Gas flow through rough microchannels in the transition flow regime

A multiple-relaxation-time lattice Boltzmann model of Couette flow is developed to investigate the rarified gas flow through microchannels with roughness characterized by fractal geometry, especially to elucidate the coupled effects of roughness and rarefaction on microscale gas flow in the transition flow regime. The results indicate that the surface roughness effect on gas flow behavior becomes more significant in rarefied gas flow with the increase of Knudsen number. We find the gas flow behavior in the transition flow regime is more sensitive to roughness height than that in the slip flow regime. In particular, the influence of fractal dimension on rarefied gas flow behavior is less significant than roughness height.

Figure 1

Rough surface profile by WM fractal function.

Figure 2

Schematic of Couette flow in a rough microchannel with local mesh refinement.

Figure 3

Grid independence test of present model ($\mathrm{Kn}=1$).

Figure 4

Dimensionless mass flux of the Poiseuille flow for rarefied gas.

Figure 5

Dimensionless mass flux of the Poiseuille flow for rarefied gas with different tangential momentum accommodation coefficient.

Figure 6

Velocity distribution of Couette flow in microchannels ($\mathrm{Kn}=1$): (a) smooth, (b) rough $(\varepsilon =2\%,D=1.5)$.

Figure 7

Normalized streamwise velocity profile of Couette flow in microchannels.

Figure 8

Normalized streamwise velocity profiles of Couette flow in the rough microchannels with different $D$ and ε: (a) $\mathrm{Kn}=0.01,D=1.5$; (b) $\mathrm{Kn}=0.01,\varepsilon =2\%$; (c) $\mathrm{Kn}=0.1,D=1.5$; (d) $\mathrm{Kn}=0.1,\varepsilon =2\%;$ (e) $\mathrm{Kn}=1$, $D=1.5$; (f) $\mathrm{Kn}=1,\varepsilon =2\%.$

Figure 9

Rarefaction effect on gas flow in rough microchannels $(D=1.5)$.

Figure 10

Effect of surface roughness on micro gas flow: (a) statistical roughness height $(D=1.5)$, (b) fractal dimension $(\varepsilon =2\%)$.