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10
13
m/s
2
, the molecular motion becomes unstable,
causing clusters of molecules to form. This is due to the system becoming over-
constrained with molecules settling into a quasi-equilibrium state in which they
change energy states as little as possible; however, they still maintain the global
velocity distributions.
The results shown in Figure 5.7 demonstrate that the behaviour of different
flow regimes can be captured and identified from a molecular simulation, where
the high flow regime displays much higher losses than the low flow rate regime.
The low-speed flow can be likened to a laminar flow, where losses are low, mean-
ing that the exchange between layers parallel to the direction of flow should be
minimal. In the high flow case, losses are higher and a higher level of interaction
and exchange is expected to be perpendicular to the flow direction. This can be
examined by comparing further data extracted during the simulations.
simulation. At values of 6
×
5.3.3 Comparisons and Data Analysis
To further aid in the characterization of these two regions, comparisons can be
drawn between their behaviour. The presented method for obtaining the bulk prop-
erties has been used above to extract velocity profiles of the flow to plot the aver-
age velocity of the flow against the applied driving force. From these results, two
regions have been identified: one that displays significantly higher losses than the
other. Further analysis of these regions can be performed by comparing the veloc-
ity profiles extracted from simulations performed in each of the regimes. Figure
5.8 shows the velocity profiles extracted for driving forces of 2
×
10
12
m/s
2
and
10
13
m/s
2
, corresponding to flows within the low and high flow rate regimes
respectively. The velocity profiles were extracted using 29 nodes placed at 0.5 nm
intervals across the channel, sampling at 75 time step intervals (2.0 fs time step),
and each ensemble was measured over 0.4 ps.
The extracted profiles are shown in Figure 5.8. The profile extracted from the
simulation with a low flow rate (bottom) displays a profile that is much more
curved than the high flow rate profile. Accounting for the slip between the wall
and the boundary, the profile is similar in shape to the analytical Poiseuille pro-
file for describing laminar flow in pipes and channels. The profile is caused by
the smooth propagation of energy throughout the system, where a molecule dif-
fusing across the channel experiences many low-energy collisions, altering its
thermodynamic state as it passes each point. Both profiles show the same degree
of variation,
4
×
25 m/s. The variation is dependent on the thermal motion of the
underlying molecules and therefore the same for high- and low-speed flows.
The high flow profile, on the other hand, displays a markedly different shape.
For this flow regime, the molecules possess more energy and display a signif-
icantly flatter velocity profile, showing that there is less difference in kinetic
±
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