5% - eTheses Repository - University of Birmingham

Figure 7h-i. The temporal fluctuations in the magnitude of the forces in the
horizontal and vertical directions respectively on a particle falling along
trajectory D in figure 7b. The pressure and fluid gradient forces pull the
particle to the right as it approaches the core, producing the second peak in
figure 7c.
Figure 7j . The temporal fluctuation in the magnitude of the particle and
fluid velocities in the core region for a particle falling along trajectory
D in figure 7b. The lift force component in the vertical direction changes
sign at around the vortex mid-plane because the difference between the
horizontal fluid and particle velocities changes sign.
Figure 7k. The temporal fluctuations in the magnitude of the horizontal and
vertical components of the lift-force due to the change in relative fluid-
particle horizontal velocity shown in figure 7j.
Figure 71. The relaxation time between the particle and fluid horizontal
velocities for a particle following trajectory D. The particle's inertia
prevents instantaneous response to spatial changes in the fluid velocity in
this steady flow.
Figure 7m. The vector forces acting on the particle at various points along
trajectory E.
Figure 7n. The temporal fluctuations in the magnitude of vertical components
of the forces acting on a particle falling along trajectory F in figure 7b.
The third peak forms on figure 7c because the particle reaches the cusp point
where it is virtually stationary for an extended period.
Figure 7o. The sum of the forces balances the buoyancy force on the particle
at the cusp point.
Figure 8a. Graph of the critical particle terminal fall speed for a range of
core sizes. A particle with terminal fall speed less than this critical value
xv