Creeping Flow Past a Sphere
Substituting (12) and (13) into (9), the explicit expression for
the stream function becomes
The velocity components are then given by
Figure 2a shows the streamline for the creeping flow around a sphere.
Comparing the streamlines of the creeping flow conditions to the potential flow one given by
and is plotted in Figure 2 b, it appears that the stream lines are more dispersed.
a) Viscous Flow |
b) Potential Flow |
Figure 2. Comparison of the streamlines for creeping and potential flows.
For moving spheres, the stream function is given by
a) Viscous Flow |
b) Potential Flow |
Figure 3. Comparison of the streamlines for creeping
potential flows in a moving frame. For the moving sphere coordinates the corresponding streamlines are shown in
Figure 3. Figure 3a shows that the particle appears to be dragging the viscous
fluid as it moves, while Figure 3b through suggests that the particle pushes
the fluid in the potential flow regime.
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