10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
Entropy Evolution of a Coagulating Aerosol
ADAM M BOIES, Nihal El Fahim, University of Cambridge
Abstract Number: 852 Working Group: Aerosol Physics
Abstract Summary The dynamics of aerosol coagulation is often dominated by the Brownian collisions motion of particles, as described by the Smoluchowski equation. During this process, the size distribution of particles changes and is well-explained by existing kinetic theory which accounts for the evolution in time of particles number density. For sufficiently long times, the kinetic theory of the coagulation process is known to reach a self-preserving size distribution. While the kinetic process is well understood, the thermodynamics associated with coagulation has received relatively little attention. Entropy, a fundamental thermodynamic property, has been employed within the informational sense to explain the evolution of particle morphology, but no study has attempted to identify the components of entropy generation with a coalescing aerosol.
Introduction In this presentation, entropy is approached from a fundamental level using statistical mechanics and is used to analyse the thermodynamic stability of aerosol systems. First, the different forms of entropy of aerosol particles are derived and the total entropy of an aerosol system is formulated. The distribution function maximising the entropy is then derived analytically and the values of entropy for common distribution functions are calculated and compared. Finally, using different initial aerosol populations, entropy variations in time are studied using the advanced aerosol dynamics solver.
Results We first identified the primary components of entropy generation that correspond to a loss of information relating to atomic position or momentum for each atom (or monomer) within the aerosol system. We demonstrate that entropy arises from particle parameters (kinetic movement and position) and atomic arrangement (configurational and surface) within the particle. Statistical thermodynamic expressions are derived for each component of the aerosol entropy and it is shown that the rate of entropy generation is dominated by configurational entropy.
The main findings that arise from this study are that the kinetic limited process of coagulation does not reach a maximum entropy for a given volume and number concentration, but approaches a local entropy maximum rather than a global maximum for short periods of time. The maximum entropy size distribution function for example is a combination of Dirac functions, and, for a given volume and particle number constraints, the Gumbel and Lognormal distributions exceed the self-preserving distribution in their values of entropy. This self-preserving is still observed, however, in practical cases because it is the one most compatible with the kinetics of aerosols. In a dynamic process, variations of entropy are found to be very dependent on the initial population considered. As will be shown, the entropy of a coagulating system evolves to the same final state for a given total particle volumes, but at different rates depending on the initial particle concentration and size.
Further work from the Boies group seeks to expand the analysis to include non-coalescing aerosol agglomeration, as well as aerosol processes such as charging and restructuring.