Quantifying the Knudsen force on heated microbeams: A compact model and direct comparison with measurements

At the microscale, even moderate temperature differences leading to thermal nonequilibrium can result in significant Knudsen forces generated by the energy exchange between gas molecules and solids immersed in a gas. Experimental measurements of the microscale Knudsen force have been reported by Passian et al., Phys. Rev. Lett. 90, 124503 (2003) using heated microcantilevers of atomic force microscope probes. The present study investigates the mechanism and magnitude of Knudsen forces in detail based on numerical solution of the Boltzmann kinetic equation with the ellipsoidal statistical Bhatnagar-Gross-Krook approximation for the collisional relaxation process. A direct comparison between the numerical simulations and experimental measurements is presented. We show that, assuming a fully diffuse interaction of gas molecules with the surfaces of the heated cantilever, simulations agree with measurements for different operating pressures in argon and nitrogen ambients. For the helium ambient the simulations agree with measurements only when an incomplete accommodation is used. A closed-form model for the nondimensional Knudsen force coefficient on a heated microbeam is obtained that can be used for quantifying such forces in analysis and design of microsystems under a wide range of geometrical, thermal, and pressure conditions.