Negative Knudsen force on heated microbeams

Knudsen force acting on a heated microbeam adjacent to a cold substrate in a rarefied gas is a mechanical force created by unbalanced thermal gradients. The measured force has its direction pointing towards the side with a lower thermal gradient and its magnitude vanishes in both continuum and free-molecule limits. In our previous study, negative Knudsen forces were discovered at the high Knudsen regime before diminishing in the free-molecule limit. Such a phenomenon was, however, neither observed in experiment [A. Passian et al., Phys. Rev. Lett. 90, 124503 (2003)], nor captured in the latest numerical study [J. Nabeth et al., Phys. Rev. E 83, 066306 (2011)]. In this paper, the existence of such a negative Knudsen force is further confirmed using both numerical simulation and theoretical analysis. The asymptotic order of the Knudsen force near the collisionless limit is analyzed and the analytical expression of its leading term is provided, from which approaches for the enhancement of negative Knudsen forces are proposed. The discovered phenomenon could find its applications in novel mechanisms for pressure sensing and actuation.

Figure 1

Schematic illustration of the 2D problem domain. $T_b$ represents the temperature of the beam; $T_a$ denotes the temperature of the chamber wall. In this work, it is set to be uniform.

Figure 2

Computed Knudsen forces corresponding to three different ambient gases.

Figure 3

Normalized Knudsen forces as functions of Knudsen number.

Figure 4

Comparison of normalized Knudsen forces for monatomic gases with different temperature exponents of the coefficient of viscosity.

Figure 5

Variations of $P{T}^{-1/2}I$ at different Knudsen numbers.

Figure 6

Normalized Knudsen forces versus Knudsen number.

Figure 7

Schematic of the problem of Aoki et al. [22].

Figure 8

Negative Knudsen forces at different gap heights.