3.2 Flocculation Hydraulics & Floc Formation

Flocculation Physics: Perikinetic vs. Orthokinetic Aggregation

Following rapid mixing and colloidal destabilization, water enters the flocculation basin. The primary goal of flocculation is to provide continuous, gentle fluid motion that maximizes interparticle collision frequency, agglomerating destabilized microscopic particles into large, dense, settleable aggregates called macroflocs.

Particle aggregation proceeds through two distinct physical mechanisms:

1. Perikinetic Flocculation (Brownian Motion):

   • Driven by the thermal kinetic energy and random collision of water molecules against sub-micron particles ($< 1.0\text{ }\mu\text{m}$).
   • Dominates for the first few seconds immediately after flash mixing.
   • As particles grow larger than $1.0\text{ }\mu\text{m}$, Brownian motion diminishes and becomes ineffective for further aggregation.

2. Orthokinetic Flocculation (Fluid Shear & Mixing):

   • Driven by applied velocity gradients and bulk fluid movement.
   • Fluid shear creates relative velocity differentials between adjacent fluid layers, allowing faster streamlines to sweep larger particles into collision with slower particles.
   • Orthokinetic collision frequency ($N_{ij}$) between particles of diameters $d_i$ and $d_j$ is given by Smoluchowski's equation: $N_{ij} = \frac{1}{6} G (d_i + d_j)^3 n_i n_j$ Where $G$ is the velocity gradient, and $n_i, n_j$ are particle number concentrations.
   • Because collision frequency is proportional to $(d_i + d_j)^3$, as flocs grow, their collision cross-section expands exponentially, accelerating particle growth.

Flocculation Kinetics, Velocity Gradients, and the Camp Number ($Gt$)

Flocculation process design is governed by three interconnected hydraulic variables: the velocity gradient ($G$), the hydraulic detention time ($t$), and their dimensionless product, the Camp-Stein parameter ($Gt$).

1. Velocity Gradient ($G$)

• Standard Operational Range: $20\text{ to }80\text{ s}^{-1}$.
• Controls the rate of fluid shear. If $G$ is too low ($< 15\text{ s}^{-1}$), collision energy is insufficient, particles fail to contact, and heavy flocs prematurely settle on the flocculator floor. If $G$ is too high ($> 80\text{ s}^{-1}$ in late stages), hydrodynamic shear exceeds floc tensile strength, tearing flocs apart.

2. Hydraulic Detention Time ($t$)

• Standard Operational Range: $20\text{ to }40\text{ minutes}$ under average design flow ($30\text{ to }45\text{ minutes}$ in cold-climate surface water facilities to compensate for slow reaction kinetics).

3. The Camp-Stein Dimensionless Parameter ($Gt$)

The product of the velocity gradient ($G$, in $s^{-1}$) and hydraulic detention time ($t$, in seconds) represents the total mixing energy and collision opportunities applied to the water: $Gt = G \times (t_{\text{min}} \times 60\text{ s/min})$

• Target Design Criteria: $Gt = 30,000\text{ to }100,000$ (optimal $50,000\text{ to }80,000$).
• If $Gt < 30,000$: Under-flocculation occurs; microflocs remain small ("pin floc") and carry over across the clarifier into filter beds, causing short filter runs and rapid headloss accumulation.
• If $Gt > 100,000$: Over-mixing occurs; input shear energy destroys floc bridges, producing sheared, ragged particles that resist sedimentation.

The Necessity of Tapered Energy Dissipation

As flocs aggregate from microflocs ($10\text{--}50\text{ }\mu\text{m}$) into macroflocs ($1.0\text{--}3.0\text{ mm}$), their mass increases, but their structural density decreases, making them increasingly fragile. High fluid shear that is beneficial for initial microfloc collision will tear apart mature macroflocs.

To resolve this physical contradiction, modern flocculators use tapered flocculation across at least three compartmentalized stages separated by slotted baffles:

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Flocculator Configurations and Mechanical Equipment

Water treatment facilities utilize two primary classifications of flocculation basins: mechanical flocculators and hydraulic (baffled channel) flocculators.

1. Mechanical Flocculators

Mechanical units provide flexible process control by allowing operators to adjust mixing intensity via Variable Frequency Drives (VFDs) or mechanical speed variators:

• Horizontal Shaft Paddle Wheels: Large wooden or fiberglass blades mounted on horizontal shafts rotating either parallel or perpendicular to flow. Stator baffles mounted on basin walls prevent rotational bulk fluid swirling. Maximum blade peripheral tip speed must remain below $3.0\text{ ft/s}$ ($0.9\text{ m/s}$) (ideally $0.5\text{ to }2.0\text{ ft/s}$) to prevent shearing at the blade tips.
• Vertical Turbine / Axial-Flow Hydrofoils: Vertical shaft impellers mounted in individual square baffled cells. Hydrofoil impellers produce axial downward flow with minimal shear gradients compared to flat paddle blades, delivering uniform energy dissipation with lower electrical power requirements.

2. Hydraulic (Baffled Channel) Flocculators

Hydraulic flocculators use basin head loss across serpentine channels to generate velocity gradients without mechanical drives:

• Around-the-End Baffled Channels: Horizontal flow serpentines where water turns 180 degrees around partition walls.
• Over-and-Under Baffled Channels: Vertical flow channels where water flows alternately over submerged weirs and under hanging baffle walls.
• Operational Limitation: In hydraulic flocculators, the velocity gradient is directly linked to plant flow rate ($G \propto \sqrt{\Delta h} \propto Q^{1.5}$). If plant production drops during low-demand periods, head loss and $G$-values plummet, leading to under-mixing and premature solids deposition in the channels. If flow surges, excessive head loss shreds flocs.

3. Floc Transfer Hydraulics

The conduit or channel connecting the flocculation basin to the sedimentation basin must be carefully engineered:

• Maximum Transfer Velocity: $0.5\text{ to }1.5\text{ ft/s}$ ($0.15\text{ to }0.45\text{ m/s}$).
• Velocities below $0.5\text{ ft/s}$ permit mature flocs to settle and accumulate in transfer conduits.
• Velocities exceeding $1.5\text{ ft/s}$, violent drops over effluent weirs, or throttling through sharp-edged gates generate extreme hydrodynamic shear, shredding macroflocs back into non-settleable microflocs immediately before clarifier entry.

Floc Characterization and Process Monitoring

Operators monitor floc development using visual observation, jar tests, and on-line instrumentation to optimize coagulant dosage and mixing speeds:

Visual Morphology Guide

• Pin Floc ($< 0.5\text{ mm}$): Tiny, sand-grain-sized or powdery particles suspended in hazy supernatant that settle very slowly ($< 0.2\text{ ft/min}$). Indicates chemical under-dosing, low alkalinity, cold water inhibition, or insufficient $Gt$ energy.
• Well-Formed Macrofloc ($1.0\text{ to }3.0\text{ mm}$): Distinct, dense, feathery or spherical aggregates resembling snowflake structures with crystal-clear interstitial water between particles. Settles rapidly ($1.0\text{ to }4.0\text{ ft/min}$) in quiescent conditions.
• Sheared / Ragged Floc: Irregular, frayed floc fragments surrounded by cloudy, milky background water. Indicates excessive paddle RPM, conduit shear ($> 1.5\text{ ft/s}$), or sharp drops across basin gates.
• Bulky, Billowing Floc: Oversized, gelatinous flocs ($> 5\text{ mm}$) that fail to compact. Indicates excessive polymer aid dosing, which blinds filter beds rapidly.

Troubleshooting Flocculation Operating Problems