Current Team Research Focus - Spring '11
Effect of a Floc-Rollup Phenomenon on Flocs
Introduction
Traditionally, inclined plate and tube settlers are used to create compact sedimentation tanks. Conventional design guidelines are based on obtaining a desired sedimentation design capture velocity. Theoretically, this capture velocity can still be achieved while greatly reducing conventional plate spacing or tube diameter. Yet, the greatest concern with small plate spacing is the danger of settling sludge being swept out with the finished water - the phenomenon known as the floc-rollup. It is the purpose here to estimate the effect of the floc-rollup inside the plate settlers.
Particle Capture by a Lamella
The experimental testing was performed on tube settlers and the design capture velocity of tube settlers in which the ends of the tube are perpendicular to the axis of the tube is given by (Eq 1):
where
L is the length of the tube settlers,
D is the tube diameter,
Vup is the average vertical component of the fluid velocity in the tubes,
and VC is the terminal velocity of the slowest settling particle that is reliably captured by the tube settler.
Eq 1 illustrates that tube settler performance (as manifested by Vc) is maintained as long as the ratio of L/D is constant for a fixed . Thus, it is theoretically possible to reduce L by decreasing the diameter of the tube settlers, D. After a floc settles on the lower surface of a plate or a tube it continues to experience an upward drag caused by the fluid flow. The velocity at the centerline of the floc increases if the spacing between plates or the diameter of the tube is decreased while maintaining a constant average fluid velocity. Gravitational force will cause flocs to roll or slide down the incline while the fluid drag will tend to cause the floc to roll or slide up the incline. When the fluid drag and the gravitational forces balance, the floc remains stationary. This balance point is approximated by determining the point at which the velocity caused by fluid drag at the centerline of the floc is the same as the opposing component of its terminal velocity along the slope.
As seen from Figure 1, the relationship between the velocity in the direction of the slope and the vertical component is (Eq 5):
where is the vertical velocity component.
An approximate equation for the fluid velocity as a function of distance from the wall can be obtained by using the velocity gradient at the wall. The velocity at the center of a floc resting on the wall of a circular tube is (Eq 6):
Then the diameter of a floc can be estimated from the properties of the primary colloidal particles and its
terminal velocity, which is defined as (Eq 7):
From this equation, the diameter of a floc can be recovered (Eq 8):
Consequently, an equation containing both the terminal velocity of a floc and the diameter of a floc results (Eq 12):
The floc terminal sedimentation velocity in Eq 12 represents the slowest settling floc that can slide down an incline. Flocs with a terminal velocity lower than will be carried out the top of the tube (i.e., "roll up") even if they settle on the tube wall. Thus, this terminal velocity represents an additional constraint on the capture velocity for tube settlers. Unlike the design sedimentation capture velocity (equation 1Error! Reference source not found. ) which is exclusively a property of the geometry and flow characteristics of the sedimentation tank, the capture velocity needed to prevent flocs from rolling up and out of the tube (referred to here as the "roll up capture velocity") is a property of the floc as well as the sedimentation tank geometry and flow characteristics. This complexity is a result of the interaction between the size of the floc and the linear velocity gradient.
The floc roll up capture velocity can be made explicit by solving Eq 12 for the floc terminal velocity, V-t. This Floc with this terminal velocity, which is going to be named the roll up capture velocity, V_cRollup, applies to the floc that will be held stationary on the incline because of a balance of drag, as given (Eq 13):
The flocw roll up capture velocity, is a function of tube diameter, D, for the case of three different upflow velocities. However, for a given upflow velocity, a decrease in tube diameter results necessitates in a higher particle settling velocity for particle capture to occur. a higher capture velocity.
The influence of fractal dimension, up flow velocity, primary particle size, and primary particle density on the floc roll up capture velocity is dramatic. If the floc fractal dimension is only slightly greater than 2 , the exponent of the right hand side in equation 1310 can be quite large. The exponent on the up flow velocity, , is . For a fractal dimension of 2.3 the exponent has a value of 4.3 and for a fractal dimension of 2.2 it increases to 6. Flocs with a fractal dimension slightly above 2.0 are especially vulnerable to rolling up the tube settlers. The effect of fractal dimensions less than 2.0 is described below.
The smallest diameter tube settler that will capture a floc with a given terminal sedimentation velocity may be obtained by solving equation 1310 13 for D:
(14)
Experiments
Constant 0.10 mm/s design capture velocity experiments have been conducted using tube settlers of two different inner diameters, 6.35 mm and 9.53 mm respectively, for a range of V-alpha. The figure below shows the measured pC*s as a function of V-alpha. When V¬α increases, the performance of the system decreases, while the performance of the floc blanket remains relatively consistent with the increasing V¬α for an average value of pC* of 1.12. The graph shows a first order decreasing trend of the system performance.
Results and Conclusions
All the above results are given for tubes. V-rollup is dependent on the velocity gradient, which is ¾ less for plates than for tubes. All equations with the linearized velocity gradient at the wall are therefore changed by a factor of ¾ for plates. Thus for a given V_↑, for plates will be of a smaller magnitude than the V-rollup for tubes. Thus plates are slightly less vulnerable to floc roll up than are tubes given the same diameter and spacing.
The floc roll up model delineates a failure mechanism that prevents flocs from sliding along an inclined surface in the countercurrent direction. This failure is caused by fluid drag resulting from velocity gradients at the plate or tube wall that oppose gravity forces. Velocity gradients increase as the plate settler spacing or tube diameter is decreased and as the upflow velocity is increased. We expect that high velocity gradients will cause flocs to "roll up" an inclined surface and act to increase effluent turbidity. If the tube settler diameter or plate settler spacing is too small, high velocity gradients can cause roll-up of flocs that would otherwise be captured. Evaluated this phenomenonm utilizing a combined tube-settler floc blanket system to characterize the removal effectiveness for colloidal particles at different flow conditions, but at a constant design capture velocity of 0.1 mm s-1. Experimental data suggests that plate spacing as small as 1 cm for an upflow velocity of 1 mm/s can be implemented without causing performance deterioration.
Tube settler performance deteriorated when the the floc roll up capture velocity was larger than the sedimentation design capture velocity.
