Normal‐Mode Propagation Calculations for a Parabolic Velocity Profile

1970 ◽  
Vol 48 (3B) ◽  
pp. 745-752 ◽  
Author(s):  
N. C. Nicholas ◽  
H. Überall
Keyword(s):  
Velocity Profile ◽  
Normal Mode ◽  
Mode Propagation ◽  
Parabolic Velocity Profile

scholarly journals The lift on a small sphere in a slow shear flow

1965 ◽  
Vol 22 (2) ◽  
pp. 385-400 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Kinematic Viscosity ◽  
Lift Force ◽  
Flow Direction ◽  
Functional Dependence ◽  
Small Sphere ◽  
Translation Velocity ◽  
Parabolic Velocity Profile ◽  
Direction Opposite

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

scholarly journals Band Edge Effects and Normal Mode Propagation in Waveguide Magnetophotonic Crystals

2006 ◽  
Vol 30 (6−2) ◽  
pp. 561-566 ◽  
Author(s):  
M. Levy ◽  
R. Li ◽  
A. A. Jalali ◽  
X. Huang
Keyword(s):  
Normal Mode ◽  
Edge Effects ◽  
Band Edge ◽  
Mode Propagation ◽  
Magnetophotonic Crystals
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