Abstract
The Plate Settler Spacing team is currently investigating the Floc Roll-Up Phenomenon in the tube settler. By developing a velocity gradient model, we hope to both analytically and experimentally determine the critical velocity floc particles experience when they begin to roll up the settler tube and into the effluent rather than settling back down the tube and into the floc blanket. Additionally, we hope to understand how properties of the flocs themselves affect floc roll-up.
Overview of Methods
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 contributes to the force that a floc experiencing roll-up feels. The sharp slope of the velocity gradient in the tube will cause the particle to experience a much higher velocity on the side closest to the center of the tube. This discrepency between velocities on either side of the particle will cause the floc to being to roll, creating this floc roll-up phenomenon. Flocs actually begin to roll up when the velocity at their edge exposed to the flow exceeds the settling velocity that the floc particle experiences. The velocity experienced by the floc particles at the point at which they begin to roll up the tube rather than settle out is called the critical velocity. The settling velocity of a floc particle is dependent on floc diameter and floc density. Conversely, the critical velocity a floc experiences is dependent on floc diameter and the inner tube diameter.