Analytic Solution of the Aerosol Rigorous General Dynamic Equation Without Coagulation in Multidimension

Abstract

ABSTRACT. We present the an alytic solution to the problem of multicomponent aerosol evolution due to condensation and /or evaporation of its components, sources, and deposition mechanisms. We use the rigorou s formulation , which utilizes a p article number distribution depending on time and on the am ount of each component, being that the particle size is a derived variable. This allows us to an alyze the aerosol without the usual assumption of intern al mixing. We solve the hyperbolic equ ation obtained through the method of characteristic curves. When all components condense, the obtained solution is always valid. When some of the components evaporate, the problem is more complex and its solution (which is not provided here) has to incorporate nonlinear phenomen a such as shock and rarefaction waves, which are dif® cult to h andle. The an alytic solution s can be used to validate the numerical methods th at could be developed in the future for more complex cases. We h ave an alyzed a bicomponent case, and we h ave shown th at in the aerosol evolution followin g condensation, nearly vertical ª wallsº appear in the particle size distribution.

Integrated Framework for the Numerical Solution of Multicomponent Population Balances. 2. The Split Composition Distribution Method

“…The species mass distribution method − addresses the number conservation caveats of the multicomponent sectionalization method by implementing a continuous analogue of the multicomponent sectionalization method. This can also be interpreted as reducing the dimensionality of multicomponent population balance problems via the internally mixed assumption, which states that particles of the same size all have the same composition and effectively reduces the governing equation set to ps equations representing each species in the system at p node points. The sacrifice for this reduction in complexity, of course, is the lack of ability to account for compositional variations at each size range of the population.…”