Journal of Nanotechnology

Volume 2018, Article ID 4631253, 7 pages

https://doi.org/10.1155/2018/4631253

## Molecular Dynamics Simulation of Nanoscale Channel Flows with Rough Wall Using the Virtual-Wall Model

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

Correspondence should be addressed to Fu-bing Bao; nc.ude.uljc@3705020a80

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

Academic Editor: Xiaoke Ku

Copyright © 2018 Xiaohui Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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

#### 1. Introduction

Micro/nano-electromechanical systems (MEMS/NEMS) have received considerable attentions over the past two decades. Fluid flows are usually encountered in these systems [1–3]. Fluid transport and interaction with these systems serve an important function in system operations [4]. Understanding the behaviors and manipulations of fluids within nanoscale confinements is significant for a large number of applications [5–7].

The effect of the wall serves as a distinct feature of fluid flow in micro/nanoscale-confined devices [8–10]. The wall plays an increasing role in fluid flow when decreasing the flow characteristic length scale. Barisik and Beskok found that, in a channel with 5 nm in height, 40% of the channel is immersed in the wall force field [11]. Therefore, the fluid transport characteristics, such as momentum and energy, significantly deviate from predictions of kinetic theory [11]. Therefore, the effect of this near-wall force field on the nanoscale channel flow must be understood and evaluated.

Molecular dynamics simulation (MD) investigates the interactions and movements of atoms and molecules, using N-body simulation [12]. This method has been employed by many researchers in the past to study the liquid flow in nanochannels [13–16]. Recently, the MD simulation is also adopted to investigate the gaseous flow in nanoscale-confined channels [11, 17–19]. Barisik and Beskok [11, 17] investigated shear-driven gas flows in nanoscale channels to reveal the gas-wall interaction effects for flows in the transition and free molecular regimes. Hui and Chao [18] studied the gas flows in nanochannels with the Janus interface and found that the temperature has a significant influence on the particle number near the hydrophilic surface. Recently, Babac and Reese [19] investigated classical thermosize effects by applying a temperature gradient within the different-sized domains.

In some MD simulations, idealized-wall models are considered. The interactions of fluid-wall atoms are usually considered as functions, for example, the diffuse and specular reflections, Maxwell's scattering kernel [20], or Cercignani–Lampis model [21]. These idealized-wall models are feasible in some specific situations. However, when we study the detailed flow behaviors in the rear-wall region, the atomic-wall model must be considered. But the atomic-wall model is expensive both in computational time and memory. In confined channel flows, most atoms are requisite to describe the atomic wall. The number of wall atoms is much larger than that of fluid molecules. This drawback is particularly fatal for the gas flow. For example, Barisik et al. [22] studied a nanoscale Couette flow at *K*_{n} = 10. The simulation box is 162 nm × 3.24 nm × 162 nm. In their study, the number of gas molecule is 4900, while the number of wall atom is 903003. As a result, most of the computational resource is consumed on the computation of wall atoms.

Recently, Qian et al. [23] proposed a virtual-wall model for the MD simulation to reduce the computing time. The unit cell structures are infinite repetitive in the atomic wall. As a result, the force on a fluid molecule from wall molecules is periodical. This force was first calculated and stored in memory. During the simulation, when a fluid molecule moves into the near-wall region, the force on this fluid molecule from wall molecules can be determined directly, according to the position of the molecule relative to the wall. The near-wall region here refers to the region near the wall with distance smaller than the cutoff radius. Excessive calculations of fluid-wall interactions can be avoided, and the computing time can be reduced drastically. The time reduction is more significant for lower fluid density in nanoscale channels.

In present study, the virtual-wall model is adopted to describe the rough wall. The remainder of this paper is organized as follows. Section 2 introduces the MD simulation and the virtual-wall model. Section 3 describes the application of this model to the rough wall. Finally, Section 4 elaborates 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 using the truncated and shifted Lennard–Jones (LJ) 12-6 potential given as follows:where *r*_{ij} is the intermolecular distance between atoms *i* and *j*, *ε* is the potential well depth, *σ* is the atomic diameter, and *r*_{c} is the cutoff radius. Lorentz–Berthelot mixing rule [24] is employed to calculate the LJ parameters between fluid-wall atoms.

In the virtual-wall model, the force on a fluid atom from wall atoms can be expressed aswhere *N* is the number of wall atoms which interact with the fluid atom. The atomic wall is composed of FCC lattices and the unit cell structures in repetition. When wall atoms are fixed to their lattice point, the force on the fluid atom is periodic in both *x* and *z* directions. For example, the force of a fluid molecule located at *x*, *y*, and *z* is exactly the same as the force of the same molecule located at *x *+* iL*, *y*, and *z *+* kL*, where *i* and *k* are integers and *L* is the lattice constant. If the force distributions in the unit cuboid domain (*L *×* r*_{c}* *×* L*) are known, then the force can be determined anywhere else. This is the core concept of the virtual-wall model.

The virtual-wall model for the smooth wall is first examined. Without losing generality, gas argon flow confined between FCC platinum walls is considered. The walls are along the *xz* plane and the simulation box are periodic in both *x* and *z* directions. For argon-argon interactions, *σ*_{Ar} and *ε*_{Ar} are 0.3405* *nm and 119.8*k*_{B}, respectively. For argon-platinum interactions, *σ*_{Ar-Pt} is 0.3085* *nm and *ε*_{Ar-Pt} is 64.8*k*_{B}, according to the Lorentz–Berthelot mixing rule [24]. In this study, *r*_{c} is set as 0.851* *nm, which is approximately equal to 2.5*σ*_{Ar}. The masses of argon and platinum atoms are 6.64* *×* *10^{−26}* *kg and 3.24* *×* *10^{−25}* *kg, respectively. These parameters have been validated in previous studies [25, 26].

The simulation box is set to be 40.9* *nm* *×* *17.1* *nm* *×* *40.9* *nm in *x*, *y*, and *z* directions. A force of 0.008*ε*_{Ar}*/σ*_{Ar} is acted on each gas molecule as an external force [27] to drive the gas to flow in the nanoscale channel. The atomic-wall model is also carried out here to make a comparison. The thickness of the wall is 1.18* *nm, which is larger than the cutoff radius. The lattice constant of the FCC platinum lattice is 0.393* *nm.

In the MD simulation, the neighbor-list method is used to calculate the force between atoms while the velocity-Verlet algorithm is adopted to integrate the equations of motion [28]. The timestep in the simulation is set to be 10.8* *fs. The first 1 million steps are used to equilibrate the system, and another 5 million steps are used to accumulate properties in the *y* direction, with the bin size to be 0.0614* *nm. The Langevin thermostat method [29] is employed to control the gas temperature before equilibrium. Only thermal velocities are used to compute the temperature and pressure. The above parameters and techniques are adopted in all simulations.

The open-source MD code called large-scale atomic/molecular massively parallel simulator (LAMMPS) [30], developed by Sandia National Laboratories, is adopted to carry out the MD simulations.

The density and velocity profiles across the nanoscale channel calculated using the atomic- and virtual-wall models are compared in Figure 1. Perfect agreement between these two models can be found, which indicates that the virtual-wall model works well in the MD simulation.