Photophoresis on particles hotter/colder than the ambient gas for the entire range of pressures

TL;DR

This paper develops a comprehensive model for photophoretic forces on particles with varying temperatures across all pressure regimes, improving accuracy over previous approximations especially in optically thin gases.

Contribution

It introduces a unified equation for photophoretic forces valid across all Knudsen numbers, accounting for non-uniform particle and gas temperatures and extending previous free molecular flow models.

Findings

Overestimates force by up to three magnitudes in optically thin gases.

Derived a formula with only 4% error in the continuum limit.

Proposed an interpolated equation for all Knudsen numbers.

Abstract

Small, illuminated aerosol particles embedded in a gas experience a photophoretic force. Most approximations assume the mean particle surface temperature to be effectively the gas temperature. This might not always be the case. If the particle temperature or the thermal radiation field strongly differs from the gas temperature (optically thin gases), given approximations for the free molecule regime overestimate the photophoretic force by an order of magnitude on average and for individual configurations up to three magnitudes. We apply the radiative equilibrium condition from the previous paper (Paper 1) -- where photophoresis in the free molecular flow regime was treated -- to the slip flow regime. The slip-flow model accounts for thermal creep, frictional and thermal stress gas slippage and temperature jump at the gas-particle interface. In the limiting case for vanishing Knudsen numbers -- the continuum limit -- our derived formula has a mean error of only 4 \% compared to numerical values. Eventually, we propose an equation for photophoretic forces for all Knudsen numbers following the basic idea from Rohatschek by interpolating between the free molecular flow and the continuum limit.