Aerosols
Introduction to Aerosols | Drag, Lift Forces | Aerosol Kinetics | Virtual Mass, Basset Forces & BBO Equation | Nonspherical Particles | Brownian Motions | Particle Deposition Mechanisms | Electrodynamics | Aerosol Coagulation |

Coagulation of Particles Coagulation of Monodisperse Spheres  Equation (1) may be restated as (4) The concentration field then is given by (5)

Calculation Model Particle Collision

The flux to surface of the reference particle is given by

(6)

where  is the total flux to the surface of the reference particle per unit time. Using (5), it follows that

(7)

For large ,

(8)

 In reality, the reference particle is not fixed and is diffusing itself. The relative diffusivity of two particles is sum of their diffusivities. That is according to Einstein's equation

 ,

(9)

In the derivation of (9) it is assumed that , the reference particle collides with

(10)

particles. Here,  collisions if all the particles collide once. Assuming that the particles stick to each other upon collision, it follows that

(11)

where

(12)

is the collision frequency function of coagulation constant.

Equation (11) may be solved. i.e.,

(13)

or

(14)

Here,  is the half-value time, which is the time that the concentration becomes half of its original value.

Dr. Goodarz Ahmadi | Turbulence & Multiphase Fluid Flow Laboratory | Department of Mechanical & Aeronautical Engineering
Copyright © 2002-2005 Dr. Goodarz Ahmadi. All rights reserved.
Potsdam, New York, 13699
ahmadi@clarkson.edu