The motion of a small particle in a non-uniform gas mixture

Abstract

The problem of the behaviour of a small aerosol particle (smallgr than the mean free path of gaseous molecules) in a non-uniformly heated gas mixture is examined on the basis of the Chapman-Enskog method. The velocity at which the particle moves through such a mixture is calculated. A numerical computation is made for a CC4+He mixture.Inversion of the particle velocity was observed, i.e., the particle may be attracted to an evaporatiag drop and repelled from a growing one. By way of particular cases the velocity of motion has been found for a particle in an isothermal binary mixture and in a simple non-uniformly heated gas.* This case was also discussed by the same method in a paper 9 published later than our work.4

Thermophoresis of Janus particles at large Knudsen numbers

“…The first line in this expression agrees with the results of Bakanov and Derjaguin [5] and Waldmann [4] for the thermophoretic and drag forces on a sphere with surface-temperature T P = T and homogeneous accommodation coefficient a = a + = a − . Under these conditions the net force on the particle vanishes when it moves with a drift velocity u d = q/[5p(1 + aπ/8)].…”

“…The earliest estimate for the thermophoretic force on a particle at large Knudsen numbers seems to be due to Einstein [3]. More exact calculations for the force and drag on a homogeneous sphere at large Knudsen numbers were later performed by Waldmann [4] and simultaneously by Bakanov and Derjaguin [5], allowing the determination of the thermophoretic velocity in this limit. Our analytical calculations largely follow these early presentations.…”

Diffusiophoresis under turbulent conditions

“…Thus the contribution of the second term is minor, but it does indicate that for m-^ = m 2 , the particle may travel in either direction, depending on the sign of a T . It is no coincidence that Brock's expression for large particles is identical to that derived by Bakanov and Derjaguin (1960) for small particles (when the accommodation coefficients are unity). This is a consequence of the assumption, made in both cases, that molecule molecule interaction near the surface is negligible.…”

“…They improved the accuracy of the analysis by carrying an extra term in the velocity distribution function for the molecules. When rewritten in term of common gas properties, and if temperature effects are ignored, their expression for equimolar counter-diffusion becomes In comparison with Bakanov and Derjaguin's (1960) result, the Thermal diffusion to separate when subjected to thermal diffusion factor is a separation.…”

Knudsen pump inspired by Crookes radiometer with a specular wall

“…Thus F ∼−d 2 k B n ∂ x T , which, since n is constant, is a regime where the force is approximately independent of the Knudsen number. This is essentially the regime considered for thermophoresis of small particles [21,48,49].…”