Knudsen torque: A rotational mechanism driven by thermal force

Thermally induced mechanical loading has been shown to have significant effects on micro- and nano-objects immersed in a gas with a nonuniform temperature field. While the majority of existing studies and related applications focus on forces, we investigate the torque, and thus the rotational motion, produced by such a mechanism. Our study has found that a torque can be induced if the configuration of the system is asymmetric. In addition, both the magnitude and the direction of the torque depend highly on the system configuration, indicating the possibility of manipulating the rotational motion via geometrical design. Based on this feature, two types of rotational micromotor that are of practical importance, namely pendulum motor and unidirectional motor, are designed. The magnitude of the torque at $\mathrm{Kn}=0.5$ can reach to around $2\mathrm{nN}\times \mu \mathrm{m}$ for a rectangular microbeam with a length of $100\mu \mathrm{m}$.

Figure 1

Schematic illustration of a heated microbeam placed inside a cold chamber.

Figure 2

Temperature contour, flow structure, and pressure variation of gas surrounding the heated microbeam; (a) temperature distribution; (b) flow structure; (c) pressure $P_{xx}$; (d) pressure $P_{yy}$.

Figure 3

The Knudsen torque acting on a rectangular microbeam as a function of the orientation of the beam located at $O_b=\left(0,-1.0\right)$.

Figure 4

The Knudsen torque acting on the microbeam as a function of the orientation of the beam located at $O_b=\left(-2.0,-1.0\right)$.

Figure 5

The relationship between the net torque indicated by the solid line and the rotating angle $\theta$. The dashed line represents the Knudsen torque, that is, the thermally induced torque.

Figure 6

The Knudsen force (a) and torque (b) acting on the cylinder as functions of the horizontal distance $d$ between the center of the chamber and the center of the cylinder.

Figure 7

The flow structure of gas surrounding the heated cylinder: (a) $O_b=\left(-1.5,-1.0\right)$; (b) $O_b=\left(-2.5,-1.0\right)$.