中文摘要：

将Cantor集分形引入到微通道粗糙表面形貌的构建中，建立了粗糙微通道内气体流动的理论模型，采用格子Boltzmann方法模拟研究了表面粗糙对微尺度气体流动的影响，比较了粗糙和光滑微通道内气体流动特性。研究结果表明，气体的稀薄程度对微通道内气体流动特性有重要影响。无论通道是否光滑，随着Knudsen数的增加，微通道内气体流动Poiseuille数都将随之减小，但粗糙微通道中气动Poiseuille数大于光滑微通道。另外，粗糙微通道内的气体流动Poiseuille数受统计粗糙高度变化的影响较大，受分形维数变化的影响则较弱。

英文摘要：

A model of gas flow in microchannels with rough surface characterized by Cantor structures is developed and numerically analyzed by using lattice Boltzmann method so as to investigate the effect of surface roughness on micro gas flow. The gas flow behavior in rough microchannels is evaluated and compared with that in smooth microchannel. The results indicate that the rarefaction plays a significant role in gas flow behavior in microchannels. Regardless of whether the microchannel is smooth or rough, Poiseuille number of gas flow decreases with the increase of Knudsen number, but the Poiseuille number in rough microchannels is larger than that in smooth microchannels. In addition, the roughness height has a great impact on the gas flow characteristics, however, the effect of fractal dimension on the gas flow behavior in rough microchannels is relatively inferior.