โ Scribed by Y.S. Mayya; B.K. Sapra
No coin nor oath required. For personal study only.
The spatial and temporal evolution of the charge distribution on aerosol particles undergoing bipolar charging due to small ions in the presence of electric fields is generally described by a charging equation set up in charge-position space. Being a phenomenological description, this requires to be derived from a more fundamental kinetic description by explicitly incorporating Brownian velocity fluctuations in position-velocity-charge space. This paper presents such a derivation and obtains correction factors for the conventionally used mobility and diffusion coefficients in the charging equation. Although mobility correction is negligible for small particles at low ion concentrations, it is significant for particles of sizes above 10 microm at high ion densities (>10(6)/cc). The analysis predicts a new electrical diffusion mechanism in addition to Brownian diffusion, which arises as a result of dispersion in the electromigration velocities of particles having the same charge. This mechanism is contrasted with the charging-induced diffusion mechanism proposed earlier by Y. S. Mayya and S. V. Malvankar (J. Colloid Interface Sci.156, 78, 1993). The electrical diffusion coefficients and the corresponding velocity persistence lengths are several orders higher than their Brownian counterparts. The study also obtains the boundary conditions to be employed for computing charge particle deposition rates near absorbing surfaces and discusses specific solutions.
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