Predicting the Transport Properties of Aerosol Particles in Creeping Flow from the Continuum to the Free Molecule Regime
Zachariah, Michael R
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The transport of nanoscale aerosol particles plays an important role in many natural and industrial processes. Despite its importance, the transport behavior of aerosol aggregates is poorly understood, largely due its complex dependence on particle size, shape, and orientation. Often, these particles are in the transition regime, where neither the continuum approximation for large particles nor the free molecule approximation for small particles is valid. At present, methods for calculating the aerodynamic force on and diffusive behavior of fractal aggregates in the transition regime either rely upon scaling laws fitted to experimental data or computationally-intensive direct simulation Monte Carlo or molecular dynamics approaches. Thus, there is a pressing need for a new method for determining aerosol transport properties. This dissertation introduces such a method for calculating the drag and torque on an aerosol aggregate as a function of the primary sphere size and the aggregate size and shape. This method is an extension of Kirkwood-Riseman theory to the transition regime, using an appropriate model for interactions between the individual spheres in an aggregate. This dissertation also describes the application of this extended Kirkwood-Riseman (EKR) method to a number of problems related to aerosol transport, including computation of the scalar translational and rotational friction coefficients of aggregates formed by diffusion-limited processes, analysis of the effects of alignment on particle migration in an electric field, and the strength of interactions between particles due to their effects on the surrounding fluid flow field. In each of these applications, results from the EKR method are in good agreement with published experimental data and computational results. EKR results also demonstrate that particle translational and rotational behavior becomes more continuum-like as both primary particle size and the number of spheres in the aggregate increase. Using these results, new correlations have been developed for the translational and rotational friction coefficients of aggregates formed by diffusion-limited processes (e.g.~soot); these correlations are more accurate than the empirical models currently available in the literature.