Molecular Dynamics Simulation of Nanoscale Channel Flows ...downloads.hindawi.com/journals/jnt/2018/4631253.pdf · ResearchArticle Molecular Dynamics Simulation of Nanoscale Channel

Research ArticleMolecular Dynamics Simulation of Nanoscale ChannelFlows with Rough Wall Using the Virtual-Wall Model

Xiaohui Lin Fu-bing Bao Xiaoyan Gao and Jiemin Chen

Institute of Fluid Measurement and Simulation China Jiliang University Hangzhou 310018 China

Correspondence should be addressed to Fu-bing Bao 08a0205073cjlueducn

Received 1 February 2018 Accepted 10 May 2018 Published 24 June 2018

Academic Editor Xiaoke Ku

Copyright copy 2018 Xiaohui Lin et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Molecular dynamics simulation is adopted in the present study to investigate the nanoscale gas flow characteristics in roughchannels -e virtual-wall model for the rough wall is proposed and validated -e computational efficiency can be improvedgreatly by using this model especially for the low-density gas flow in nanoscale channels -e effect of roughness elementgeometry on flow behaviors is then studied in detail -e fluid velocity decreases with the increase of roughness element heightwhile it increases with the increases of element width and spacing

1 Introduction

Micronano-electromechanical systems (MEMSNEMS) havereceived considerable attentions over the past two decadesFluid flows are usually encountered in these systems [1ndash3]Fluid transport and interaction with these systems serve animportant function in system operations [4] Understandingthe behaviors and manipulations of fluids within nanoscaleconfinements is significant for a large number of applications[5ndash7]

-e effect of the wall serves as a distinct feature of fluidflow in micronanoscale-confined devices [8ndash10] -e wallplays an increasing role in fluid flow when decreasing theflow characteristic length scale Barisik and Beskok foundthat in a channel with 5 nm in height 40 of the channel isimmersed in the wall force field [11] -erefore the fluidtransport characteristics such as momentum and energysignificantly deviate from predictions of kinetic theory [11]-erefore the effect of this near-wall force field on thenanoscale channel flow must be understood and evaluated

Molecular dynamics simulation (MD) investigates theinteractions and movements of atoms and molecules usingN-body simulation [12] -is method has been employed bymany researchers in the past to study the liquid flow innanochannels [13ndash16] Recently the MD simulation is also

adopted to investigate the gaseous flow in nanoscale-confinedchannels [11 17ndash19] Barisik and Beskok [11 17] investigatedshear-driven gas flows in nanoscale channels to reveal the gas-wall interaction effects for flows in the transition and freemolecular regimes Hui and Chao [18] studied the gas flows innanochannels with the Janus interface and found that thetemperature has a significant influence on the particle numbernear the hydrophilic surface Recently Babac and Reese [19]investigated classical thermosize effects by applying a tem-perature gradient within the different-sized domains

In some MD simulations idealized-wall models are con-sidered -e interactions of fluid-wall atoms are usually con-sidered as functions for example the diffuse and specularreflections Maxwellrsquos scattering kernel [20] or CercignanindashLampis model [21] -ese idealized-wall models are feasible insome specific situations However when we study the detailedflow behaviors in the rear-wall region the atomic-wall modelmust be considered But the atomic-wall model is expensiveboth in computational time and memory In confined channelflows most atoms are requisite to describe the atomic wall-enumber of wall atoms is much larger than that of fluid mol-ecules -is drawback is particularly fatal for the gas flow Forexample Barisik et al [22] studied a nanoscale Couette flow atKn 10 -e simulation box is 162nmtimes 324nmtimes 162nm Intheir study the number of gas molecule is 4900 while the

HindawiJournal of NanotechnologyVolume 2018 Article ID 4631253 7 pageshttpsdoiorg10115520184631253

number of wall atom is 903003 As a result most of thecomputational resource is consumed on the computation ofwall atoms

Recently Qian et al [23] proposed a virtual-wall model fortheMD simulation to reduce the computing time-e unit cellstructures are infinite repetitive in the atomic wall As a resultthe force on a fluid molecule fromwall molecules is periodical-is force was first calculated and stored in memory Duringthe simulation when a fluidmoleculemoves into the near-wallregion the force on this fluid molecule from wall moleculescan be determined directly according to the position of themolecule relative to the wall -e near-wall region here refersto the region near the wall with distance smaller than the cutoffradius Excessive calculations of fluid-wall interactions can beavoided and the computing time can be reduced drastically-e time reduction is more significant for lower fluid densityin nanoscale channels

In present study the virtual-wall model is adopted todescribe the rough wall -e remainder of this paper isorganized as follows Section 2 introduces the MD simu-lation and the virtual-wall model Section 3 describes theapplication of this model to the rough wall Finally Section 4elaborates the conclusions of the study

2 MD Simulation and Virtual-Wall Model

In the present MD simulation interactions between fluid-fluid atoms and fluid-wall atoms are both described usingthe truncated and shifted LennardndashJones (LJ) 12-6 potentialgiven as follows

V rij1113872 1113873

4ε σrij

1113874 111387512minus σ

rij1113874 1113875

6minus σ

rc1113874 1113875

12+ σ

rc1113874 1113875

61113890 1113891 rij le rc

0 rij gt rc

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(1)

where rij is the intermolecular distance between atoms i andj ε is the potential well depth σ is the atomic diameter and rcis the cutoff radius LorentzndashBerthelot mixing rule [24] isemployed to calculate the LJ parameters between fluid-wallatoms

In the virtual-wall model the force on a fluid atom fromwall atoms can be expressed as

F 1113944N

i

minusnablaVi( 1113857 (2)

where N is the number of wall atoms which interact with thefluid atom -e atomic wall is composed of FCC lattices andthe unit cell structures in repetition When wall atoms arefixed to their lattice point the force on the fluid atom isperiodic in both x and z directions For example the force ofa fluid molecule located at x y and z is exactly the same asthe force of the same molecule located at x+ iL y and z+ kLwhere i and k are integers and L is the lattice constant If theforce distributions in the unit cuboid domain (Ltimes rc times L) areknown then the force can be determined anywhere else-isis the core concept of the virtual-wall model

-e virtual-wall model for the smooth wall is first ex-amined Without losing generality gas argon flow confinedbetween FCC platinum walls is considered -e walls arealong the xz plane and the simulation box are periodic inboth x and z directions For argon-argon interactions σAr andεAr are 03405nmand 1198kB respectively For argon-platinuminteractions σAr-Pt is 03085nm and εAr-Pt is 648kB accordingto the LorentzndashBerthelot mixing rule [24] In this study rc isset as 0851nm which is approximately equal to 25σAr -emasses of argon and platinum atoms are 664times10minus26 kg and324times10minus25 kg respectively -ese parameters have been vali-dated in previous studies [25 26]

-e simulation box is set to be 409 nmtimes 171 nmtimes 409 nmin x y and z directions A force of 0008εArσAr is acted on eachgas molecule as an external force [27] to drive the gas to flow inthe nanoscale channel -e atomic-wall model is also carriedout here to make a comparison -e thickness of the wall is118nm which is larger than the cutoff radius -e latticeconstant of the FCC platinum lattice is 0393nm

In the MD simulation the neighbor-list method is used tocalculate the force between atoms while the velocity-Verletalgorithm is adopted to integrate the equations of motion [28]-e timestep in the simulation is set to be 108 fs -e first1 million steps are used to equilibrate the system and another5 million steps are used to accumulate properties in the ydirection with the bin size to be 00614nm -e Langevinthermostat method [29] is employed to control the gas tem-perature before equilibrium Only thermal velocities are used tocompute the temperature and pressure -e above parametersand techniques are adopted in all simulations

-eopen-sourceMDcode called large-scale atomicmolecularmassively parallel simulator (LAMMPS) [30] developed bySandia National Laboratories is adopted to carry out theMD simulations

-e density and velocity profiles across the nanoscalechannel calculated using the atomic- and virtual-wall modelsare compared in Figure 1 Perfect agreement between thesetwo models can be found which indicates that the virtual-wall model works well in the MD simulation

In order to compare the computational time these twosimulations are performed on a single Inter i7-4790K CPUprocessor -e computational time for the virtual-wallmodel is 04 h while for the atomic-wall model the timeis 675 h-e virtual-wall model is muchmore efficient in thepresent case

3 Rough Wall Simulations

31 Virtual-Wall Model for the Rough Wall From themicropoint of view all walls are rough Surface roughnessplays an important role in fluid flow and heat transfer [31]So in the present study the virtual-wall model is adopted todescribe the rough wall

In the present study platinum atom cuboids on thesmooth atomic wall are used to represent the roughnesselement as illustrated in Figure 2 -e roughness element isperiodic in both x and z directions -e geometry of theroughness element is shown in Figure 2(b) -e height of theroughness element is h and the widths in x and z directions

2 Journal of Nanotechnology

are both l -e spaces between two elements in x and zdirections are both L

In order to perform the virtual-wall model a unit cuboidis first introduced as shown in Figure 2 -e rough wall canbe considered as the close-packed array of this unit cuboid-e size of the unit cuboid is LtimesHtimes L where H h+ rcFluid molecules interact with wall atoms only when they arelocated within these cuboids When fluid molecules areoutside these cuboids the distances are larger than rc and nointeractions between fluid and wall atoms are needed

-e cuboid is periodic in both x and z directions-erefore the force of a fluid molecule located at x y and zis exactly the same as the force of the same molecule locatedat x+ iL y and z+ kL where i and k are integers If the forcedistribution in the unit cuboid domain (LtimesHtimes L) is known

then the force on a molecule anywhere else can be deduced-e unit cuboid domain is then divided intoMXtimesMYtimesMZbins and the forces in each bin are calculated and stored inthe memory [23] During the simulation the correspondingforce of a fluid molecule located in the near-wall region iscalled directly from memory according to its position

-e virtual-wall model for the rough wall is first vali-dated Argon molecules are supposed to flow betweennanoscale rough platinum walls -e simulation setup is thesame as in Section 2 For the roughness element h l 2aand L 4a where a is the lattice constant of the FCCplatinum lattice which is 0393 nm In the simulation gasdensity is set to be 717 kgm3 -e Knudsen number whichis defined as the ratio of gas mean free path to the channelheight is 095 and the flow is in transition regime In order

y (nm)0 4 8 12 16

0

40

80

120

160

Atomic wallVirtual wall

ρ (k

g∙m

ndash3)

(a)

y (nm)0 4 8 12 16


v x (m

middotsminus1)

0

50

100

150

(b)

Figure 1 Comparisons between the atomic- and virtual-wall models for the smooth wall (a) density profile (b) velocity profile

Y

XZ

(a)

Y

Z X

L

rcl

H

h

(b)

Figure 2 Schematics of the rough wall and the unit cuboid domain (a) axonometric view (b) side view

Journal of Nanotechnology 3

to make a comparison the atomic-wall model is also carriedout here In the simulation 3087 gas argon atoms and218406 wall platinum atoms are used

-e density and velocity profiles of the virtual-wallmodel are shown in Figure 3 -ese profiles are comparedwith the corresponding atomic wall simulation Perfectagreement between these two models can be found which

indicates that the virtual-wall model works well for the gasflows in rough wall channels

-e gaseous flows in nanoscale channels with smoothand rough walls are first compared -e schematic diagramof channel geometry is shown in Figure 4(a) -ree channelsare investigated-e outer channel and the inner channel areboth smooth with channel heights equal to Hprime and Hprime minus 2h

y (nm)0 05 1 15 2 25

0

6

12

18


ρ (k

gmiddotm

minus3)

(a)

0 4 8 12 160

10

20

30

40

50

y (nm)


v x (m

middotsminus1)

(b)

Figure 3 Comparisons between the atomic- and virtual-wall models for the rough wall (a) density profile (b) velocity profile

Hprime Hprime ndash 2h

h

(a)

y (nm)0 4 8 12 16

0

30

60

90

120

Outer channelInner channelRough channel

v x (m

middotsminus1)

(b)

Figure 4 Comparison of gas flows in nanoscale smooth and rough channels


respectively Here h is the height of the roughness element-e third channel is rough with the channel height equal toHprime and the roughness element height is equal to h In thesimulation Hprime is 1535 nm and h is 0786 nm So the heightof the inner channel is 1367 nm -e other parameters arekept the same as in Section 2

-e velocity profiles for these three channels are shownin Figure 4(b) It can be found that the velocity of the roughchannel is much smaller than those of smooth channels It iswell known that in nanoscale channel flows the wall playsan extremely important role in the fluid flow Here in therough channel the total surface area is much larger than thosein smooth channels because of the existence of roughnesselements As a result the collision probability between fluid-wall atoms is larger and more fluid molecules are affected bythe wall in the rough channel So the fluid velocity of gas in therough channel is smaller -e effect of roughness is of greatimportance to nanoscale channel flows

32 Roughness Element with Different Heights -e influencesof roughness element geometry on flow behaviors are thenstudied Roughness elements with different heights are firststudied -e widths l and the spacing L of the roughnesselement are kept the same while the element height h isvariable -ree element heights (h a 2a and 3a) areconsidered

-e velocity profiles of the rough wall with differentelement heights are shown in Figure 5 It can be found fromthe figure that the fluid velocity decreases with the increaseof element height -is is because the total surface area islarger at higher element height According to the explana-tion in Section 31 the wall effect is larger at higher elementheight So the fluid velocity is smaller

Fitting curves are obtained for each velocity profile atdifferent roughness element heights based on the gas ve-locity in the central part of the channel From the fittingcurves we can deduce the slip velocity on the wall conve-niently It can be found from Figure 5 that the slip velocityalso decreases with the increase of element height

33 Roughness Element with Different Widths Roughnesselements with different widths are then studied -e heighth and spacing L of the roughness element are kept the samewhile the width l is variable-ree roughness element widths(l a 2a and 3a) are considered

-e velocity profiles at different roughness elementwidths are shown in Figure 6 It can be found from the figurethat the element width has a great influence on the velocityprofile -e fluid velocity increases with the increase ofelement width -e total surface areas are the same in thesethree cases so are the wall effects according to Section 31However at large roughness width for example l 3a thegap between two roughness elements is small As a result itis hard for the gas molecules to enter into the gap because ofthe repulsive force between fluid-wall atoms according to(1) -at is to say the effective surface area diminishes Sothe fluid velocity increases in the rough channel with theincrease of the element width

-e fitting curves obtained for each velocity profile atdifferent roughness element widths are also shown in Fig-ure 6 It can be found that the slip velocity increases with theincrease of the element width

34 Roughness Element with Different Spacings Roughnesselements with different spacings are studied at last -eheight h and width l of the roughness element are kept thesame while the spacing L is variable -ree roughness

y (nm)

v x (m

middotsminus1)

0 4 8 12 160

15

30

45

60

h = ah = 2a

h = 3aFitting curve

Figure 5 Velocity profiles at different roughness element heights

y (nm)0 4 8 12 16

0

15

30

45

60

l = al = 2a

l = 3aFitting curve

v x (m

middotsminus1)

Figure 6 Velocity profiles at different roughness element widths


element spacings (L 4a 6a and 8a) are considered Otherparameters are kept the same as introduced above

-e velocity profiles of rough walls with different ele-ment spacings are shown in Figure 7 It can be found fromthe figure that the fluid velocity increases with the increase ofelement spacing -is is because the total surface area issmaller at larger element spacing According to the expla-nation in Section 31 the wall effect is smaller at largerelement spacing so the fluid velocity is larger

-e corresponding fitting curves for each velocity profileat different roughness element spacings are also shown inFigure 7 -e results show that the greater the spacing thelarger the velocity slip

4 Conclusions

-e wall plays an extremely important role in the nanoscalechannel flows In the present study MD simulation is carriedout to investigate the nanoscale gas flows in rough channels-e virtual-wall model for the rough wall is proposed and itsvalidity is confirmed -e computational efficiency can beimproved greatly by using this model especially for the low-density gas flow in nanoscale channels-e effects of roughnesselement geometry on flow behaviors are then studied in detail

From the simulations we found that the total surface areais of great importance in nanoscale channel flows -e fluidvelocity is inversely proportional to the total surface area -efluid velocity and velocity slip decrease with the increase ofroughness element height while they increase with the in-crease of element width and spacing

Data Availability

-edata used to support the findings of this study are availablefrom the corresponding author upon request

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the National Key RampD Pro-gram of China (Grant no 2017YFB0603701) and NationalNatural Science Foundation of China (Grant nos 11672284and 11602266)

References

[1] M W Collins and C S KonigMicro and Nano Flow Systemsfor Bioanalysis Springer New York NY USA 2012

[2] M Z Yu X T Zhang G D Jin J Z Lin andM SeipenbuschldquoA new moment method for solving the coagulation equationfor particles in Brownian motionrdquo Aerosol Science andTechnology vol 42 no 9 pp 705ndash713 2008

[3] M Gad-el-HakMEMS Introduction and Fundamentals CRCPress Boca Raton FL USA 2010

[4] B-Y Cao J Sun M Chen and Z Y Guo ldquoMolecular mo-mentum transport at fluid-solid interfaces in MEMSNEMSa reviewrdquo International Journal of Molecular Sciences vol 10no 11 pp 4638ndash4706 2009

[5] J Z Lin P F Lin and H J Chen ldquoResearch on the transportand deposition of nanoparticles in a rotating curved piperdquoPhysics of Fluids vol 21 no 12 article 122001 2009

[6] G Karniadakis A Beskok and N R Aluru Microflows andNanoflows Fundamentals and Simulation Springer NewYork NY USA 2006

[7] M-Z Yu J-Z Lin and T-L Chan ldquoEffect of precursor loadingon non-spherical TiO2 nanoparticle synthesis in a diffusionflame reactorrdquo Chemical Engineering Science vol 63 no 9pp 2317ndash2329 2008

[8] S ColinMicrofluidics ISTE Ltd and JohnWiley amp Sons IncLondon UK 2013

[9] C-M Ho and Y-C Tai ldquoMicro-electro-mechanical-systems(MEMS) and fluid flowsrdquo Annual Review of Fluid Mechanicsvol 30 pp 579ndash612 1998

[10] TM Squires and S R Quake ldquoMicrofluidics fluid physics at thenanoliter scalerdquo Reviews of Modern Physics vol 77 p 977 2005

[11] M Barisik and A Beskok ldquoMolecular dynamics simulationsof shear-driven gas flows in nano-channelsrdquoMicrofluidics andNanofluidics vol 11 pp 611ndash622 2011

[12] D Frenkel and B Smit Understanding Molecular SimulationFrom Algorithms to Applications Academic Press LondonUK 2002

[13] J L Barrat and L Bocquet ldquoLarge slip effect at a nonwettingfluid-solid interfacerdquo Physical Review Letters vol 82 p 46711999

[14] M Majumder N Chopra R Andrews et al ldquoNanoscalehydrodynamics enhanced flow in carbon nanotubesrdquoNaturevol 438 pp 44ndash46 2005

[15] G Hummer J C Rasaiah and J P Noworyta ldquoWaterconduction through the hydrophobic channel of a carbonnanotuberdquo Nature vol 414 pp 188ndash190 2001

[16] M Cieplak J Koplik and J R Banavar ldquoNanoscale fluidflows in the vicinity of patterned surfacesrdquo Physical ReviewLetters vol 96 article 114502 2006

[17] M Barisik and A Beskok ldquoSurfacendashgas interaction effects onnanoscale gas flowsrdquo Microfluidics and Nanofluidics vol 13no 5 pp 789ndash798 2012

y (nm)

v x (m

timessndash1

)

0 4 8 12 160

15

30

45

60

L = 4aL = 6a

L = 8aFitting curve

Figure 7 Velocity profiles at different roughness element spacings


[18] X Hui and L Chao ldquoMolecular dynamics simulations of gasflow in nanochannel with a Janus interfacerdquo AIP Advancesvol 2 no 4 article 042126 2012

[19] G Babac and J M Reese ldquoMolecular dynamics simulation ofclassical thermosize effectsrdquo Nanoscale and Microscaleermophysical Engineering vol 18 no 1 pp 39ndash53 2014


[21] C Cercignani andM Lampis ldquoKinetic models for gas-surfaceinteractionsrdquo Transport eory and Statistical Physics vol 1pp 101ndash114 1971

[22] M Barisik B Kim and A Beskok ldquoSmart wall model formolecular dynamics simulations of nanoscale gas flowsrdquoComputer Physics Communications vol 7 pp 977ndash993 2010

[23] L J Qian C X Tu and F B Bao ldquoVirtual-wall model formolecular dynamics simulationrdquo Molecules vol 21 no 12p 1678 2016

[24] J Delhommelle and P Millie ldquoIn adequacy of the Lorentz-Berthelot combining rules for accurate predictions of equi-librium properties by molecular simulationrdquo MolecularPhysics vol 99 no 8 pp 619ndash625 2001

[25] J Sun and Z X Li ldquoEffect of gas adsorption on momentumaccommodation coefficients in microgas flows using molec-ular dynamic simulationsrdquoMolecular Physics vol 106 no 19pp 2325ndash2332 2008

[26] B Y CaoM Chen and Z Y Guo ldquoTemperature dependence ofthe tangential momentum accommodation coefficient forgasesrdquoApplied Physics Letters vol 86 no 9 article 091905 2005

[27] J Koplik J R Banavar and J FWillemsen ldquoMolecular dynamicsof Poiseuille flow and moving contact linesrdquo Physical ReviewLetters vol 60 p 1282 1988

[28] D C Rapaport e Art of Molecular Dynamics SimulationCambridge University Press New York NY USA 2004

[29] S Richardson ldquoOn the no-slip boundary conditionrdquo Journalof Fluid Mechanics vol 59 pp 707ndash719 1973

[30] S Plimpton ldquoFast parallel algorithms for short-range mo-lecular dynamicsrdquo Journal of Computational Physics vol 117pp 1ndash19 1995

[31] Q D To C Bercegeay G Lauriat et al ldquoA slip model formicronano gas flows induced by body forcesrdquo Microfluidicsand Nanofluidics vol 8 pp 417ndash422 2010


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Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

number of wall atom is 903003 As a result most of thecomputational resource is consumed on the computation ofwall atoms

Recently Qian et al [23] proposed a virtual-wall model fortheMD simulation to reduce the computing time-e unit cellstructures are infinite repetitive in the atomic wall As a resultthe force on a fluid molecule fromwall molecules is periodical-is force was first calculated and stored in memory Duringthe simulation when a fluidmoleculemoves into the near-wallregion the force on this fluid molecule from wall moleculescan be determined directly according to the position of themolecule relative to the wall -e near-wall region here refersto the region near the wall with distance smaller than the cutoffradius Excessive calculations of fluid-wall interactions can beavoided and the computing time can be reduced drastically-e time reduction is more significant for lower fluid densityin nanoscale channels

In present study the virtual-wall model is adopted todescribe the rough wall -e remainder of this paper isorganized as follows Section 2 introduces the MD simu-lation and the virtual-wall model Section 3 describes theapplication of this model to the rough wall Finally Section 4elaborates the conclusions of the study

2 MD Simulation and Virtual-Wall Model

In the present MD simulation interactions between fluid-fluid atoms and fluid-wall atoms are both described usingthe truncated and shifted LennardndashJones (LJ) 12-6 potentialgiven as follows

V rij1113872 1113873

4ε σrij

1113874 111387512minus σ

rij1113874 1113875

6minus σ

rc1113874 1113875

12+ σ

rc1113874 1113875

61113890 1113891 rij le rc

0 rij gt rc

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(1)

where rij is the intermolecular distance between atoms i andj ε is the potential well depth σ is the atomic diameter and rcis the cutoff radius LorentzndashBerthelot mixing rule [24] isemployed to calculate the LJ parameters between fluid-wallatoms

In the virtual-wall model the force on a fluid atom fromwall atoms can be expressed as

F 1113944N

i

minusnablaVi( 1113857 (2)

where N is the number of wall atoms which interact with thefluid atom -e atomic wall is composed of FCC lattices andthe unit cell structures in repetition When wall atoms arefixed to their lattice point the force on the fluid atom isperiodic in both x and z directions For example the force ofa fluid molecule located at x y and z is exactly the same asthe force of the same molecule located at x+ iL y and z+ kLwhere i and k are integers and L is the lattice constant If theforce distributions in the unit cuboid domain (Ltimes rc times L) areknown then the force can be determined anywhere else-isis the core concept of the virtual-wall model

-e virtual-wall model for the smooth wall is first ex-amined Without losing generality gas argon flow confinedbetween FCC platinum walls is considered -e walls arealong the xz plane and the simulation box are periodic inboth x and z directions For argon-argon interactions σAr andεAr are 03405nmand 1198kB respectively For argon-platinuminteractions σAr-Pt is 03085nm and εAr-Pt is 648kB accordingto the LorentzndashBerthelot mixing rule [24] In this study rc isset as 0851nm which is approximately equal to 25σAr -emasses of argon and platinum atoms are 664times10minus26 kg and324times10minus25 kg respectively -ese parameters have been vali-dated in previous studies [25 26]

-e simulation box is set to be 409 nmtimes 171 nmtimes 409 nmin x y and z directions A force of 0008εArσAr is acted on eachgas molecule as an external force [27] to drive the gas to flow inthe nanoscale channel -e atomic-wall model is also carriedout here to make a comparison -e thickness of the wall is118nm which is larger than the cutoff radius -e latticeconstant of the FCC platinum lattice is 0393nm

In the MD simulation the neighbor-list method is used tocalculate the force between atoms while the velocity-Verletalgorithm is adopted to integrate the equations of motion [28]-e timestep in the simulation is set to be 108 fs -e first1 million steps are used to equilibrate the system and another5 million steps are used to accumulate properties in the ydirection with the bin size to be 00614nm -e Langevinthermostat method [29] is employed to control the gas tem-perature before equilibrium Only thermal velocities are used tocompute the temperature and pressure -e above parametersand techniques are adopted in all simulations

-eopen-sourceMDcode called large-scale atomicmolecularmassively parallel simulator (LAMMPS) [30] developed bySandia National Laboratories is adopted to carry out theMD simulations

-e density and velocity profiles across the nanoscalechannel calculated using the atomic- and virtual-wall modelsare compared in Figure 1 Perfect agreement between thesetwo models can be found which indicates that the virtual-wall model works well in the MD simulation

In order to compare the computational time these twosimulations are performed on a single Inter i7-4790K CPUprocessor -e computational time for the virtual-wallmodel is 04 h while for the atomic-wall model the timeis 675 h-e virtual-wall model is muchmore efficient in thepresent case

3 Rough Wall Simulations

31 Virtual-Wall Model for the Rough Wall From themicropoint of view all walls are rough Surface roughnessplays an important role in fluid flow and heat transfer [31]So in the present study the virtual-wall model is adopted todescribe the rough wall

In the present study platinum atom cuboids on thesmooth atomic wall are used to represent the roughnesselement as illustrated in Figure 2 -e roughness element isperiodic in both x and z directions -e geometry of theroughness element is shown in Figure 2(b) -e height of theroughness element is h and the widths in x and z directions







y (nm)0 4 8 12 16

0

40

80

120

160


ρ (k

g∙m

ndash3)

(a)

y (nm)0 4 8 12 16


v x (m

middotsminus1)

0

50

100

150

(b)


Y

XZ

(a)

Y

Z X

L

rcl

H

h

(b)







y (nm)0 05 1 15 2 25

0

6

12

18


ρ (k

gmiddotm

minus3)

(a)

0 4 8 12 160

10

20

30

40

50

y (nm)


v x (m

middotsminus1)

(b)



h

(a)

y (nm)0 4 8 12 16

0

30

60

90

120


v x (m

middotsminus1)

(b)












y (nm)

v x (m

middotsminus1)

0 4 8 12 160

15

30

45

60

h = ah = 2a

h = 3aFitting curve


y (nm)0 4 8 12 16

0

15

30

45

60

l = al = 2a

l = 3aFitting curve

v x (m

middotsminus1)






4 Conclusions



Data Availability




Acknowledgments


References


















y (nm)

v x (m

timessndash1

)

0 4 8 12 160

15

30

45

60

L = 4aL = 6a

L = 8aFitting curve




















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









y (nm)0 4 8 12 16

0

40

80

120

160


ρ (k

g∙m

ndash3)

(a)

y (nm)0 4 8 12 16


v x (m

middotsminus1)

0

50

100

150

(b)


Y

XZ

(a)

Y

Z X

L

rcl

H

h

(b)







y (nm)0 05 1 15 2 25

0

6

12

18


ρ (k

gmiddotm

minus3)

(a)

0 4 8 12 160

10

20

30

40

50

y (nm)


v x (m

middotsminus1)

(b)



h

(a)

y (nm)0 4 8 12 16

0

30

60

90

120


v x (m

middotsminus1)

(b)












y (nm)

v x (m

middotsminus1)

0 4 8 12 160

15

30

45

60

h = ah = 2a

h = 3aFitting curve


y (nm)0 4 8 12 16

0

15

30

45

60

l = al = 2a

l = 3aFitting curve

v x (m

middotsminus1)






4 Conclusions



Data Availability




Acknowledgments


References


















y (nm)

v x (m

timessndash1

)

0 4 8 12 160

15

30

45

60

L = 4aL = 6a

L = 8aFitting curve




















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








y (nm)0 05 1 15 2 25

0

6

12

18


ρ (k

gmiddotm

minus3)

(a)

0 4 8 12 160

10

20

30

40

50

y (nm)


v x (m

middotsminus1)

(b)



h

(a)

y (nm)0 4 8 12 16

0

30

60

90

120


v x (m

middotsminus1)

(b)












y (nm)

v x (m

middotsminus1)

0 4 8 12 160

15

30

45

60

h = ah = 2a

h = 3aFitting curve


y (nm)0 4 8 12 16

0

15

30

45

60

l = al = 2a

l = 3aFitting curve

v x (m

middotsminus1)






4 Conclusions



Data Availability




Acknowledgments


References


















y (nm)

v x (m

timessndash1

)

0 4 8 12 160

15

30

45

60

L = 4aL = 6a

L = 8aFitting curve




















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls













y (nm)

v x (m

middotsminus1)

0 4 8 12 160

15

30

45

60

h = ah = 2a

h = 3aFitting curve


y (nm)0 4 8 12 16

0

15

30

45

60

l = al = 2a

l = 3aFitting curve

v x (m

middotsminus1)






4 Conclusions



Data Availability




Acknowledgments


References


















y (nm)

v x (m

timessndash1

)

0 4 8 12 160

15

30

45

60

L = 4aL = 6a

L = 8aFitting curve




















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







4 Conclusions



Data Availability




Acknowledgments


References


















y (nm)

v x (m

timessndash1

)

0 4 8 12 160

15

30

45

60

L = 4aL = 6a

L = 8aFitting curve




















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




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Molecular Dynamics Simulation of Nanoscale Channel Flows ...downloads.hindawi.com/journals/jnt/2018/4631253.pdf · ResearchArticle Molecular Dynamics Simulation of Nanoscale Channel