Thermo- and photophoretic mobilities of an oscillating spherical aerosol particle

This paper presents a comprehensive analytical investigation into the thermophoretic and photophoretic dynamics of an oscillating spherical aerosol particle within a time-periodic temperature gradient. The theoretical framework is developed for the slip-flow regime (0.01<Kn<0.1) under low Péclet and Reynolds number conditions, incorporating temperature jump, frictional slip, and thermal stress slip phenomena. A central focus is placed on the Womersley number (s). Our analysis reveals that the Womersley number is not merely influential but governs the fundamental transition of the system from a quasi-steady regime at low frequencies to a thermally inertial regime at high frequencies. This transition gives rise to complex dynamic behaviors absent in steady-state models. A key unique discovery of this work is the prediction of frequency-induced phoretic force reversals and resonant phase-lag effects. Specifically, we demonstrate that under certain photophoretic conditions, increasing the oscillation frequency can reverse the direction of the in-phase force component. Expressions for the in-phase and out-of-phase components of both the phoretic force and particle velocity are derived and analyzed. While this study is purely analytical, it provides a crucial predictive benchmark and compares favorably with the steady-state limits reported in previous literature. The findings have direct implications for practical applications, including the high-frequency manipulation of particles in microfluidic devices, the dynamic modeling of black carbon aerosol lifetimes in the atmosphere, and the optimization of thermophoretic precipitators.