Effect of Aggregation and Adsorption Behavior on the Flow Resistance

Article Cite This: Langmuir 2019, 35, 8110−8120

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Effect of Aggregation and Adsorption Behavior on the Flow Resistance of Surfactant Fluid on Smooth and Rough Surfaces: A Many-Body Dissipative Particle Dynamics Study Peng Zhou,†,‡,§ Jian Hou,*,†,‡ Youguo Yan,∥ Jiqian Wang,§ and Wei Chen‡ Key Laboratory of Unconventional Oil & Gas Development (Ministry of Education), ‡School of Petroleum Engineering, §State Key Laboratory of Heavy Oil Processing, Centre for Bioengineering and Biotechnology and College of Chemical Engineering, and ∥ School of Materials Science and Engineering, China University of Petroleum (East China), 66 Changjiang West Road, Qingdao 266580, P. R. China

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†

S Supporting Information *

ABSTRACT: To study the effect of surfactant on the resistance of wall-bound flow, the adsorption and aggregation behaviors of surfactant fluid on both smooth and groovepatterned rough surface are investigated through many-body dissipative particle dynamics (MDPD) simulation. The MDPD models of surfactants were carefully parametrized and have been validated to be able to simulate the aggregation and adsorption behavior of surfactants. The simulation results show that the surfactant in laminar flow can only increase the flow resistance on the smooth surface. On the rough surface, surfactant with strong adsorption performance on the channel wall shows a drag reduction effect at moderate concentration. The surfactant with weak adsorption properties can enhance the flow resistance, which is even more significant than that of those surfactants with no adsorption capacity. Although heating (high temperature) can generally reduce the viscosity and flow resistance of surfactant fluid, it would cause a poor drag reduction efficiency. It may arise from the destruction of the adsorption layer and the interruption of the fluid/boundary interface. Surfactant adsorption can tune the roughness of the fluid boundary on either the smooth or rough surface in a different manner, which turns out to be highly correlated to the change in flow resistance. Compared with the adsorption layer, surfactant in the bulk fluid makes a greater contribution to enhancing the flow resistance as the concentration rises. This study is expected to be helpful in guiding the application of surfactants on the micro- and nanoscale such as lab-on-a-chip nanodevices and EOR in a low-permeability porous medium.

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INTRODUCTION

forming a soft interface layer which is similar to polymer layers.14,15 Because the surface roughness itself can alter the hydrophobicity and wetting of the surface and subsequently affect the slippage length of the fluid,9,16,17 the influence of surfactant adsorption on surface roughness should be considered in addition to the effect on flow resistance. Many experimental works have been done to study the surfactant adsorption morphologies as well as the surface roughness by using neutron reflection, ellipsometry, UV absorption, vibrational sum frequency spectroscopy, quartz crystal microbalance with dissipation (QCM-D), and atom force microscopy (AFM).3,10,18,19 However, there have been few reports on the changes in roughness for smooth and rough surfaces caused by surfactant adsorption. Besides the surfactant micelles adsorbed on the rock surface, particle image velocimetry (PIV) experiments have found that rodlike micelles in the bulk fluid phase of a wall-bound flow are beneficial to reducing the drag resistance.20,21 Hence, it is more reasonable to study the two

Surfactants could aggregate and form micelles both in the bulk fluid and at the solid/liquid interface, which can drastically affect the flow resistance via changing the fluid viscosity and the boundary properties,1 playing essential roles in many nanofluid-related technological and industrial fields including microfluidic devices such as lab-on-a-chip devices, microelectromechanical systems (MEMSs), drug delivery, and oil recovery.2−5 The influence of boundary conditions is of particular importance in nanoflows. Roughness alone becomes significant as the dimension decreases. On the atomic scale, the definition of a smooth surface is somewhat imprecise because the wall substrates are formed by individual particles with finite roughness.6 Compared with smooth surfaces, rough surfaces exhibit different properties in surfactant adsorption and fluid flow resistance.7−10 On the one hand, the rough surfaces with nanoscale patterns usually have lateral confinement on the adsorbed surfactant aggregates and affect the orientation of molecular packing.11,12 On the other hand, the adsorption of surfactants in return influences the surface properties such as hydrophobicity, wettability,13 and surface roughness by © 2019 American Chemical Society

Received: December 24, 2018 Revised: May 7, 2019 Published: May 10, 2019 8110

DOI: 10.1021/acs.langmuir.8b04278 Langmuir 2019, 35, 8110−8120

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phase and the adsorption layer at the solid/liquid interface contribute to the flow resistance? (3) How does surfactant adsorption change the roughness of the fluid boundary under different conditions?

aspects (aggregation and adsorption) of the role that surfactant plays in both the bulk fluid phase and the fluid boundary, which require us to access the microscopic structure of the aggregated surfactants at the molecular level and unravel the interplay between the bulk fluid phase and the solid/liquid interface.2,13 Benefiting from the advantages of microscopic observation, molecular simulations have been utilized widely to study the aggregation and adsorption of surfactants at the solid/liquid interface as well as fluid in smooth/rough channels on the molecular level.1,22−30 On the microscopic scale, different types of surfactants and different adsorbed amounts usually have various aggregated morphologies,3,4,18,31 resulting in different drag reduction effects.32,33 Some research reported the influence of the boundary roughness on the friction of the fluid, but the intrinsic roughness of the surface was unchanged under the shear flow, which is different from a dynamic rough adsorption layer formed by surfactants.9 Therefore, it requires a systematic and molecular-level study to explore the influence mechanism of surfactant adsorption morphologies, fluid boundary roughness, and fluid viscosity on the flow resistance of wall-bound fluid. Molecular simulations such as molecular dynamics (MD) have been successfully used in modeling surfactant and fluid systems for applications such as the interfacial tension calculation, adsorption morphology characterization, and viscosity calculation.13,24,34−38 However, it is still a challenge for MD to simulate the aggregation behavior on a large scale because of time and space limitations.39−44 The aggregation behavior requires larger mesoscale simulation methods in which the molecular models are generally coarsegrained and the potential function is simplified.45−47 Manybody dissipative particle dynamics (MDPD) is a promising mesoscale simulation method because of its advantages in simulating phase interfaces, micelle formation, and fluid in channels with high calculation efficiency.46,48−53 In this article, surfactant fluids on both smooth and rough solid surfaces were simulated by the MDPD method to investigate the effects of aggregation and adsorption of surfactant on the flow resistance. The MDPD coarse-grained model for different surfactant molecules (DTAB and SDS) and silica surfaces (smooth and rough) was established and carefully parametrized. The interaction parameters in the MDPD models were parametrized using the experimental data of density and interfacial tension and then validated by the simulations of the critical micelle concentration (CMC) and wetting angle on the silica surface. Using equilibrium manybody dissipative particle dynamics (EMDPD), the aggregation states in bulk fluid phases and the adsorption morphologies of different surfactant on the varied surface were obtained. Then the density distribution was calculated to analyze the surfactant aggregated morphology and adsorbed amount under different conditions. The velocity profile was monitored, and the effect of the aggregated micelles in bulk fluid and the surfactant adsorption layer at the boundary on the flow resistance was examined via nonequilibrium many-body dissipative particle dynamics (NEMDPD). The effects of concentration, temperature, adsorption capacity of surfactant, and surface roughness were further analyzed to explore the mechanism that determines the fluid friction near the boundary. This study is expected to explore the answers to the following questions: (1) What is the difference in the surfactant adsorption morphology on the smooth and rough solid surfaces at the molecular level? (2) How much do the surfactant micelles in the bulk fluid

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MODELS AND METHODS

MDPD Theory. To study micro- and mesoscale phenomena, many coarse-grained simulation methods such as the dissipative particle dynamics (DPD) method and its many-body modification have been developed to improve the computational time scale and spatial scale.50 The DPD method was originally proposed by Hoogerbrugge and Koelman.54 Compared with the MD method, the DPD method has two important innovations:53 the interaction potentials are relatively soft and the thermostat is locally momentum-conserved, which allow DPD methods to simulate larger systems at faster speed. Forces (Fij) between DPD particles (beads) include the conservative (FCij ), dissipative (FDij ), and random (FRij ) parts, defined as follows50

Fij = FCij + FijD + FijR

(1)

where Fij has a cutoff distance rc (in the reduced unit of length). As shown in eq 2, Aij is the maximum repulsion between beads i and j, wc(rij) is a weight function that is vanishing for r > rc = 1, and rij = rj − ri, rij = |rij|, and eij = rij/rij. The conservative part has solely repulsive interactions (Aij > 0) between particles but with no attractive interactions, which makes it impossible to simulate systems containing interfaces such as fluid flows in pores.

FCij = Aij wC(rij)eij

(2)

To compensate for the shortage of a conventional DPD method, Warren reported a many-body modification method named MDPD,50 where “M” denotes many-body or multibody. In the MDPD method, both the random and dissipative parts are kept unchanged while the conservative part is redefined as FCij = Aij wC(rij)eij + B(ρi + ρj )wd(rij)eij

(3)

in which the soft potential becomes attractive by setting Aij < 0, the repulsive force (B > 0) is tuned to be dependent on the local density ρi and ρj, and wc(rij) is a weight function that is vanishing for r > rd = 0.75. These modifications have been proven to be able to simulate the vapor−liquid interface and fluid in capillaries.50−52 MDPD Coarse-Grained Models and Their Parametrization. In the present work, the attraction parameter of water−water interactions (AWW) is set equal to −40.0,50,52 while the other interactions, Aij, are parametrized. All of the repulsion parameters, B, are kept at 25,46 and the resulting equilibrium number density of water is 6.05.46,53,55 As shown in Table 1, one water bead (W) is

Table 1. Correspondence between the MDPD Parameters in Reduced Units and the Real Values MDPD

MDPD → real units

parameter

value

bead rc ρ γ

1 1 6.05 7.62

physical units value

Nm (ρNmV)1/3 ρNmM/Narc γkBT/rc2

3

3H2O 0.817 nm 997 kg·m−3 72 nm·m−1

defined to contain three water molecules, which results in a DPD reduced length unit (rc) of 0.817 nm. The surface tension of water is calculated to be 7.62, which corresponds to the real value of 72 nm· m−1. As shown in Figure 1A, both cationic surfactant dodecyltrimethylammonium bromide (DTAB) and anionic surfactant sodium dodecyl sulfate (SDS) were modeled with an HT3 model which includes one hydrophilic bead group (H) and three hydrophobic tail beads (T). To parametrize the T bead, we first modeled the oil molecule 8111


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Figure 1. MDPD model of molecules and its parametrization and validation. (A) MDPD model of water, oil, and surfactants. (B) Surface tension of water and oil and interfacial tension of oil/water and oil/surfactant/water. (C) Aggregation of DTAB with the HT3 model at concentrations of 0.3, 1, 3, and 10 times the CMC. (hexadecane) which is divided into four coarse-grained beads (C). Because both T and C beads contain four carbon atoms, they share the same parameters in the MDPD simulation. When ACC was set to −40, the surface tension of C4 (hexadecane) was calculated to be beyond the experimental value of 27.3 nm·m−1 (hexadecane, 25 °C). Thus, we tuned the ACC and then found that when ACC = −22 the surface tension is 27.3 nm·m−1 and the density is 773 kg·m−3, which are consistent with the experimental values (Figures 1B and S2). Afterward, we adjusted AWC in the same way and found that when AWC = −27, the oil/water interfacial tension of C4 and W (hexadecane and water) agrees with the experimental value of 53.0 nm·m−1 (Figure 1B). Using classical FH theory,56,57 χwc was calculated to be 8.55 from

χij =

Table 2. Intra- and Inter-MDPD Bead Potential Parameters aij W H(DTAB) H(SDS) T/C Si bonds/angles

(4)

where ⟨···⟩ is the average ensemble, Zij is the coordination number of bead i (the nearest neighbor of j around i), and Eij is the energy between beads i and j when i is surrounded by j.56,58 Because χwc and Awc are in a linear relationship from Aii + A jj yz i zz χij = 2αρjjjjAij − z 2 k {

H(DTAB)

H−T T−T C−C H−T−T T−T−T C−C−C

Zij⟨Eij⟩ + Zji⟨Eji⟩ − (Zii⟨Eii⟩ + Zjj⟨Ejj⟩) 2RT

W −40 −28.66 −32.18 −27 −32.83

H(SDS)

T/C

−19 −5.98 −27.17

−22 −15.42

Si

−17 −7.79 −27.72 r0

kB

0.64 0.64 0.64

4 4 4

θ0

160 160 160

−40 kV

100 100 100

= 0.75, and the time step in all simulations was set to be 0.01 MDPD time unit. Boxes with different sizes were built to simulate different systems. In surface tension simulation, 3872 W beads or 968 C4 molecules were placed in an 8 × 8 × 20 box with an NVT ensemble. All length units are the DPD length unit, which corresponds to 0.817 nm (Table 1). In the interfacial tension simulation, 3872 W beads, 728 C4, and an additional 408 HT3 molecules were placed in a box which has a size of 8 × 8 × 20 initially and is controlled by an NPT ensemble. As indicated in Figure 1B, the water surface tension (γwv), oil surface tension (γov), and oil/water interfacial tension (γwo) were calculated from

(5)

we then get the value of 2αρ to be 2.138 by fitting the data as shown in Figure S1. To parametrize the H bead, we built up a model to calculate the oil/surfactant/water interfacial tension. In the process of fitting, we found that when AHH is −17 the interfacial tension of the C4/HT3/W (hexadecane/DTAB/water) systems is consistent with the experimental value of 8.7 nm·m−1 (Figures 1B and S2). We then got the AHH for SDS to be −19 via a similar fitting process. For the silica model, the density was set manually to be 6.0, which is equal to that of the W (water) system and therefore ASS = AWW = −40. Using eq 5, we then calculated the other interaction parameters Aij and collected them in Table 2. Simulation Methods. Equilibrium many-body dissipative particle dynamics (EMDPD) simulations were performed using the DL_MESO software package.59 Cutoff rc = 1 and shorter cutoff rd

γ = Lx Pxx −

Pyy + Pzz 2

(6)

where Lx is the box length in the X direction and γ can be derived by subtracting mean tangential stress tensors (i.e., Pyy and Pzz) from the normal one (i.e., Pxx).35,40 8112


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Figure 2. Morphologies of DTAB adsorption and density profiles on the smooth and rough surfaces in static and flow states at 300 K. EMD simulations on the smooth surface with low (A), medium (B), and high (C) concentrations and on the rough surface with low (D), medium (E), and high (F) concentrations. NEMD simulations on the smooth surface with low (G), medium (H), and high (I) concentrations and on the rough surface with low (J), medium (K), and high (L) concentrations. In the surfactant aggregation simulation, to study the dependence on the critical micelle concentration (CMC), a series of concentrations (0.3, 1, 3, and 10 times the CMC) of surfactant were simulated in an initial 28 × 28 × 28 box with an NPT ensemble. Because the CMC of DTAB is 0.0213 mol·L−139 and the volume V of the box is 1.20 × 10−20 L, the 1 CMC system contains CMC × V × NA = 153 surfactant molecules and 132 197 W beads (396 591 water molecules). In the contact angle simulation, two parallel silica layers were built with dimensions of 32.8 × 32.8 × 2.40 with a spacer of 18. One water drop containing 4000 W beads was initially placed in the center of the box. Because some of the silanol groups on the quartz surface are deprotonated, the charge density of the silica surface is −0.12 C·m−2. The parametrizing process for a Si bead is based on the silica models in our previous MD study.13 In the adsorption and fluid simulations, the box size is fixed at 13.1 × 6.55 × 30.0. Both smooth and groove-patterned rough silica surfaces were constructed (Figures 2 and S4). The length and width of the smooth surface are 13.1 and 6.55, respectively, and its thickness is 2.40. For the groove-patterned surface, there are three protrusion plates aligned parallel along the Y direction. The width and height of the protrusion plate are 2.19 and 1.80, respectively. The cavity between the protrusions is 2.19. The roughness of the solid surface is characterized by the normalized surface roughness factors rx and rootmean-square roughnesses (R), which are defined in detail in Figure S4. The values of rx for smooth and rough surfaces are 0.00 and 0.50, respectively. The values of R for smooth and rough surfaces are 0.00 and 0.98 nm, respectively. Water particles (8000) were added to the box. There were 68, 136, and 272 HT3 molecules in low-concentration (LC), mediumconcentration (MC), and high-concentration (HC) models. To improve the observation of the adsorption of surfactant, the concentrations are all beyond the CMC value. The numbers of

surfactant molecules are referenced to the values of the area per molecule of the complete surfactant adsorption on the smooth surface, which are 0.84, 0.42, and 0.21 nm2 for LC, MC, and HC models, respectively. The surfactant molecules were placed randomly in the box at the beginning of all simulations. The simulations were 4000 MDPD time units long, with the first 2000 MDPD time units for equilibrium and the last 2000 MDPD time units for data production. A gravitational force of Fg = 0.02 was placed on all of the beads in the Z direction for the contact angle, adsorption, and fluid simulations. In the nonequilibrium many-body dissipative particle dynamics (NEMDPD) simulations, an external driving force of Fe = 0.02 was applied to the W beads in the X direction to generalize the continuous flow in the fluid simulation. All of the simulation results are visualized using the VMD software.60 Validation of MDPD Models. Different concentrations of DTAB solutions were simulated to validate the aggregation property of the surfactant. As shown in Figure 1C, in the concentration below CMC, the surfactant molecules were utterly dispersed. When the concentration is above the CMC, the surfactant molecules began to aggregate and form micelles. The wetting property of the silica surface was also validated by measuring the contact angles of the water drop on the silica surface. The measured contact angle is ∼45°, which is consistent with the AFM experimental data at around 27.8−50.3 (Figure S3).61 The MDPD models have been proven to be able to simulate the aggregation behavior of the surfactant and the wetting behavior of the water/silica interface, thus they qualify for application in the following simulations of surfactant fluid on the rock surface.

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RESULTS Surfactants in solution may aggregate in the bulk water phase or adsorb on the surface of the fluid boundary. The 8113


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Figure 3. Morphologies of surfactant adsorption and density profiles of DTAB at 390 K and SDS at 300 K on the smooth and rough surfaces. DTAB simulations at 390 K on the smooth surface with low (A), medium (B), and high (C) concentrations and on the rough surface with low (D), medium (E), and high (F) concentrations. SDS simulations at 300 K on the smooth surface with low (G), medium (H), and high (I) concentrations and on the rough surface with low (J), medium (K), and high (L) concentrations.

pushing, no matter if they are adsorbed onto the rock surface or floating in the fluid phase (Figure 2H,I). The density profiles show that the amount of surfactant adsorbed on the rough surface is more than that on the smooth surface. The two distribution peaks of the hydrophilic headgroup and hydrophobic tail chain are separated, which illustrates that the surfactants adsorbed on the smooth surface have a “head-on” orientation.13,36 On the rough surface, the distance between the two distribution peaks becomes closer, indicating a lower anisotropy of molecular packing. It is speculated that the surfactants are adsorbed within the cavities and form nearly spherical micelles (Figure 2K), in which case the direction of the surfactant molecules is no longer perpendicular to the fluid direction (Y dimension). As the concentration increases, more surfactants are found to be punched into cavities by water flow. At high concentration, surfactants adsorbed onto the grooves connect and form a tight double layer (Figure 2L). Effect of High Temperature on the Surfactant Adsorption Morphology. Generally, increasing temperature can accelerate the thermal movement of both surfactant and water molecules and reduce the viscosity of the fluid. In a static state, high temperature increases the number of single surfactant molecule and decreases the size or number of micelled in the bulk water phase (Figure S5). Because of the strong adsorption capacity, there are still a considerable number of DTAB molecules adsorbed on the silica surface (Figure S6). Under the shearing of the water flow, the surfactant micelles both in the bulk water phase and on the rock substrate become unstable and dispersed, leading to a

morphologies of the aggregation and adsorption of surfactants in both static and flow states were studied by MDPD simulations. The effects of different concentrations, temperature, and surfactant species were investigated. The density profile and velocity profile are calculated and analyzed as well. Morphologies of Surfactant Adsorption on Smooth and Rough Surfaces in the Static State and Flow State. In the EMDPD simulations of surfactant solution on the smooth silica surface, most DTAB molecules aggregate into hemimicelles and adsorb on the rock substrate, leaving a small number of surfactant molecules dispersed in the bulk water phase (Figure 2A). As the concentration increases, more surfactant joins the hemimicelles adsorbed on the rock surface while more surfactant leaves the bulk water phase to aggregate into spherical micelles (Figure 2B). When the concentration increases further, the amount of surfactant increases both on the rock substrate and in the water phase, with more or larger micelles (Figure 2C). On the rough surface, the hemimicelles on the surface become smaller but more numerous because of the separation of the grooves (Figure 2D). Some surfactant adsorbed into the cavities while some adsorbed on the edges of the protrusions (Figure 2E). At high concentration, the micelles in the cavities and on the protrusions connect to form a continuous adsorption layer (Figure 2F). Generally, the adsorption morphologies of DTAB with different concentrations are consistent with the previously reported adsorption isotherm of the cationic surfactant at the solid/aqueous interface.62,63 In NEMDPD simulations, the shape of the micelles changes from sphere to spindle under the shearing of water flow 8114


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Langmuir fuzzy fluid boundary and a rough surfactant adsorption layer (Figure 3C,F). Effect of Surfactant Types on Surfactant Adsorption Morphology. To study the effect of surfactant types on the adsorption morphologies, an anion-type surfactant, SDS, was chosen because of its weaker aggregation and adsorption capacity on silica compared to DTAB. In the static state, more SDS micelles are observed to be solvated in the bulk water phase, and there are still some spherical micelles attached to the smooth substrate (Figures S7 and S8). Under a flow of water, the adsorbed SDS micelles on the smooth surface become very unstable and are almost punched away from the rock surface, indicating a feeble adsorption ability (Figure 3I,L). At low concentration below the CMC, all of the SDS molecules are dispersed in the solution, and no micelle is formed. As the concentration rises, SDS molecules begin to form micelles, which then connect with each other at high concentration. On the rough surface, however, more SDS molecules are in the aggregated micelles adsorbed on the grooves. At high concentration, the micelles adsorbed on the surface are interconnected and form an adsorption layer under the shearing of the water flow. The number of SDS molecules dispersed in the bulk water phase becomes smaller, and fewer micelles are formed at high concentrations. Flow Resistance of Surfactant Fluid on Smooth and Rough Surfaces. The flow resistance of surfactant fluids on smooth and rough surface was analyzed by calculating the velocity profiles of the pressure-driven water flow in different adsorption models (Figures 4 and S13).6 For a better view, the drag reduction effect of surfactant (HT3) solution compared with pure water (W) was represented by the ratio of velocity

growth (rHT3‑W), which was calculated on the basis of velocity with eq 7

Figure 4. Velocity profile of surfactant fluids on the smooth and rough surfaces in NEMDPD simulations. DTAB on the smooth (A) and rough (B) surfaces at 300 K, DTAB on the smooth (C) and rough (D) surfaces at 390 K, and SDS on the smooth (E) and rough (F) surfaces at 300 K.

Figure 5. Drag reduction ratio of different surfactants with different concentrations, temperature, and adsorption properties. The drag reduction ratio is evaluated by the ratio of velocity growth (rHT3‑W) in different simulations. Negative values of rHT3‑W represent the increase in the flow resistance.

rHT3 ‐ W =

VHT3 − VW × 100% VW

(7)

in which VW is the velocity of pure water fluid at Z = 17.5 and VHT3 is the velocity of surfactant fluid at Z = 17.5. On the smooth surface, as the surfactant concentration increases, the flow resistance gradually increases (Figure 4A), which is possibly because of the enhanced roughness of the surfactant adsorption layer or the increased viscosity caused by the more numerous surfactant molecules in the bulk fluid phase. On the rough surface, there is no noticeable change in the flow resistance in the LC simulation. With the increase in concentration, the flow resistance decreases first and then increases (Figure 4B). As shown in Figure 2E, when the flow resistance reaches its minimum, almost all of the surfactant micelles adsorb into the cavities of the rough surface, which dramatically reduces the surface roughness of the rock. When the concentration of surfactant increases further, the adsorbed surfactants form a double layer on the rough surface with a large number of hydrophilic headgroups being exposed to the fluid phase, which could enhance the friction of the fluid boundary.13 Typically, when the concentration of surfactant is low or the substrate is smooth, the slip length is long. As the concentration rises or the substrate is rough, the slip length becomes shorter or disappears (Figure 4). However, the VW value is not proportional to the slip length, which is probably because the fluid density is not uniformly distributed along the Z direction as some micelles are formed in the bulk phase. At room temperature, DTAB exhibits a drag reduction effect at low and moderate concentrations. At high temperature, although all of the velocity of the fluid is larger than that at room temperature because of the reduced viscosity (Figure 4C,D), the drag reduction efficiency is weakened (Figure 5). The values of rHT3‑W become smaller or negative, showing a drag enhancement effect. DTAB causes greater flow resistance on the smooth surface but less resistance on the rough surface. At the optimal

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Figure 6. Changes in the density profile of the surfactant adsorbed amount on the rock surface under heating and fluidic shearing conditions on the smooth and rough surfaces. Difference in the density profile in the static state (A) and flow state (B) between 300 and 390 K. Difference in the density profile at 300 K (C) and 390 K (D) between static and flow states.

Figure 7. Morphologies of surfactant aggregation and density profiles of DTAB and SDS on the smooth and rough surfaces without adsorption. DTAB simulations on the smooth surface with low (A), medium (B), and high (C) concentrations and on the rough surface with low (D), medium (E), and high (F) concentrations. SDS simulations on the smooth surface with low (G), medium (H), and high (I) concentrations and on the rough surface with low (J), medium (K), and high (L) concentrations.

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Figure 8. Roughness of the surfactant adsorption layer on the solid surface. The roughness is evaluated by the density gradient at the interface between the adsorption layer and water. The density gradient of the rough surface is 3.36; the density gradient of the smooth surface is 6.72. A higher density gradient represents a smaller amount of roughness.

enhances the adsorbed amount of cationic surfactant DTAB for both smooth and rough surfaces. For anionic surfactant SDS, water flow reduces the adsorbed amount on the smooth surface but increases the adsorbed amount on the rough surface (Figure 6C). When both the heating and fluidic shearing coexist, the adsorbed amounts of surfactants decrease under all conditions (cationic and anionic surfactants and smooth and rough surfaces) as shown in Figures 6B,D and S9− S12. Aggregates of Surfactant in the Bulk Fluid Phase. The changes in the adsorbed amount of surfactant on the solid surface affect its concentration in the bulk fluid phase. Evaluating the pure effect of aggregation of different surfactants in the bulk fluid phase on the flow resistance requires us to avoid the influence from the fluid boundary. Interaction parameters AHS and ATS are set equal to 0, which causes the surfactants to lose their adsorption ability on the rock substrate but maintain their aggregation ability. As shown in Figure 7, there is no adsorption of surfactant molecules on the rock surface in these simulations, and the flow resistance of the fluid could be affected only by the viscosity of the fluid. Normally, a higher surfactant concentration causes larger internal friction in the fluid, which would increase the flow resistance. As the concentration increases, the surfactants begin to aggregate from the dispersed state. At the same concentration, the difference between the aggregation morphology of the two surfactants was mainly affected by their different CMCs and intermolecular interactions. Under flow shearing, DTAB forms continuous threadlike micelles parallel to the flow direction, while the micelles formed by SDS have poor continuity. As shown in Figures 5 and S13, at the same concentrations in MC and LC simulations the DTAB micelles have a slightly smaller resistance than do the SDS micelles. It is speculated that the continuity of the surfactant is the reason that DTAB causes lower resistance (Figures 4 and 5). As the concentration rises, surfactant micelles in the bulk fluid make a greater contribution to enhancing the flow resistance compared to those in the adsorption layer (Figure 4). Roughness of the Fluid Boundary. Effect of Intrinsic Substrate Surface Roughness on Adsorption. The inherent roughness of a solid surface could cause a different amount of adsorption and different morphologies of the surfactant. More surfactant molecules are found to adsorb on the rough surface

concentration, DTAB exhibits a drag reduction effect by increasing the velocity by 8.5% (Figure 5). The flow resistance of the SDS solution on the smooth surface is smaller than that of DTAB, but its flow resistance on the rough surface is larger. In a word, for either the smooth surface or SDS surfactant, there is no drag reduction effect.

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DISCUSSION AND MECHANISMS The simulation results above have shown the effects of concentration, temperature, and surfactant type on the adsorption morphologies and flow resistance. In the following section, the aggregation of surfactants in the solution and the roughness of the surfactant adsorbed fluid boundary are analyzed in detail to explore the mechanism of the surfactant aggregation and adsorption on the drag reduction effect. Distribution of Surfactant on the Solid Surface and in the Fluid Phase. Because surfactant molecules either adsorb on the rock surface or aggregate into micelles floating in the bulk water phase, in order to study the effect mechanism of surfactant on the flow resistance of fluid it is necessary to consider the effects of surfactants on the adsorption layer at the fluid boundary and in the bulk fluid phase separately. Therefore, the density distributions of surfactants in the adsorption layer on the rock surface and fluid phases under different conditions are analyzed first and summarized in Table S1. The adsorbed amount is calculated by summarizing the density profile of the surfactant molecules in the adsorption layer within Z = 7.5, and the rest of the surfactants are considered to be in the bulk fluid phase. The amount of surfactant is numerically normalized with the total concentration in LC models. The changes in the adsorbed amount are obtained by calculating the difference in the density profile. The amount of surfactant adsorbed on the rock surface is found to be affected by various factors, including the temperature, fluidic shearing, and substrate roughness. Heating Effect on Adsorption. When the temperature is high, in static simulation, the adsorbed amount of cationic surfactant DTAB increases for both smooth and rough surfaces (Figure 6A). For anionic surfactant SDS, the adsorbed amount is reduced on the smooth surface but is enhanced on the rough surface (Figure 6A). Fluidic Shearing Effect on Adsorption. When a continuous flow is set up, at room temperature, 300 K, water flow 8117


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condition is relatively smooth when the drag reduction efficiency is high on a rough substrate. The system with a drag enhancement effect often has greater fluid boundary roughness on a smooth substrate. Only the surfactant with strong adsorptive performance can reduce the drag. For the surfactant with a weak adsorptive capacity, more surfactant molecules aggregate in the bulk fluid phase and increase the viscosity of the fluid. Besides, a loose adsorption layer formed by fewer surfactant molecules together enhances the friction between the boundary and micelles in the bulk phase, which makes the flow resistance even larger than that of the surfactant with no adsorption ability. As the concentration rises, surfactant in the bulk fluid makes an increasing contribution to enhancing the flow resistance compared to that in the adsorption layer. Heating (high temperature) could reduce the flow resistance by decreasing the viscosity. However, it would cause a poor drag reduction efficiency as a result of the enhancement of the friction of the fluid boundary condition by increasing its roughness. This work also complements the previously reported effect of surfactant on the flow resistance of a wall-bound fluid by successfully simulating the interplay between the bulk and the solid/liquid interface.

compared to on the smooth surface, except for a few cases. For example, as shown in Figure S13, in the static state and at low concentration, there is slightly more DTAB adsorbed on the smooth surface than on the rough surface. For most cases as in the flow state and at higher concentrations, the advantage of the rough surface on enhancing the surfactant adsorption becomes obvious by trapping the hemimicelles into the cavities. The adsorption enhancement of the rough surface is possibly due to the fact that the diffusion coefficient is small inside the cavities and the velocity of fluid tends to decrease near the rough wall, which reduces the shearing of fluid toward the surfactant adsorption layer.6 Roughness of the Surfactant Adsorption Layer. Surfactant adsorption can tune the roughness of the fluid boundary condition on both smooth and rough surfaces. To study the effect of surfactant on fluid boundary roughness and the flow resistance, the density gradient of the fluid boundary was calculated. As shown in Figure 8, the higher density gradient represents a lower roughness. The density gradient of the rough surface is 3.36, and the density gradient of the smooth surface is 6.72. On the smooth surface, the adsorption of surfactants decreases the density gradient and increases the roughness of the fluid boundary. At room temperature, the adsorption of cationic surfactant DTAB with low and medium concentrations on rough surfaces can increase the density gradient to up to 4. This enhancement results in a comparable smooth boundary condition by trapping the surfactant micelles into the cavities, exhibiting the drag reduction effect at the same time (Figure 4B). When the concentration increases further, the density gradient decreases rapidly, implying an enhancement of the roughness. At high temperature, the roughness of DTAB adsorbed layers increases. Only the density gradient in the medium concentration is >4 and therefore shows a slight drag reduction effect. The adsorption of SDS always causes a lower density gradient and enhances the surface roughness. At high concentration, the density gradient is even less than 1 (Figure 8B), which might be due to the blurry interface between the surfactant adsorption layer and the bulk fluid phase (Figure 3I,L). These results imply that the roughness of the fluid boundary condition could also reflect the strength of the interplay between the bulk fluid and the boundary.2 Therefore, high-concentration surfactant fluid generally has the strongest interaction with the micelles in the adsorption layer and the bulk phase, which always causes the largest amount of friction. This might be the reason that only the surfactant with strong adsorptive performance can reduce the drag under the appropriate concentration.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.8b04278.

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Parametrization and validation of MDPD models, density profiles and morphologies of surfactant on smooth and rough surfaces in EMDPD simulations, density profiles and morphologies of SDS at 390 K on smooth and rough surfaces in EMDPD and NEMDPD simulations, velocity profile of surfactant fluids on smooth and rough surface in NEMDPD simulations, and density distribution of surfactant on the solid surface and in the bulk fluid phase (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86 546 8395660. ORCID

Peng Zhou: 0000-0002-6849-3855 Jiqian Wang: 0000-0002-7525-5943 Notes

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The authors declare no competing financial interest.

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CONCLUSIONS We demonstrate that the carefully parametrized MDPD models can simulate the aggregation and adsorption behavior of surfactants, allowing the study of the drag reduction behavior of surfactant fluids on smooth and rough surfaces. The simulation results illustrate that surfactants always lead to drag enhancement in wall-bound flow on the smooth surface. With an optimized concentration and adsorption ability, the surfactant solution could achieve drag reduction on a nanoscale patterned rough surface by trapping adsorbed surfactant within the cavities and forming a comparable smooth boundary condition. The adsorption of surfactant has a significant influence on the roughness of the fluid boundary. The fluid boundary

ACKNOWLEDGMENTS The authors greatly appreciate the financial support of the National Natural Science Foundation of China (grant no. 51574269), the project supported by the National Science Foundation for Distinguished Young Scholars of China (grant no. 51625403), the Important National Science and Technology Specific Projects of China (grant no. 2016ZX05011-003), and Fundamental Research Funds for the Central Universities (grant no. 15CX08004A). P.Z. thanks the Chinese Postdoctoral Science Foundation (grant no. 2017M620297) and the Natural Science Foundation of Shandong Province of China for support (grant no. ZR2017BEE015). Allocations of computer time from the 8118


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Langmuir

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Supercomputing Centre in the Computer Network Information Centre at the Chinese Academy of Sciences are gratefully acknowledged.

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Effect of Aggregation and Adsorption Behavior on the Flow Resistance

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