Experimental measurements and numerical simulations of the Knudsen force on a non-uniformly heated beam

Rarefied thermally-induced flows generate Knudsen thermal force on structures immersed in a gas and are significant for vacuum microbalances as well as for microsystem sensors and actuators. We study experimentally and numerically the influence of transverse thermal gradients on the Knudsen thermal force. A Peltier device provided the thermal gradient in a beam located in close proximity of a large reaction plate, whose displacement has been sensed using a torsional balance. The pressure in the vacuum chamber varied between 1 and 100 Pa giving a range of Knudsen numbers from the slip to nearly free molecular regimes, based on the gap between the beam and the movable plate. Switching polarity of the Peltier heater produces reversal of the Knudsen thermal force, from repulsive to attractive. The numerical solution of Ellipsoidal Statistical Bhatnagar-Gross-Krook (ESBGK) kinetic model of the Boltzmann equation agrees well with experimental data. The obtained non-dimensional Knudsen force coefficient, dependent on the Knudsen number, temperature ratio and the gap height to beam width aspect ratio, quantifies the magnitude of the force for a wide range of generic conditions and could be used for design and analysis of sensors and actuators exploiting this rarefied flow effect.