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Engineering Mathematics
Review of Viscous Flows
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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 |

Lift Force

Small particles in a shear field as shown in Figure 1 experience a lift force perpendicular to the direction of flow. The shear lift originates from the inertia effects in the viscous flow around the particle and is fundamentally different from the aerodynamic lift force. The expression for the inertial shear lift was first obtained my Saffman(1965.1968). That is

(1)

Calculation Model

Saffman Lift Force

Saffman Lift Force


Here uƒ is the fluid velocity at the location of the mass center of the particle, up is the particle velocity, is the shear rate, d is the particle diameter, and ρ and ν are the fluid density and viscosity. Note that FL is in the positive-y direction if uf>up.
Equation 1 is subjected to the following constraints:
Here Ω is the rotational speed of the sphere. Dandy & Dwyer(1990) found that the Saffman lift force is approximately valid at larger Res and small ε. McLaughlin(1991) showed that the lift force decreases as ε decreases. Based on these studies, Mei(1992) suggested the following empirical fit to the results of Dandy and Dwyer and McLuaghlin. For large ε and Res,

(2)

where

(3)

For 0.1<ε<20

(4)

For large and small ε McLaughlin obtained the following expressions

(5)
Note the change in sign of the lift force for the small values of ε.



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