Measurements of the thermophoretic force on submicrometer particles in gas mixtures

Thermophoresis, i.e. particle migration driven by a thermal energy gradient, has been of long-standing interest in aerosol science, yet is incompletely understood. For instance, for submicrometer particles in multicomponent gas mixtures, theories describing the thermophoretic force have not been fully developed and experimentally tested. Such particles fall outside both the continuum limit, where gas mixtures act on particles as a continuous fluid, and the free molecular limit, wherein the individual gas components act individually on particles. In this study, we propose and test an expression for the dimensionless thermophoretic force $F_{th}^{*}$ and for an appropriate thermophoretic Knudsen number, ${Kn}_{th}$, applicable to n-component gas mixtures. Prior expressions for the thermophoretic force in the transition regime can be cast into $F_{th}^{*}$ versus ${Kn}_{th}$ relationships. By requiring that the thermophoretic Knudsen number is proportional to the ratio of the continuum limit thermophoretic force to the free molecular thermophoretic force, we suggest that the thermophoretic mean free path is equivalent to the commonly-used hard sphere mean free path for single component gases, but that these two are not necessarily equivalent in multicomponent gas mixtures. The proposed relationship between $F_{th}^{*}$ and ${Kn}_{th}$ is tested experimentally through measurements of the thermophoretic force acting on 100 nm–750 nm monodisperse KCl particles in a parallel plate precipitator in air, CO₂, and three CO₂–He gas mixtures. In the latter gas mixtures, thermophoresis is primarily driven by the lighter, more thermally-conductive gas, but particle drag is affected by both gases. We find data collapse to a reasonably narrow band spanning from the free molecular limit at high ${Kn}_{th}$ to the continuum limit at low ${Kn}_{th}$. However, data points at high ${Kn}_{th}$ in CO₂–He gas mixtures of high He mole fraction have thermophoretic force values which exceed the free molecular limit predictions. Even including these anomalous data points, measurements do support the definition proposed of ${Kn}_{th}$ for the thermophoretic Knudsen number in gas mixtures through the collapse of $F_{th}^{*}$ versus ${Kn}_{th}$ data. Data from previous studies for a similar particle-to-gas thermal conductivity ratio similarly collapse to the narrow band for data obtained here and data show reasonable agreement with prior theories for the thermophoretic force in the transition regime.