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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