Mechanism of tangential Knudsen force at different Knudsen numbers

Abstract

In a rarefied gas with a non-uniform temperature field, one phenomenon that arises is the tangential Knudsen force. Various researches have investigated the tangential Knudsen force but have been limited to specific cases. In this study, we investigated the mechanism of the thermally induced tangential Knudsen force, using theoretical analysis under fully diffusive conditions and for a range of Knudsen numbers. Specifically, we formulated a theoretical expression to describe the tangential Knudsen stress by considering the two kinds of -momentum fluxes transferred on a surface of interest. One is brought by molecules directly coming from the other surface without experiencing intermolecular collisions and the other is brought by molecules coming from the bulk region after experiencing intermolecular collisions there. As reference, we used a channel where the lower surface is a hot ratchet structure and the upper surface is a flat cold object. The tangential Knudsen force on the object obtained by the theoretical analysis was compared with the results from our previous work where we performed numerical experiments by the direct simulation Monte Carlo (DSMC) method. Based on the comparison, it is found that the tangential Knudsen force is caused by three mechanisms. First is the contribution of impinging molecules coming from the other surface with different temperature. Second is the contribution of viscous effect of thermally driven flows. While the third is the contribution of thermal stress, which is noticeable in small Knudsen numbers.

Thermally Induced Knudsen Forces for Contactless Manipulation of a Micro-Object

“…Such technologies include microstructure actuation [ 5 , 6 ], gas sensing [ 7 , 8 , 9 ], atomic force microscopy [ 1 , 4 ], and high-precision force measurements [ 3 ], among others. In addition to experimental [ 2 , 10 ] and theoretical approaches [ 1 , 11 , 12 , 13 ], numerical approaches have also been used to study the Knudsen forces [ 7 , 10 , 14 , 15 , 16 , 17 ]. Computational studies are particularly significant to reproduce the thermally induced flow field in complex systems that is difficult to observe experimentally.…”

“…The above studies [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ] proved that thermally induced Knudsen forces can displace an object without physical contact and any moving parts. This displacement is usually repulsive, such as a heated cantilever being deflected away from a colder flat substrate [ 1 , 2 , 8 ].…”

“…In this case, the thermally induced Knudsen force can displace the object closer to the substrate. Furthermore, if the substrate has a microstructure, the tangential Knudsen force will be induced on the object and can induce the self-propulsion of the object [ 11 , 14 ]. Combining these two ideas, it may be possible to use the thermally induced Knudsen forces to capture or manipulate an object without contact.…”