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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

When a small particle is suspended in a fluid, it subjected to the impact gas or liquid molecules. For ultra fine particles (colloids), the instantaneous momentum imparted to the particle varies random which causes the particle to move on an erratic path now known as Brownian motion.  Figure 1 illustrates the Brownian motion process. 

Figure 1. Schematics of a Brownian motion process.

The Brownian motion of a small particle in a stationary fluid in x-direction is governed by the following Langevin equation,

(1)

where u is the velocity of the particle,

Brownian Motion Calculation Models

Brownian Motion - Introductory

Brownian Motion in Poiseuille Flow
Spherical particle motion in poiseuille flow with brownian effects...


Brownian Motion - Advanced

Brownian Motion in Poiseuille Flow
Spherical particle motion in poiseuille flow with brownian effects...

(2)

and n(t) is a white noise excitation due to the impact of fluid molecules on the particle. The intensity of noise is specified by its spectral intensity given as

(3)

where is the Boltzmann constant and T is the temperature. It should be emphasized that the Brown motion occurs in three dimensions and Equation (1) applies only to the x-component of the motion.

 For the stochastic equation given by (1), using the standard linear system analysis, it follows that

(4)

where is the power spectrum of the velocity of the Brownian particle, and is the system function given by

(5)

Hence,

(6)



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