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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics

Particle Adhesion
Simulation Methods
Experimental Techniques
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The National Science Foundation
ME 537 The National Science Foundation
 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 |

Brownian Motions

The autocorrelation of the particle velocity field defined as (with a bar standing for the expected value) is the inverse Fourier transform of the power spectrum function. i.e.,

(7)

Hence

(8)

From (6) and (7) it follows that

(9)

The mass diffusivity is defined as

  for large t, (10)

where x(t) is the position of particle given by

(11)

Using (11), one finds

(12)

Changing variables, after some algebra it follows that

(13)

Thus,

(14)

Using (6) or (9) in (14), we find

  (15)



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