Theoretical Analysis of the Velocity Gradient
This analysis was for both a tube and plate settler. Although tube settlers are used in the lab, plate settlers are used in the Honduras plants. Therefore, a model that takes into account the differences between the two apparatuses must be developed. With an accurate way to model floc roll up in a tube or plate settler, we can predict when floc roll up will happen given a set of conditions. This can help us optimize the plate settler spacing in order to prevent floc roll up from occuring.
Laminar Flow Profile
Calculation of Ratio of Settling Velocity to Particle Velocity
Plate Settler Spacing
Recommendations
*More detail on the calculation process outlined above can be found in the Math CAD File
When an incompressible fluid flows through a cylindrical tube its velocity relative to the walls changes as a function of the tube radius. In general, this velocity distribution is parabolic: the greatest velocities are achieved at the center of the tube (where R=0) eventually tapering off to 0 at the walls. The parabolic nature of the distribution arises from cylindrical symmetry as well as the fact that the fluid does not move at the walls (the "no-slip" condition).
This gradient in the velocity profile contibutes to the force that a floc experiencing roll-up feels. Flocs actually begin to roll up when the velocity at their edge exposed to the flow exceeds some critical value, which is highly dependent on the floc's diameter, its density, and the capture velocity of the system, among other things.
Applying a force balance to this: