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Engineering Mathematics
Review of Viscous Flows
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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 |

Aerosol Kinetics

Terminal Velocity

For a particle starting from rest, the solution to equiaton 2 is given as

(5)

where uƒ is assumed to be a constant vector. For uƒ=0 and large t, the terminal velocity of particle ut is given by

(6)

Table 7: Relaxtion time τ for a unit density particle in the air(p=1 atm, T=20°C)

Diameter, µmut=τ gτ (sec)Stop Distance
uo = 1m/s
Stop Distance
uo=10m/s
0.050.39 µm/s4x10-80.04 µm4x10-4 mm
0.10.93 µm/s9.15-80.092 µm9.15x10-4 mm
0.510.1 µm/s1.03x10-61.03 µm0.0103 mm
135 µm/s3.57x10-63.6 4µm0.0357 mm
50.77 mm/s7.86x10-578.6 µm0.786 mm
103.03 mm/s3.09x10-4309 µm3.09 mm
507.47 cm/s7.62x10-37.62 mm76.2 mm

Stopping Distance

In the absence of gravity and fluid flow, for a particle with an initial veolocity of u, the solution to 2 is given by

(7)

(8)

where xp is the position of the particle. As t→&infin, up→0 and

(9)

is known as the stopping distance of the particle. For an initial veolocity of 1000 cm/s, the stop distance for various particles is listed in Table 7.



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