Aerosol

Computational and Applied Mathematics Vol. 23, N. 2-3, pp. 401–423, 2004 Copyright © 2004 SBMAC www.scielo.br/cam

Modeling and simulation of multi-component aerosol dynamics
YALCHIN EFENDIEV
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368 E-mail: efendiev@math.tamu.edu

Abstract.

In this paper we consider the modeling of heterogeneous aerosol coagulationwhere the heterogeneous aerosol particles (called droplets) contain smaller particles (enclosures). Droplets and enclosures coagulate with different collision kernels. We discuss macroscopic modeling and simulation of these processes using both deterministic and Monte-Carlo methods.

Mathematical subject classification: 65C05, 65C35. Key words: multi-component, aerosol, Monte Carlo,heterogeneous. 1 Introduction

The study of aerosol dynamics is often limited to homogeneous, singlecomponent aerosol particles. Furthermore, even those studies that have employed more than one component assume that aerosol is a homogeneous mixture of all multi-component constituents. However, it is known that phase segregation will take place within an aerosol droplet if the thermodynamics and kineticsare favorable, in a manner analogous to that observed in bulk materials. So in order to accurately predict and control multi-component particle production it is not sufficient to assume that aerosol is a homogeneous mixture of all multicomponent constituents. In a manner analogous to bulk materials our goal is to be able to control and characterize the overall behavior of the multi-component aerosolparticles. It is becoming increasingly apparent that multi-component aerosol particles are of both industrial importance and an area in need of significant research activity.
#567/04. Received: 16/IV/03. Accepted: 23/VI/04.

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MODELING AND SIMULATION OF MULTI-COMPONENT AEROSOL DYNAMICS

There have been a number of multi-component aerosol dynamics studies with heterogeneous aerosolparticles that have shown the importance of multi-component aerosol particles in material synthesis. There are experimental studies on the formation of binary metal oxide systems with application to removal of heavy metals [4, 5] as well as the formation of materials with novel and interesting properties [10, 11, 26]. One of the main goals in this research is to study the evolution of the internalstate of the aerosol droplets and accurately predict and control their internal morphology. Initial success in growing interesting microstructures [26] indicated that further research was warranted. In subsequent studies both in-situ investigation into the formation process [18], multi-component aerosol dynamic modeling [3] and molecular dynamics computation [27] have been employed. One of the primaryconclusions was that for high temperatures where these materials are typically grown, nanodroplets are in liquid-like state, and that phase segregation taking place within the nanodroplet was probably limited by the transport within nanodroplet. This was one of our working assumptions in modeling and simulation [7, 8 9] of multi-component nanodroplets. In Figure 1 we present an example of TEMresults for the SiO2 /F e2 O3 system. In the course of this paper, we shall use the terms minor phase and enclosure interchangeable to refer to the component within each aerosol droplet, and droplet or aerosol when referring to the major phase. The mathematical formulation of the problem allows one to consider the enclosures as particles inside the droplet that coagulate with collision kernel that isdifferent from that of droplet coagulation. The temporal evolution of the aerosol and enclosures is schematically depicted in Figure 2. Instantaneous coalescence assumption is used in the modeling that is justified by experiments. More detailed description of the experiment can be found in [26]. In the paper we will be interested when collision processes governing droplet coagulation and...