Molecular Dynamics Simulation of Binary Fluid in a Nanochannel Shanta Mullick, Y. Pathania, and P. K. Ahluwalia Citation: AIP Conf. Proc. 1393, 87 (2011); doi: 10.1063/1.3653622 View online: http://dx.doi.org/10.1063/1.3653622 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1393&Issue=1 Published by the American Institute of Physics.

Related Articles Shear-induced particle migration in binary colloidal suspensions Phys. Fluids 20, 043306 (2008) Particle concentration and tube size dependence of viscosities of Al2O3-water nanofluids flowing through microand minitubes Appl. Phys. Lett. 91, 243112 (2007) Dynamics of viscoelastic fluid filaments in microfluidic devices Phys. Fluids 19, 073103 (2007) On three-dimensional linear stability of Poiseuille flow of Bingham fluids Phys. Fluids 15, 2843 (2003) Laser induced fluorescence measurements of dissolved oxygen concentration fields near air bubble surfaces Rev. Sci. Instrum. 71, 3494 (2000)

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Molecular Dynamics Simulation of Binary Fluid in a Nanochannel Shanta Mullick*, Y. Pathania†, P. K. Ahluwalia* *Department of Physics, Himachal Pradesh University, SummerHill, Shimla - 171005 †Chitkara University, Atal Shiksha Kunj, Atal Nagar, Barotiwala, Dist Solan, Himachal Pradesh – 174103 Abstract. This paper presents the results from a molecular dynamics simulation of binary fluid (mixture of argon and krypton) in the nanochannel flow. The computational software LAM M PS is used for carrying out the molecular dynamics simulations. Binary fluids of argon and krypton with varying concentration of atom species were taken for two densities 0.65 and 0.45. The fluid flow takes place between two parallel plates and is bounded by horizontal walls in one direction and periodic boundary conditions are imposed in the other two directions. To drive the flow, a constant force is applied in one direction. Each fluid atom interacts with other fluid atoms and wall atoms through Week-ChandlerAnderson (WCA) potential. The velocity profile has been looked at for three nanochannel widths i.e for 12σ, 14σ and16σ and also for the different concentration of two species. The velocity profile of the binary fluid predicted by the simulations agrees with the quadratic shape of the analytical solution of a Poiseuille flow in continuum theory. Keywords: Nanochannel, M olecular Dynamics, Velocity, Poiseuille flow. PACS : 47.11.M n, 47.27.nd

on the velocity profile of the binary fluid, taken as the mixture of the inert gases Ar and Kr for varying concentration of the two species and subsequent study of variation in viscosity with concentration.

INTRODUCTION Nanomaterial and nanodevices are of great interest these days because of their novel applications [1,2,3]. Such devices use many innovative constructs such as nanochannels for many applications. The present work has been undertaken to understand the flow of binary fluids in nanochannels. Molecular Dynamics (MD) simulation is one of the effective practical techniques to simulate flow of fluids in nano channels [2]. MD Simulation presented is modeled as a Poiseuille flow [4,5] which is the best tool for a systematic study of density, velocity and temperature profile in a nanochannel leading to estimation of viscosity and thermal conductivity. In a Poiseuille flow the fluid is driven through a long, straight and rigid channel formed by wall atoms which can at most oscillate about their mean positions by imposing a pressure difference between two ends of the channel. Focus of this paper is to study the effect of the width of the nanochannel and force applied in the direction of flow

SIMULATION DETAILS The MD simulations reported here were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)[6]. The binary fluid mixture (of varying concentrations of Ar and Kr atoms) was moving in a nanochannel bounded by two solid walls subject to a streaming driving force at the inlet. The simulation region is a three dimensional box with the size of Lx=10σ, Ly =20σ, and Lz=10σ. The fluid atoms and the wall atoms were arranged in an fcc lattice with each atom having a mass of m=1.0 in dimensionless units. However, the density of the wall atoms was 0.85, which is always chosen higher than the densities of the fluid atoms. The simulations were run using the Week-Chandler-Anderson (WCA) potential both among the fluid atoms and the wall atoms. The interaction parameters for the Ar, Kr and their mixture are given in Table 1. Velocity verlet algorithm was used for integrating the equations of motion with a timestep of 0.005 and run time 100000 timesteps ≈ 10-9 s, data was time averaged over 100 timestep . To drive the flow, a constant force Fe was applied

TABLE 1. Lenanrd- Jones parameter for Ar/Ar, Kr/Kr and Ar- Kr interactions in reduced units(*) Interaction σ* ϵ* Ar-Ar 1 1 Kr-Kr 1.067 1.394 Ar-Kr 1.033 1.180

International Conference on Advances in Condensed and Nano Materials (ICACNM-2011) AIP Conf. Proc. 1393, 87-88 (2011); doi: 10.1063/1.3653622 © 2011 American Institute of Physics 978-0-7354-0963-7/$30.00

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TABLE 2 Viscosity of the binary mixture with various concentration and channel width in reduced units(*) Concentration ᶯ(Ly =12σ) ᶯ(Ly =14σ) ᶯ(Ly =16σ) (Kr) 0.0 181.39 201.58 239.08 0.2 201.72 252.77 271.00 0.4 241.23 286.93 323.73 0.6 278.23 307.72 361.73 0.8 305.88 355.86 396.19 1.0 362.79 395.65 449.72

on the y-z plane in the x-direction,. The values of Fe were chosen to keep the temperature from increasing so as not to cause walls to break down thermally. The wall atoms were kept in place using a combination of harmonic restoring forces and atomic re-centering that kept the center of mass of each layer constant in the y direction. The restoring forces were modelled by a restoring potential defined as

φ=

1 k ri rei 2 2

, where rei is

the initial site of atom i and k is the spring constant. A value of k=57.15 was used to ensure optimal heat transfer between wall and fluid atoms, and to keep fluid atoms from penetrating the wall. To allow the fluid to dissipate heat, the walls were kept at a constant temperature of 0.722 using a Gaussian thermostat.

We note in Figure 1(a) that an increase in the mean velocity is due to both decrease in ρ and increase in Ly . for Ly = 14σ and ρ=0.65) on the velocity profile figure 1(b). It is interesting that velocity profile appears as expected. We also looked at the effect of the increasing force (Fe = 0.1, 0.2, 0.3 and 0.4). It was found that the mean velocity also increases as the force at the inlet is increased. Thereafter, we looked at the effect of the varying concentration of the Kr (0% to 100% of Kr in the binary fluid in the step of 10%) on the velocity profile. We noted that as the concentration of the Kr is increased the mean velocity decreases and the mean velocity of the pure Kr is less than that of the pure Ar figure1(c). Further, we calculated the viscosity for different concentration by fitting the simulated velocity profile to analytical velocity profile NavierStoke equation, vx (y) = [ ρgL2 y /2η ] [1 / 4 (y 1 / 2 )2 ] . It was

RESULTS AND DISCUSSION In our analysis we first looked at the steady value of the streaming velocity v x. The velocity profiles of each simulation for different nanochannel widths and densities are shown in figure 1(a),(b) and (c). These agree with the quadratic shape of the analytic solution of the Poiseuille flow[7].

found that for the different channel width the viscosity shows an increasing trend with concentration [table-2].

ACKNOWLEDGMENTS Shanta M ullick thanks UGC Special Assistance Programme for the award of project fellowship to undertake this work.

REFERENCES 1. X. Chen, G. Cao, A. Han, V. K. Punyamurtula, L. Liu, P. J. Culligan, T. Kim and Y. Qiao, Nano letters, 2988 (8), (2008). 2. A. S. Ziarani and A. A. M ohamad., M icrofluid Nanofluid, 12 (2), (2005). 3. Y. Li, J. Xu, D. Li, M icrofluid Nanofluid, 1011(9),(2010). 4. Jeremy Fried. Numerical Simulation of Viscous flow: A Study of M olecular Dynamics and Computational Fluid Dynamics. M aster's Thesis, Virginia Polytechnic Institute and State University, (2007). 5. Tim Sirk. Numerical Simulation of nanoscale flow: A M olecular Dynamics Study of drag. M aster's Thesis, Virginia Polytechnic,Institute and State University, (2006). 6. http://lammps.sandia.gov 7. J. Zhang ,B. D. Todd and K. P. Travis, J.Chem.Phys 10780, (121),(2004).

FIGURE 1. (a) Streaming velocity plot for two different densities and varying channel widths (b) effect of applied force Fe on the velocity profile (c) effect of the atom species concentration on the velocity profile

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Related Articles Shear-induced particle migration in binary colloidal suspensions Phys. Fluids 20, 043306 (2008) Particle concentration and tube size dependence of viscosities of Al2O3-water nanofluids flowing through microand minitubes Appl. Phys. Lett. 91, 243112 (2007) Dynamics of viscoelastic fluid filaments in microfluidic devices Phys. Fluids 19, 073103 (2007) On three-dimensional linear stability of Poiseuille flow of Bingham fluids Phys. Fluids 15, 2843 (2003) Laser induced fluorescence measurements of dissolved oxygen concentration fields near air bubble surfaces Rev. Sci. Instrum. 71, 3494 (2000)

Additional information on AIP Conf. Proc. Journal Homepage: http://proceedings.aip.org/ Journal Information: http://proceedings.aip.org/about/about_the_proceedings Top downloads: http://proceedings.aip.org/dbt/most_downloaded.jsp?KEY=APCPCS Information for Authors: http://proceedings.aip.org/authors/information_for_authors

Downloaded 23 Jan 2012 to 130.127.238.233. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions

Molecular Dynamics Simulation of Binary Fluid in a Nanochannel Shanta Mullick*, Y. Pathania†, P. K. Ahluwalia* *Department of Physics, Himachal Pradesh University, SummerHill, Shimla - 171005 †Chitkara University, Atal Shiksha Kunj, Atal Nagar, Barotiwala, Dist Solan, Himachal Pradesh – 174103 Abstract. This paper presents the results from a molecular dynamics simulation of binary fluid (mixture of argon and krypton) in the nanochannel flow. The computational software LAM M PS is used for carrying out the molecular dynamics simulations. Binary fluids of argon and krypton with varying concentration of atom species were taken for two densities 0.65 and 0.45. The fluid flow takes place between two parallel plates and is bounded by horizontal walls in one direction and periodic boundary conditions are imposed in the other two directions. To drive the flow, a constant force is applied in one direction. Each fluid atom interacts with other fluid atoms and wall atoms through Week-ChandlerAnderson (WCA) potential. The velocity profile has been looked at for three nanochannel widths i.e for 12σ, 14σ and16σ and also for the different concentration of two species. The velocity profile of the binary fluid predicted by the simulations agrees with the quadratic shape of the analytical solution of a Poiseuille flow in continuum theory. Keywords: Nanochannel, M olecular Dynamics, Velocity, Poiseuille flow. PACS : 47.11.M n, 47.27.nd

on the velocity profile of the binary fluid, taken as the mixture of the inert gases Ar and Kr for varying concentration of the two species and subsequent study of variation in viscosity with concentration.

INTRODUCTION Nanomaterial and nanodevices are of great interest these days because of their novel applications [1,2,3]. Such devices use many innovative constructs such as nanochannels for many applications. The present work has been undertaken to understand the flow of binary fluids in nanochannels. Molecular Dynamics (MD) simulation is one of the effective practical techniques to simulate flow of fluids in nano channels [2]. MD Simulation presented is modeled as a Poiseuille flow [4,5] which is the best tool for a systematic study of density, velocity and temperature profile in a nanochannel leading to estimation of viscosity and thermal conductivity. In a Poiseuille flow the fluid is driven through a long, straight and rigid channel formed by wall atoms which can at most oscillate about their mean positions by imposing a pressure difference between two ends of the channel. Focus of this paper is to study the effect of the width of the nanochannel and force applied in the direction of flow

SIMULATION DETAILS The MD simulations reported here were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)[6]. The binary fluid mixture (of varying concentrations of Ar and Kr atoms) was moving in a nanochannel bounded by two solid walls subject to a streaming driving force at the inlet. The simulation region is a three dimensional box with the size of Lx=10σ, Ly =20σ, and Lz=10σ. The fluid atoms and the wall atoms were arranged in an fcc lattice with each atom having a mass of m=1.0 in dimensionless units. However, the density of the wall atoms was 0.85, which is always chosen higher than the densities of the fluid atoms. The simulations were run using the Week-Chandler-Anderson (WCA) potential both among the fluid atoms and the wall atoms. The interaction parameters for the Ar, Kr and their mixture are given in Table 1. Velocity verlet algorithm was used for integrating the equations of motion with a timestep of 0.005 and run time 100000 timesteps ≈ 10-9 s, data was time averaged over 100 timestep . To drive the flow, a constant force Fe was applied

TABLE 1. Lenanrd- Jones parameter for Ar/Ar, Kr/Kr and Ar- Kr interactions in reduced units(*) Interaction σ* ϵ* Ar-Ar 1 1 Kr-Kr 1.067 1.394 Ar-Kr 1.033 1.180

International Conference on Advances in Condensed and Nano Materials (ICACNM-2011) AIP Conf. Proc. 1393, 87-88 (2011); doi: 10.1063/1.3653622 © 2011 American Institute of Physics 978-0-7354-0963-7/$30.00

87 Downloaded 23 Jan 2012 to 130.127.238.233. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions

TABLE 2 Viscosity of the binary mixture with various concentration and channel width in reduced units(*) Concentration ᶯ(Ly =12σ) ᶯ(Ly =14σ) ᶯ(Ly =16σ) (Kr) 0.0 181.39 201.58 239.08 0.2 201.72 252.77 271.00 0.4 241.23 286.93 323.73 0.6 278.23 307.72 361.73 0.8 305.88 355.86 396.19 1.0 362.79 395.65 449.72

on the y-z plane in the x-direction,. The values of Fe were chosen to keep the temperature from increasing so as not to cause walls to break down thermally. The wall atoms were kept in place using a combination of harmonic restoring forces and atomic re-centering that kept the center of mass of each layer constant in the y direction. The restoring forces were modelled by a restoring potential defined as

φ=

1 k ri rei 2 2

, where rei is

the initial site of atom i and k is the spring constant. A value of k=57.15 was used to ensure optimal heat transfer between wall and fluid atoms, and to keep fluid atoms from penetrating the wall. To allow the fluid to dissipate heat, the walls were kept at a constant temperature of 0.722 using a Gaussian thermostat.

We note in Figure 1(a) that an increase in the mean velocity is due to both decrease in ρ and increase in Ly . for Ly = 14σ and ρ=0.65) on the velocity profile figure 1(b). It is interesting that velocity profile appears as expected. We also looked at the effect of the increasing force (Fe = 0.1, 0.2, 0.3 and 0.4). It was found that the mean velocity also increases as the force at the inlet is increased. Thereafter, we looked at the effect of the varying concentration of the Kr (0% to 100% of Kr in the binary fluid in the step of 10%) on the velocity profile. We noted that as the concentration of the Kr is increased the mean velocity decreases and the mean velocity of the pure Kr is less than that of the pure Ar figure1(c). Further, we calculated the viscosity for different concentration by fitting the simulated velocity profile to analytical velocity profile NavierStoke equation, vx (y) = [ ρgL2 y /2η ] [1 / 4 (y 1 / 2 )2 ] . It was

RESULTS AND DISCUSSION In our analysis we first looked at the steady value of the streaming velocity v x. The velocity profiles of each simulation for different nanochannel widths and densities are shown in figure 1(a),(b) and (c). These agree with the quadratic shape of the analytic solution of the Poiseuille flow[7].

found that for the different channel width the viscosity shows an increasing trend with concentration [table-2].

ACKNOWLEDGMENTS Shanta M ullick thanks UGC Special Assistance Programme for the award of project fellowship to undertake this work.

REFERENCES 1. X. Chen, G. Cao, A. Han, V. K. Punyamurtula, L. Liu, P. J. Culligan, T. Kim and Y. Qiao, Nano letters, 2988 (8), (2008). 2. A. S. Ziarani and A. A. M ohamad., M icrofluid Nanofluid, 12 (2), (2005). 3. Y. Li, J. Xu, D. Li, M icrofluid Nanofluid, 1011(9),(2010). 4. Jeremy Fried. Numerical Simulation of Viscous flow: A Study of M olecular Dynamics and Computational Fluid Dynamics. M aster's Thesis, Virginia Polytechnic Institute and State University, (2007). 5. Tim Sirk. Numerical Simulation of nanoscale flow: A M olecular Dynamics Study of drag. M aster's Thesis, Virginia Polytechnic,Institute and State University, (2006). 6. http://lammps.sandia.gov 7. J. Zhang ,B. D. Todd and K. P. Travis, J.Chem.Phys 10780, (121),(2004).

FIGURE 1. (a) Streaming velocity plot for two different densities and varying channel widths (b) effect of applied force Fe on the velocity profile (c) effect of the atom species concentration on the velocity profile

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