlikely being additive with the double-layer force suggest thatthe classic surface force theories should be used with caution inmodeling the disjoining pressure in brine films in OBRsystems. Furthermore, the significant modification of the EDLstructure and the decrease of the effective dielectric constant asthe brine films are thinned will likely affect processes such assurface charge regulation.85 Therefore, although these factorsdo not substantially change the disjoining pressure under thefixed surface charge condition that is explored here, they mayplay an important role in practice. Finally, the slip at brine−oilinterfaces can substantially facilitate the transport of oil slugs innarrow pores by effectively providing a thicker slip layer forsuch transport.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.lang-muir.9b01477.

Table 2. Effective Water Viscosity and Brine−Oil Slip Coefficient for Brine Filmsa

film thickness (h/nm) 0.94 0.94 0.74 0.74 4.00piston speed (m/s) 40 20 40 20 70μe, w (mPa·s) 0.40 ± 0.05 0.37 ± 0.02 0.33 ± 0.03 0.32 ± 0.01 0.39 ± 0.04β (MPa·s/m) 0.41 ± 0.04 0.40 ± 0.08 0.46 ± 0.03 0.44 ± 0.05 0.39 ± 0.04

aThe ion concentration in the brine reservoir is 0.1 M.

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Force fields parameters; relaxation of thin brine filmswithin the last 100 ns; structure of water−oil interfacesat 1 M brine concentration; quantification of thegeometry of decane molecules; Na+ ion hydrationnumber profile across brine films, static dielectricconstant of SPC/E water; radial distribution functionsin NaCl solutions; Na+ ion density profiles across brinefilms in equilibrium with 1 M brine reservoirs ; Cl− iondensity profiles across brine films in equilibrium with 1M brine reservoirs; water dipole orientation profiles;hydrodynamic properties of the thick water film inFigure 8; and shear flow velocity profiles in thin brinefilms (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: ruiqiao@vt.edu.ORCIDShuyu Sun: 0000-0002-3078-864XRui Qiao: 0000-0001-5219-5530NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank the ARC at Virginia Tech for generous allocations ofcomputer time. R.Q. acknowledges the financial support of theNSF under grant CBET 1705287, and S.S. acknowledges thefinancial support of King Abdullah University of Science andTechnology (KAUST) through the grants BAS/1/1351-01 andURF/1/2993-01.

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