A correction tensor for approximating drag on slow-moving particles of arbitrary shape

Abstract

A new form of the Cunningham correction factor is presented that requires no experimental fitting. It is expanded to provide a predictive heuristic for non-spherical particles, via definition of a "correction tensor''. Its accuracy is tested against experiments and kinetic theory for the sphere, and stochastic solutions to the Boltzmann equation for a range of spheroids. It represents a simple, general tool for approximating transport properties of non-spherical micro/nano particles in a gas.

Figures (3)

• Figure 1: Drag on a slowly translating sphere against ${K\space n}$. Comparison of Millikan's data millikan_general_1923 ($+$), experiments of allen_slip_1985 ( $\boldsymbol{\cdots}$), kinetic theory of beresnev_motion_1990 ($\bigcirc$) and the proposed heuristic ($1/C_{\mathrm{new}}$, --- ), equation (\ref{['eq:NewCC']}).
• Figure 2: Resistance tensor components for prolate (a, b) and oblate (c, d) spheroids of aspect ratio 4 (a, c) and 10 (b, d). Motion parallel ($\triangle$, $K_{x\space x}$) and perpendicular ($\bigcirc$, $K_{y\space y}$) to the polar axis. Comparison of DSMC clercx_modeling_2024 to Eq. (\ref{['eq:KC']}).
• Figure 3: Resistance component in the direction of motion ($x'$) for prolate (a) and oblate (b) spheroids of aspect ratio 2, against $\theta$, the angle (in degrees) between $x'$ and $x$ (where $x$ is the spheroid's axis of revolution). DSMC data livi_drag_2022 at ${K\space n}=1(\square),\,5(\triangle),\,7(\Diamond),\,9($$\bigcirc$$)\,$and $10(\triangleleft);$ Eq. (10) (---).