Modeling of Microstructures Actuation by the Knudsen Thermal Force

Abstract

Heated microscale objects immersed in a gas ambient are subject to thermal Knudsen forces generated by the non-equilibrium energy exchange between gas molecules and solid surfaces. Knudsen forces are significant when the length scale of a temperature gradient is comparable to the gas molecular mean free path. This can occur for very low gas pressures or at extremely small length scales. The overall goal of this work is to study the feasibility of using Knudsen force as an alternative actuation mechanism for N/MEMS. The kinetic solution of Boltzmann equation using the discrete ordinate/finite volume discretization in the high-dimensional phase space is circumventing difficulties associated with traditional stochastic DSMC approach in dealing with the slow bulk motion. The comparison to measurements by (Passian et al, PRL, 2003) shows that Knudsen force is well reproduced by simulations assuming full momentum accommodation for nitrogen and argon gas and an incomplete accommodation for helium. It provides a pathway for design and analysis of devices taking advantage of the benign mechanism of the Knudsen forces, in particular, the absence of high electric fields. The analysis shows that the Knudsen force results in an impact velocity of only 0.9 cm/s whereas electrostatic forces with low voltages below 0.5V result in impact velocity in the range of 6–20 cm/s. We further discuss how Knudsen force can be used for low impact velocity actuation and also to overcome the stiction problem.