The thermophoretic force in the Knudsen regime near a wall

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Abstract
The thermophoretic forces acting on a Small Knudsen particle in the neighborhood of a boundary have been investigated. The applied temperature gradient is constant, but it is not normal to the wall, thereby leading to thermophoretic forces both normal to and parallel with the wall. Using the velocity distribution of the gas atoms for this problem it has been possible to obtain the variation of the thermophoretic force as a function of distance from the boundary. It is noted, that for equal temperature gradients, the force is greater in the direction normal to the wall than along it. In addition, it is observed that the velocity dependence of the mean free path has a significant effect on the force in the neighborhood of the wall. In contrast to the normal force, which is in the direction of decreasing temperature, the mass flow induced by thermal creep along the wall leads to a parallel wall force that moves the particle in the direction of increasing temperature. When these two forces are compounded they indicate that particles can move in curved paths en route to the wall surface. As a by‐product of the calculation, an exact expression for the thermal creep velocity as a function of distance from the wall for the case of constant collision cross‐section is presented.