The rate of energy transfer from air as an initially stationary particle acquires Brownian motion

Abstract

Physical simulation methods are used to determine the average time that is required for the molecules in standard air to transfer sufficient energy to an initially stationary particle to bring it to equilibrium with the gas as a Brownian particle. Individual particle trajectories are subject to random fluctuations and the average relaxation times are determined as ensemble averages over thousands of trajectories. The average initial power input to the particle is given by the equilibrium energy divided by the relaxation time. The relaxation time is determined for both spherical and cylindrical particles which vary in mass, diameter and, in the case of the cylinder, aspect ratio. The particle mass is normalized by the mass of an average air molecule, the diameter through the Knudsen number (the mean free path divided by the diameter) and the aspect ratio is the cylinder length to diameter. The relaxation time is found to be directly proportional to the product of the mass ratio and the square of the Knudsen number and inversely proportional to the aspect ratio. Empirical relations are developed for the relaxation times in each case. Should a cylindrical particle be fixed to a surface, it becomes a cantilevered nanowire that, if piezotronic, is capable of extracting energy. The relevance of the second law to this process is discussed together with speculations about the possibility of energy harvesting from nanodevices in air.