Simulation of hard-disk flow in microchannels

The dynamic flow behavior of a hard-disk fluid under external force field in two-dimensional microchannels is investigated using an event-driven molecular dynamics simulation method. Simulations have been carried out under laminar and subsonic conditions in both slip regime and transition regime, and the effects of three main factors, Knudsen number (Kn), force field intensity, and packing fraction, on flow and heat transfer behavior have been studied. It is shown that all the factors play important roles in the velocity distribution of the flow, and the temperature profile of the gas flow may exhibit a bimodal shape with a local minimum instead of a maximum in the center. These findings verify the predictions of nonequilibrium kinetic theories on the so-called “temperature dip.” At high Kn, the two maxima of temperature shift to two walls and the temperature profile changes to a “parabola” opening upward with a minimum in the center. A slight setback of the temperature is also found before the fluid flow eventually arrives at a steady state when the shear rate is high enough.

Figure 1

Schematic of gravity-driven flow composed of hard disks.

Figure 2

Schematic of original arrangement of hard-disk system.

Figure 3

Schematic of measurements and temporal evolution of the total kinetic energy with $N=240,000$ in hard-disk system at $g=6.0\times {10}^{-6}$, $\eta =0.0873$ and $\text{Kn}=0.154$.

Figure 4

(Color online) Velocity profiles and temperature profiles with different member of subchannels at $g=6.0\times {10}^{-6}$, $\eta =0.0873$, and $\text{Kn}=0.154$: continuous line (black with solid square), results with 41 subchannels; dashed line (red with hollow circle), results with 21 subchannels.

Figure 5

(Color online) Schematic of the velocity profiles used in different statistical methods (a), and the corresponding simulation results (b): continuous line (black with solid square), results from the method using Eqs. (12, 13, 14, 15, 16); dashed line (red with hollow circle), results from the method using Eqs. (12, 15, 16, 17).

Figure 6

(Color online) Velocity profile at $g=8.0\times {10}^{-7}$, $\eta =0.0873$, and $\text{Kn}=0.044$.

Figure 7

(Color online) Temperature profile at $g=8.0\times {10}^{-7}$, $\eta =0.0873$, and $\text{Kn}=0.044$.

Figure 8

(Color online) Velocity profiles for different Kn at $\text{Fr}=0.45$ and $\eta =0.0873$.

Figure 9

(Color online) Relative velocity profiles for different Kn at $\text{Fr}=0.45$ and $\eta =0.0873$.

Figure 10

(Color online) Velocity profiles for different Fr at $\text{Kn}=0.154$ and $\eta =0.0873$.

Figure 11

(Color online) Relative velocity profiles for different Fr at $\text{Kn}=0.154$ and $\eta =0.0873$.

Figure 12

(Color online) Velocity profiles for different $\eta$ at $\text{Kn}=0.154$ and $\text{Fr}=0.45$.

Figure 13

(Color online) Relative velocity profiles for different $\eta$ at $\text{Kn}=0.154$ and $\text{Fr}=0.45$.

Figure 14

(Color online) Temperature profiles for different Kn at $\text{Fr}=0.45$ and $\eta =0.0873$.

Figure 15

(Color online) Relative temperature profiles for different Kn at $\text{Fr}=0.45$ and $\eta =0.0873$.

Figure 16

(Color online) The development of temperature profile with the decrease of Kn at $\text{Fr}=0.60$ and $\eta =0.0873$.

Figure 17

(Color online) $T_x\left(x\right)$ with the decrease of Kn at $\text{Fr}=0.60$ and $\eta =0.0873$.

Figure 18

(Color online) $T_y\left(x\right)$ with the decrease of Kn at $\text{Fr}=0.60$ and $\eta =0.0873$.

Figure 19

(Color online) Temperature profiles for different Fr at $\text{Kn}=0.154$ and $\eta =0.0873$.

Figure 20

(Color online) Relative temperature profiles for different Fr at $\text{Kn}=0.154$ and $\eta =0.0873$.

Figure 21

(Color online) Relative temperature profiles for high Fr values at $\text{Kn}=0.154$ and $\eta =0.0873$.

Figure 22

(Color online) Temperature profiles for different $\eta$ at $\text{Kn}=0.154$ and $\text{Fr}=0.45$.

Figure 23

(Color online) Relative temperature profiles for different $\eta$ at $\text{Kn}=0.154$ and $\text{Fr}=0.45$.

Figure 24

(Color online) Temporal evolution of the temperature profile at $\text{Kn}=0.0616$, $\text{Fr}=2.025$ and $\eta =0.0873$.