Variation of momentum accommodation coefficients with pressure drop in a nanochannel

Accommodation coefficients (ACs) are the phenomenological parameters used to evaluate gas-wall interactions. The gas transport through a finite length nanochannel will confront the variation of properties along the length of the channel. A three-dimensional molecular dynamics simulation has been carried out to examine this streamwise inhomogeneity of flow characteristics in a nanochannel. The rarefaction of the flow to the downstream direction is a crucial behavior in a pressure-driven nanochannel flow. This is manifested as the variation in velocity and temperature along the length of the channel. Subsequently, the interactions between the gas and wall particles will get reduced considerably. Moreover, the characteristics near the wall are examined in detail. A nonhomogeneous behavior in density and velocity profile near the wall is reported. Further, the momentum accommodation coefficient (MAC) in both the tangential and normal directions is examined along the lengthwise sections of the channel. The results show a significant variation of tangential and normal MACs along the length. Further, three channels with different length-to-characteristic dimension ($L/H$) ratios are considered to investigate the effect of $L/H$ ratio. All three channels are subjected to the same pressure drop along the length. It is observed that the MACs and slip length show distinct behavior for different ($L/H$) ratios. The work establishes that the variation of MAC along the length of the channel has to be considered in modeling the nano- and microtransport systems.

Figure 1

An isometric view of the simulation domain. The fluid atoms are shown in blue.

Figure 2

Molecular trajectory of a single gas atom and a wall atom. The vertical dotted line represents the entry of the channel section. The dashed lines represent the system boundaries. a, b, c, and $d$ represent the position of the bins.

Figure 3

The pressure drop $\mathrm{\Delta }{P}_i^{*}$ shows a linear variation with the normalized length. The pressure drop is normalized with the $P_0$, the pressure at the reservoir. The inset shows the pressure drop at first bin $a$ of the 6 nm channel over a finite simulation period.

Figure 4

The velocity increases along the length of the channel whereas the temperature decreases and the variation in the temperature is nominal at the downstream. The velocity and temperature are normalized with the corresponding values at the reservoir. The plots for a 6 nm channel are shown.

Figure 5

The density profiles across the nanochannel at the respective bins. The local density is normalized with the center line density. Only half of the channel section is shown.

Figure 6

The velocity profile across the nanochannel is shown. The local velocity is normalized with the center line velocity. The extreme points near the wall indicate the amount of slip. Only half of the channel section is shown.

Figure 7

Variation of tangential momentum accommodation with the normalized pressure drop and $H$. As the solid surface is in $\mathit{xz}$ plane it will have two tangential components, the momentum accommodation in the $x$ and $z$ directions [7(a) and 7(b)].

Figure 8

Variation of normal momentum accommodation (NMAC) with the normalized pressure drop and $H$.

Figure 9

The variation of Maxwell's slip length $l_{sM}$ with the normalized pressure drop for different channel height $H$. The slip length is obtained from the calculated values of TMAC.