Driving mechanisms and streamwise homogeneity in molecular dynamics simulations of nanochannel flows

In molecular dynamics simulations, nanochannel flows are usually driven by a constant force, that aims to represent a pressure difference between inlet and outlet, and periodic boundary conditions are applied in the streamwise direction resulting in an homogeneous flow. The homogeneity hypothesis can be eliminated adding reservoirs at the inlet and outlet of the channel which permits us to predict streamwise variation of flow properties. It also opens the door to drive the flow by applying a pressure gradient instead of a constant force. We analyze the impact of these modeling modifications in the prediction of the flow properties, and we show when they make a difference with respect to the standard approach. It turns out that both assumptions are irrelevant when low pressure differences are considered, but important differences are observed at high pressure differences. They include the density and velocity variation along the channel (the mass flow rate is constant) but, more importantly, the temperature increase and slip length decrease. Because viscous heating is important at high shear rates, these modeling issues are also linked to the use of thermostating procedures. Specifically, selecting the region where the thermostat is applied has a critical influence on the results. Whereas in the traditional homogeneous model the choices are limited to the fluid and/or the wall, in the inhomogeneous cases the reservoirs are also available, which permits us to leave the region of interest, the channel, unperturbed.

Figure 1

Traditional molecular dynamics model of an homogeneous nanochannel flow. Fluid particles are shown in blue and solid particles in red and black.

Figure 2

(a) New configuration suggested in this work for inhomogeneous MD simulations of nanochannel flows. Fluid particles in the reservoirs (in green) are thermostated and allowed to move freely in the $y$ direction. The properties of the fluid inside the channel (atoms in blue) varies along the $x$ direction. Solid particles are shown in red. (b) Alternative configuration where vertical motion is constrained in the left and right reservoirs by extensions of the channel walls.

Figure 3

Averaged fluid profiles in the section $x=150\sigma$ across the flow direction, obtained with the SH (black solid line) and the SIFD-CR model (red dashed line), for an applied force $f_x=0.020\epsilon /m\sigma$ and $L_x=200\sigma$: (a) fluid density, (b) temperature, (c) streaming velocity, and (d) pressure. The dotted green curves in panels (b) and (c) are the fits of the homogeneous temperature [Eq. (19)] and velocity [Eq. (15)] profiles, respectively (see text). Vertical dashed lines indicate the position of the innermost walls layers.

Figure 4

Averaged fluid profiles in the plane $y=0$ along the flow direction, obtained with the SH (black line) and the SIFD-CR model for different applied force values: (a) fluid density, (b) temperature, (c) streaming velocity, and (d) pressure. Vertical dashed lines indicate the entrance and exit of the channel.

Figure 5

(a) Velocity and (b) temperature profiles across different channel sections obtained using the SIFD-CR model with a force $f_x=0.02\epsilon /m\sigma$ in a channel of length $L_x=400\sigma$. The eight curves correspond to sections from $x=25\sigma$ to $x=375\sigma$ (from bottom to top, in successive steps of $50\sigma )$. Inset in (a) shows the velocity profile in $x=75\sigma$ for a force $f_x=0.04\epsilon /m\sigma$ in a channel of length $L_x=400\sigma$ (empty circles), together with the best quadratic [Eq. (15), green curve] and hyperbolic [Eq. (20), red curve] fits. Dashed curves in (b) are the fits of temperature profiles with the form in Eq. (22).

Figure 6

Slip length calculated along the flow direction for the SH (black dashed curve) and SIFD-CR models with different $f_x$. In the inset, the shear rate distributions along the channel for different values of $f_x$ are shown. The squared black symbols correspond to simulations in which the fluid is thermostated (see text).

Figure 7

Averaged fluid profiles in the plane $y=0$ along the flow direction, obtained with the SIFD model: (a) density, (b) temperature, (c) streaming velocity, and (d) pressure. Solid and dashed curves correspond to closed reservoirs (SIFD-CR) and open reservoirs (SIFD-OR) model, respectively.

Figure 8

Velocity distribution across the channel in reservoir region $\left(x=-25\sigma \right)$ with $f_x=0.02\epsilon /m\sigma$. Solid and dashed curves correspond to closed reservoirs (SIFD-CR) and open reservoirs (SIFD-OR) model, respectively.

Figure 9

Averaged fluid profiles in the plane $y=0$ along the flow direction, obtained with the SIPD model: (a) density, (b) temperature, (c) streaming velocity, and (d) pressure.

Figure 10

Averaged fluid profiles across different sections of a channel of length $L_x=200\sigma$, obtained with the SIPD model and a pressure difference $\mathrm{\Delta }p=6.0\epsilon /{\sigma }^3$: $x=25\sigma$ (black curves), $x=75\sigma$ (blue curves), $x=125\sigma$ (red curves), and $x=175\sigma$ (green curves): (a) density, (b) temperature, (c) streaming velocity, and (d) pressure. Dashed curves in (b) are the best fits for temperature profiles with the form in Eq. (22).

Figure 11

Left panel: Pressure versus fluid density obtained for various pressure differences $\mathrm{\Delta }p$. Black squares are extracted from the phase diagram reported in Ref. [55] from MD simulations at a temperature of $1.15\epsilon /K_B$. Right panel: Viscosity along the channel for different $\mathrm{\Delta }p$. In the inset we compare the evolution of $\mu$ with fluid density in these same simulations to the MD results of [56] for a temperature of $1.23\epsilon /K_B$.

Figure 12

Open symbols: Velocity profile across section $x=175\sigma$ obtained with a pressure-driven model with $\mathrm{\Delta }p=8.0\epsilon /{\sigma }^3$ and $L_x=200\sigma$. Solid curves are the best quadratic [green curve, Eq. (15)] and hyperbolic [red curve, Eq. (20)] velocity fits.