The fractal roughness effect of micro Poiseuille flows using the lattice Boltzmann method

The fractal roughness effect of the two-dimensional micro Poiseuille gas flows is studied by a modified lattice Boltzmann model at high Knudsen numbers. A simple expression of the relaxation time as a function of dynamical viscosity and density is re-deduced from the gas dynamics theory. The rough wall of the microchannel is described by a self-affine fractal, and then the effect of the accommodation coefficient on the slip velocity of rough boundary is discussed. Numerical simulations of nitrogen and helium show that surface roughness influences not only velocity distribution but also pressure distribution. Reverse flow or eddy appears in the vicinity of the tips of the roughness surface. The mass flow rate decreases greatly and the resistance coefficient rises at an increasing rate as the relative roughness is enhanced. These phenomena different from macroscopic flows are of great importance in understanding the characteristics of micro Poiseuille flows.