On the Comparability of Chemical Structure and Roughness of Nanochannels in Altering Fluid Slippage

Research Article

Austin Chem Eng. 2016; 3(2): 1031.

On the Comparability of Chemical Structure and Roughness of Nanochannels in Altering Fluid Slippage

Misra CA and Bakli C*

Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, India

*Corresponding author: Chirodeep Bakli, Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, India

Received: April 08, 2016; Accepted: May 10, 2016; Published: May 13, 2016


Interfacial hydrodynamic slippage of water depends on both on surface chemistry and roughness. This study tries to connect the effect of chemical property and the physical structure of the surface on the interfacial slippage of water. By performing Molecular Dynamics Simulations (MDS) of Couette flow of water molecules over a reduced Lennard-Jones (LJ) surface, the velocity profile is obtained and extrapolated to get the slip lengths. The slip lengths are measured for various surface-fluid interactions. These interactions are varied by changing the wettability of the surface (characterized by the static contact angle) and its roughness. The slip length variation with the static contact angle as is observed. However, it is also observed that the presence of surface roughness always reduces the slip length and it is proposed that the slip length varies with non-dimensionalized average surface roughness as (1+a*)-2. Thus a relation between the chemical wettability and the physical roughness is established and their coupled interactions modifying slip length is probed.

Keywords: Wettability; Slip length; Roughness


NEMS: Nano Electro Mechanical Systems; LJ: Lennard-Jones; MDS: Molecular Dynamics Simulations; fcc: Face Centered Cubic; SPC/E: Simple Point Charge/ Extended


The flow physics of fluid transport through nanochannels is extremely interesting and intriguing. The surface forces overweigh the volumetric forces at such small length scales, leading to an important role played by the interfacial effects. Thus modifying the surface characteristics of substrates of such channels over nanometer dimensions provides the option to engineer such flows. Study of these flow variations over sub-micron scale is warranted by the advent of research in the areas of Nano Electro Mechanical Systems (NEMS) and Nanoporous Energy Absorption System (NEAS) and also by the urge to study flow of natural fluids in biological membranes. Through extensive molecular dynamics simulations, researchers have explored various aspects of the transport processes and surface interactions concerned with micro and nano scale flows. They have studied the effects of the interface wettability on flow structure, fluid dynamics in surface-nanostructured channels [1], effects of wall lattice-fluid interactions on the density and velocity profiles [2], perturbations in fully developed pressure driven flows [3], slip behavior on substrates with patterned wettability [4], and effects of surface roughness and interface wettability on nanoscale flows [5].

Understanding fluid flow on nano-scale is crucial for designing microfluidic devices, modern developments of nanotechnology like the lab-on-a-chip [6,7], as well as for various applications of porous materials, fluid flow through pores in bio-membranes etc., [8,9]. These works have shown that contrary to the macroscopic hydrodynamic theory, the no slip boundary condition might not necessarily hold true for nano-scale channels. In such cases, the fluid velocity at the surface is more aptly described by a partial slip boundary condition that relates the fluid velocity at the surface to its gradient ∂v/ ∂z in the direction normal to the surface by v=b(∂v/ ∂z), where b is the slip length [10- 12]. This interfacial slip has immense practical applications in micro fluidics, bio-fluid dynamics, and lubrication etc. by virtue of the fact that it reduces viscous friction at the surfaces and amplifies flow rates in pressure driven flows and electro-osmotic flows [13,14]. This also provides potential to generate power from nano-scale devices [15,16]. Thus it becomes imperative to estimate or measure slip length and study its dependence on interfacial parameters. However, there is a lot of disparity between the experimental data reported for the slip length of typical hydrophobic surfaces. The experimental values of slip lengths have been measured ranging from nanometers [17,18] to micrometers [19]. Researchers have explained larger values of slip length to be due to nano-bubble formation at the interface [20], and molecular dynamics simulations of a model LJ system have shown an increase in slip due to this phenomenon. In an attempt to resolve the controversy in the experimental literature, Huang et al have reported a quasi universal dependence of the slip length on the contact angle θc by performing MDS [21]. Although Huang et al have considered rough surfaces in their study they have not analyzed the dependence of slip length on surface roughness. In this work, it is aimed to establish a mathematical relationship between slip length and average surface roughness by performing non-equilibrium MDS of Couette flow of SPC/E rigid simple point charge model of water between two parallel plates made of reduced LJ atoms. By applying a shear boundary condition, the velocity profile is obtained and extrapolated to get the slip length. In order to mimic the atomically rough surface, the attractive part of LJ interaction potential between fluid and surface [22] is modified. To estimate the contact angle, we perform an equilibrium MDS of a droplet of water on the same surface as used in Couette flow simulation. As a result of this work, it is observed that the slip length varies with non-dimensionalized average surface roughness as b* = (1+a*)-2. On the basis of this work, a correction in the formula presented by Huang et al [21] to account for variation in surface roughness is proposed.

Problem Formulation

The simulation system, for Couette flow simulation, is similar to that used by Huang et al [21] and is shown in Figure 1. A channel of height 5nm, bounded by walls made of four layers of reduced LJ atoms arranged in close packed fcc (face-centered cubic) lattice oriented such that (100) face is in contact with water is considered. The lateral dimensions of the walls are 5nm x 5nm. Wall atoms interact with each other through a LJ potential. The LJ interaction parameter between wall atoms σww is taken to be 0.35nm while εww is varied to change the wall fluid interaction and hence the contact angle. The channel is filled with 3584 water molecules SPC/E model (Simple Point Charge/ Extended). This number ensures that the density of water is 1000kg/ for the particular size of the channel considered. Hetero nuclear LJ interactions are determined by standard Lorentz-Berthelot combining rules [23]. Roughness is introduced by modifying the attractive part of the LJ potential as shown in Eq.(1).

U LJ =4 ϵ wl [ ( σ wl r ) 12 ( σ wl r ) 6 f(x,y) ]            (1) MathType@MTEF@5@5@+=feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@6B62@