Simulation of Temperature Driven Microflows Using a Lattice Boltzmann Method in Slip and Moderate Transition Regimes

Micro-electromechanical systems (MEMS) are very small devices that usually contain gas under low pressure. The motion of the fluid inside such structures is affected by rarefaction effects, which are not visible in macroscale flows. To accurately predict the behavior of the fluid in such microstructures, the Lattice Boltzmann Method needs to be modified to account for these new effects. This can be done by introducing relative fluid-wall velocity in the form of slip boundary conditions. Furthermore, temperature effects like temperature jump and thermal creep can be included using wall boundary conditions. In this paper, different models for the slip are explored and evaluated over the Knudsen number. Then, a thermal flow is simulated and benchmarked by Direct Simulation Monte-Carlo (DSMC). The results show that these extensions offer a good approximation in the slip and moderate transition regimes (Knudsen number (Kn) < 1).

1. Introduction

Micro-electromechanical systems (MEMS), especially accelerometers are crucial in automotive and consumer electronic devices (like smartphones or airbag control units). High integration densities lead to temperature gradients across MEMS devices, which can cause offset errors in the measurement signal of the accelerometer [1]. Since the dimensions of the MEMS structure are very small compared to the mean free path of the surrounding gas, the gas inside cannot be considered as a continuum flow anymore and new efficient simulation methods need to be implemented to account for rarefaction effects like radiometric effects, thermal creep, velocity slip etc.