Coagulation affects the size distribution of particles produced in aerosol
reactors. It influences the production of particulate pollutants in flames and their elimination by
electrostatic precipitators, fibrous filters, cyclones, etc. Coagulation of raindrops plays an important role
in cloud dynamics, precipitation, and the scavenging of pollutants by precipitation. Turbulent
coagulation is particularly important for particles with diameters of one to several microns and pollutants
of this size pose the greatest risk to human health.
Coagulation occurs when Brownian motion, differential sedimentation, or
turbulent flows force two particles or drops into contact and the particles stick to form an aggregate or
larger drop. The rate of coagulation depends on both the forces driving the relative motion of the
particles and the hydrodynamic, van der Waals and electrostatic interparticle interactions. A good
fundamental understanding of the mechanisms of coagulation leading to quantitative
predictions of coagulation rates has been achieved for colloidal particles suspended in liquids. This
achievement is largely attributable to the ability of researchers to isolate each of the various
driving forces (Brownian motion, laminar shear, turbulent shear and sedimentation) in turn by judicious
use of density matching of the fluid and particles and adjustment of the fluid viscosity.
In contrast, the current understanding of aerosol aggregation processes is
rudimentary. Two important features that distinguish the coagulation of aerosols and hydrosols
are: (a) the importance of particle inertia in aerosols; and (b) the non-continuum gas flow between
colliding aerosol particles. These features present interesting challenges for the theoretical prediction of
aerosol flocculation. In experimental measurements on Earth, it is difficult to obtain the ideal
situation in which aerosols coagulate solely due to turbulent flows. Instead, one is likely to observe mixed
effects of Brownian motion, sedimentation and turbulence, making a critical test of the theory
difficult.
We are planning an initial ground-based program of theoretical analysis and
experimental measurements of aerosol coagulation due to isotropic turbulence. These studies
will provide the necessary background to plan and propose a microgravity experiment on aerosol
coagulation four years from now.
For the experiments, we will produce an aerosol of nearly monodisperse aerosol
particles with a mean diameter of 1-5 •m using a Condensation Monodisperse Aerosol Generator (TSI
3475). This aerosol will flow slowly through a turbulence chamber stirred by an oscillating grid.
The pressure in the chamber will be varied to change the mean-free path of the gas. The turbulent
flow will be characterized using laser Doppler anemometry and known scaling relationships for
oscillating grid turbulence. In this way, we will obtain an accurate assessment of the flow field
to which the aerosol is subjected. The particle concentration and size distribution will be measured
in situ at various points in the chamber using Dantec's Particle Dynamics Analyzer (PDA). The PDA is based
on the latest fiber optic technology and obtains the local particle concentration, velocity,
and size distribution from the light scattered by the particles. Efforts will be made to extract data
representative of singlet-singlet coagulation events by limiting the residence time of the aerosol in the
turbulent reactor. By using monodisperse drops with a mean diameter of 1-3 •m, we can maximize the
importance of turbulence relative to Brownian motion (which dominates for smaller particles)
and sedimentation (important for larger particles). However, the extent to which we can isolate
turbulence from these other mechanisms will be limited and this forms the motivation for our future
microgravity experiment.
To predict coagulation rates, we must first determine the resistivity tensor
describing the viscous resistance to the various modes of relative motion of a pair of aerosol
particles. The particles of interest have diameters comparable with or slightly larger than the mean-free
path of the gas and the interparticle separation becomes smaller than the mean-free path during the
interparticle collision. Thus, we must solve a rarefied gas flow problem to determine this resistance. We
will adapt the direct-simulation Monte Carlo method for calculations at low Mach numbers in
order to obtain a solution of the Boltzmann equation for the non-continuum gas flow between the
colliding drops.
The viscous resistivity tensor can be used together with a description of
the van der Waals attractions between the particles to specify the interparticle
forces. We must then solve Newton's laws of motion for the dynamic encounter of
pairs of coagulating drops. The fine particles under consideration have radii
much smaller than the Kolmogorov length scale. Exploiting this fact, we will
conduct numerical simulations in which pairs of particles are subjected to a
temporally fluctuating linear flow field, whose statistics are chosen to
reproduce results from previous direct numerical simulations for the Lagrangian correlation functions of the strain and rotation rates in isotropic
turbulence. Ensemble and time averages of these stochastic flow simulations will provide the rate
constant for turbulent coagulation. In addition to simulations corresponding to the ideal case of
turbulent coagulation of non-Brownian particles in microgravity, we will also consider mixed
turbulent/sedimentation and turbulent/Brownian simulations.
Koch, D.L., Cohen, C., Turbulent Coagulation of Aerosol Particles, Proceedings of the Fifth Microgravity Fluid Physics and Transport Phenomena Conference, NASA Glenn Research Center, Cleveland, OH, CP-2000-210470, pp. 1365-1367, August 9, 2000.