Particle Migration in Velocity Fields
Small particles are subject to Brownian motion caused by bombardment by solvent
molecules. Larger particles have so much mass that no Brownian motion is observed.
Coagulation requires encounters between particles. Small particles may approach each
other by diffusion, and Brownian motion may help overcome electrostatic repulsion so
that they join together. However, as the aggregate grows, the mass increases so
that Brownian motion becomes unimportant.
Simple mixing causes the fluid to turn or rotate, and particles with their greater inertia may
be subjected to centrifugal forces. It turns out that these of roughly of the same
magnitude as Brownian motion. There must be some other reason that mixing has
a significant effect on particle motion.
Research on particle migration.
Consider a particle in a velocity gradient as might be caused by mixing. The following sketch
showns the velocity gradient as arrows of differing length:
By analogy to the lift forces on an airplane wing ( Bernouli's principle ), the unequal
velocities induce forces on the particle. These are many times the usual centrifugal
force. Furthermore, the force is proportional to the square of the particle diameter.
Still another force is important-the Magnus force because of particle rotation. Whereas
the force analogous to a Bernouli force moves the particle toward the greater
velocity of fluid elements, the rotational force due to the streamlines dragging on the
particle is in the opposite direction.
We see that forces induced by velocity gradients can play a major role in moving
particles and helping them to collide. These forces tend to be greater as the
particles increase in size. Of course, very large particles distort the velocity fields
and complicate this analysis.
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