Kinetic-contact-driven gigantic energy transfer in a two-dimensional Lennard-Jones fluid confined to a rotating pore

A two-dimensional Lennard-Jones system in a circular and rotating container has been studied by means of molecular dynamics technique. A nonequilibrium transition to the rotating stage has been detected in a delayed time since an instant switching of the frame rotation. This transition is attributed to the increase of the density at the wall because of the centrifugal force. At the same time the phase transition occurs, the inner system changes its configuration of the solid-state type into the liquid type. Impact of angular frequency and molecular roughness on the transport properties of the nonrotating and rotating systems is analyzed.

Figure 1

Visualization of the studied system.

Figure 2

Total energy $E$, kinetic energy $E_k$, and potential energy $E_p$ time dependencies of the simulated particles in a container with the radius $Z=15$ for ${\sigma }_{22}/{\sigma }_{11}=1,\rho =0.95$, and $\omega =1$. Gigantic energy transfer occurs at the transition to the rotating stage. Note that the initial total energy is equal to $-0.9$.

Figure 3

Density as a function of distance from the center of the container of size $Z=15$ obtained at the times: $t=0,t=20=\tau$ (the beginning of the rapid increase of energy), $t=100$ (the end of the simulation). Simulations were performed for ${\sigma }_{22}/{\sigma }_{11}=1,\rho =0.95$, and $\omega =1$. The curves are smoothed over ${10}^4$ time steps near a given point in time. The effect of centrifugal force is indicated by arrows showing small shift of the density peaks towards the edge of the geometry.

Figure 4

Change of the profile of the kinetic energy as a function of distance from the center of the container obtained at different simulation times for $Z=15,{\sigma }_{22}/{\sigma }_{11}=1,\rho =0.95$, and $\omega =1$. The final kinetic energy profile is parabolic.

Figure 5

Change of the kinetic energy for the roughness ${\sigma }_{22}/{\sigma }_{11}=1$. The radius of the container is $Z=15$. The angular frequency of the rotation $\omega$ varies from 0.05 to 2.00 with the step 0.05. Theoretical curve is due to the soft rotating plate model calculated using Eq. (10). Each panel shows the results for a different density: (a) $\rho =0.95$, (b) $\rho =0.85$, (c) $\rho =0.75$, (d) $\rho =0.65$.

Figure 6

Change of the potential energy for the roughness equal to ${\sigma }_{22}/{\sigma }_{11}=1$. The radius of the container is $Z=15$. The angular frequency of the rotation $\omega$ varies from 0.05 to 2.00 with the step 0.05. Each panel shows the results for a different density: (a) $\rho =0.95$, (b) $\rho =0.85$, (c) $\rho =0.75$, (d) $\rho =0.65$.

Figure 7

Change of the kinetic energy for the roughness equal to ${\sigma }_{22}/{\sigma }_{11}=2$. The radius of the container is $Z=15$. The angular frequency of the rotation $\omega$ varies from 0.10 to 4.00 with the step 0.10. Theoretical curve is due to the soft rotating plate model. Each panel shows the results for a different density: (a) $\rho =0.95$, (b) $\rho =0.85$, (c) $\rho =0.75$, (d) $\rho =0.65$.

Figure 8

Change of the kinetic energy for the roughness equal to ${\sigma }_{22}/{\sigma }_{11}=1/2$. The radius of the container is $Z=15$. The angular frequency of the rotation $\omega$ varies from 0.025 to 1.000 with the step 0.025. Theoretical curve is due to the soft rotating plate model. Each panel shows the results for a different density: (a) $\rho =0.95$, (b) $\rho =0.85$, (c) $\rho =0.75$, (d) $\rho =0.65$.

Figure 9

Times of the rapid transition for the system of the size $Z=15$, the roughness ${\sigma }_{22}/{\sigma }_{11}=1$ and the density $\rho =0.95$.

Figure 10

$a$ parameter obtained for the time $t=100$. The lines indicating the ideal hard and soft plates are presented in blue and red colors.

Figure 11

Change of the kinetic energy for the roughness ${\sigma }_{22}/{\sigma }_{11}$ equal to 1 and the density $\rho =0.95$. The radius of the container $Z$ varies from 10 (panel (a)) to 25 (panel (d)) with the step 5. The angular frequency of the rotation $\omega$ varies from 0.05 to 2.00 with the step 0.05.

Figure 12

Surplus kinetic energy parameter $a$ changes with different container radius.