Thermophoretic force and velocity of nanoparticles in the free molecule regime

Abstract

We extend our previous gas-kinetic theory analysis of drag force in a uniform temperature field [Li and Wang, Phys. Rev. E. 68, 061206 (2003); 68, 061207 (2003)] to particle transport in fluids with nonuniform temperature. Formulations for drag and thermophoretic forces are proposed for nanoparticle transport in lowdensity gases. We specifically consider the influence of nonrigid body collision due to van der Waals or other forces between the particle and gas molecules and find that these forces play a notable role for particles a few nanometers in size. It is shown that the present formulations can be easily reduced to the classical result of Waldmann [Z. Naturforsch. A 14a, 589 (1959)] by assuming rigid body collision. From the force formulations we also obtain the equation governing the thermophoretic velocity. This velocity is found to be highly sensitive to the potential energy of interactions between gas molecules and particle, and as such Waldmann's thermophoretic velocity is not expected to be accurate for nanosized particles.

Transport Properties of Small Spherical Particles

“…When these problems were recognized, a more generalized theory was advanced from a rigorous gas-kinetic derivation for dilute gases and in the large Knudsen number regime. [1][2][3] The theory accounts for the influence of potential forces of gas-particle interactions on particle drag. The mathematical treatment of this theory appeared in Li and Wang, 1 and only the results are given here.…”

“…In recent studies we proposed a generalized transport theory of small, spherical particles in dilute gases and laminar flows 1–3 . The theory features a rigorous derivation of momentum transfer upon gas collision with a particle in the large Knudsen regime.…”

“…In recent studies we proposed a generalized transport theory of small, spherical particles in dilute gases and laminar flows. [1][2][3] The theory features a rigorous derivation of momentum transfer upon gas collision with a particle in the large Knudsen regime. It considers the potential force of gas-particle interactions, so the theory may be applied to particles down to the molecular size.…”

Investigation of the size of the incandescent incipient soot particles in premixed sooting and nucleation flames of n-butane using LII, HIM, and 1 nm-SMPS

“…For the HIM detection in Bielefeld, samples were collected thermophoretically (Li and Wang 2004) by insertion of a silicon wafer into the flame. The silicon wafer was connected to a stepper motor allowing a repetitive swing movement across a horizontal plane parallel to the burner surface.…”

Size- and structure-independence of the thermophoretic transport of an aerosol particle for specular boundary conditions in the free molecule regime

“…We should, however, caution about the existence of a lower size limit for the validity of the direct application of the result derived here, as the model of rigid body collisions with gas molecules becomes inaccurate for particles approaching molecular sizes (Li & Wang, 2003b. Nevertheless, the size and morphology independence of their thermophoretic velocity could still be argued extending the derivation below, and the value computed in the way described by Li and Wang (2004).…”