Knudsen Force Modeling in Application to Microsystems

At the microscale, even moderate temperature differences can result in significant Knudsen forces generated by the energy exchange between gas molecules and solids immersed in a gas. Creating, controlling and measuring Knudsen forces in microsystems can be an arduous task since only limited theory exists at present. This present study investigates the mechanism of Knudsen forces in detail based on numerical solution of the Boltzmann kinetic equation. The Knudsen force is shown, in general, to be a result of thermal nonequilibrium between gas and solid. The simulations are validated by comparison with experimental measurements that have been reported by Passian et al. using heated atomic force microscope probes. A closed-form model for the Knudsen force on a beam is obtained based on the simulations and can be applied for analysis and design of microsystems.