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The current theory of plate settlers predicts the failure for a specific sedimentation tank and plate settler spacing based on a failure mechanism called floc roll-up. The floc roll-up theory looks at the ongoing force dynamics acting on the single floc particle. The theory
states that a floc hitting the bottom plate will experience two opposing velocities - a fluid velocity at its edge and a settling velocity due to the gravity force.


 

The velocity experienced at the edge of the particle is given by the following expression:

{latex}
\large
$$
{{ V_{ParticleEdge} }} = {{ 2 V_{\alpha} \left(1 -  \left(\frac{R - d_{Particle}}{R} \right)^2 \right)   }}
$$

{latex}

Thus, if the velocity experienced at the particle's edge is greater than the settling velocity, then the floc will roll up and exit the sedimentation tank without being captured. Ultimately, the effluent turbidity increases. Conversely, if the floc's settling velocity is greater than the upflow velocity, the floc will roll down and end up being trapped in the floc blanket.

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The current theory predicts failure by the mean of a dimensionless

{latex}\huge $$\Pi$${latex}

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