2.2 Coagulation, Flocculation & Sedimentation Processes

Colloidal Chemistry & Electrokinetic Theory

Suspended matter in surface water consists of silt, clay, microorganisms, and natural organic matter (NOM) ranging in diameter from $0.001\,\mu\text{m}$ to $1.0\,\mu\text{m}$. Because of their extremely small mass and high specific surface area, colloids remain in permanent suspension due to Brownian motion (thermal molecular bombardment) and do not settle under gravity (a $0.1\,\mu\text{m}$ colloidal clay particle requires over 20 years to settle 1 meter through quiescent water).

The Electrical Double Layer & Zeta Potential

In natural waters at neutral pH, colloidal surfaces carry a net negative electrical surface charge resulting from:

1. Isomorphous substitution of lower-valence metal ions within the mineral clay lattice.
2. Ionization of structural functional groups (carboxylic $-\text{COOH}$ and phenolic $-\text{OH}$ groups on humic/fulvic molecules).
3. Preferential adsorption of natural organic anions.

To balance this negative surface charge, waterborne cations orient themselves around each particle, establishing an Electrical Double Layer:

  Particle Surface (-) | Stern Layer (+) | Diffuse Layer (+ / -) | Bulk Solution (Neutral)
  ==================== | =============== | ===================== | =======================
         (-)           |      (+)        |        (+)   (-)      |       (+)   (-)
  Fixed Negative       | Fixed Cations   | Dynamic Counter-Ions  | Electrically Balanced
  Surface Charge       | (Adsorbed)      | (Gradual Decay)       | Water Matrix
                       |                 |                       |
                       |<-- Shear Plane / Slipping Plane -------->
                       |    [Zeta Potential Measured Here]       |

• Stern Layer: A rigidly bound, immobile monolayer of positively charged counter-ions held tightly against the negative particle surface by electrostatic attraction.
• Gouy-Chapman Diffuse Layer: A surrounding dynamic zone where positive counter-ions outnumber negative co-ions, with ion concentrations gradually equilibrating to the bulk solution.
• Shear Plane (Slipping Plane): The theoretical boundary separating ions moving with the hydrodynamic motion of the particle from the surrounding bulk fluid.
• Zeta Potential ($\zeta$): The electrical potential (measured in millivolts, $\text{mV}$) existing at the shear plane. In raw natural water, zeta potential typically ranges from $-15\text{ mV to } -30\text{ mV}$.

According to DLVO Theory (Derjaguin, Landau, Verwey, and Overbeek), the stability of a colloidal suspension is determined by the net balance between two opposing forces:

1. Van der Waals Attractive Forces ($V_A$): Universal short-range intermolecular attractive forces.
2. Electrostatic Repulsive Forces ($V_R$): Long-range repulsive forces generated by overlapping diffuse electrical double layers of adjacent negative particles.

The net energy curve creates a repulsive Energy Barrier. The fundamental purpose of chemical coagulation is to destabilize the suspension by reducing the zeta potential toward the isoelectric point ($0\text{ mV}$, with optimal coagulation typically occurring between $-5\text{ mV and } +3\text{ mV}$), suppressing the energy barrier and allowing attractive van der Waals forces to bond particles upon collision.

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Coagulation Mechanisms & Primary Chemical Reactions

Chemical coagulation achieves colloidal destabilization through four primary mechanisms depending on coagulant type, dosage, and raw water pH:

1. Double-Layer Compression: High ionic strength compresses the diffuse electrical double layer, reducing the range of electrostatic repulsion.
2. Charge Neutralization (Adsorption-Destabilization): Positively charged metal hydrolysis species or cationic polymers adsorb directly onto negative colloidal surfaces, neutralizing surface charges within $0.01\text{ to }0.1\text{ seconds}$. Risk: Overdosing causes charge reversal (positive particle charge) and colloidal restabilization.
3. Enmeshment in Precipitate (Sweep Flocculation): When metal coagulant is applied in concentrations exceeding the solubility limit of metal hydroxide, massive, sticky, amorphous precipitates ($Al(OH)_3$ or $Fe(OH)_3$) form rapidly. As these precipitates drop through the water column, they physically trap and enmesh colloids. This is the dominant mechanism in low-turbidity, high-color waters.
4. Inter-Particle Polymer Bridging: Long-chain synthetic polymer molecules attach to multiple colloids simultaneously, forming a structural molecular matrix.

   [Colloid -] --- (Polymer Chain) --- [Colloid -] --- (Polymer Chain) --- [Colloid -]

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Metal Coagulants & Alkalinity Consumption Stoichiometry

Primary coagulants are trivalent metal salts based on aluminum or iron.

1. Aluminum Sulfate (Alum): $Al_2(SO_4)_3 \cdot 14H_2O$

When standard dry or liquid commercial alum is added to water, it dissociates and hydrolyzes instantly through intermediate poly-nuclear species ($Al(OH)^{2+}, Al_7(OH)_{17}^{4+}, Al_{13}O_4(OH)_{24}^{7+}$) into solid insoluble aluminum hydroxide:

$$Al_2(SO_4)_3 \cdot 14H_2O + 3Ca(HCO_3)_2 \rightarrow 2Al(OH)_3\downarrow + 3CaSO_4 + 6CO_2\uparrow + 14H_2O$$

• Optimal Coagulation pH: $5.8\text{ to }7.5$
• Alkalinity Consumption: Each $1.0\text{ mg/L}$ of commercial alum consumes approximately $0.50\text{ mg/L}$ of natural alkalinity as $CaCO_3$ and releases free carbonic acid ($CO_2$).
• If raw water total alkalinity is below $30-45\text{ mg/L as } CaCO_3$, alum addition will depress the pH severely below the optimal precipitation range, leaving soluble aluminum residuals in finished water and creating highly corrosive conditions. Supplementary base (hydrated lime $Ca(OH)_2$, soda ash $Na_2CO_3$, or caustic soda $NaOH$) must be dosed.

2. Ferric Chloride ($FeCl_3$) & Ferric Sulfate ($Fe_2(SO_4)_3$)

Iron-based coagulants hydrolyze into dense, insoluble ferric hydroxide flocs:

$$2FeCl_3 + 3Ca(HCO_3)_2 \rightarrow 2Fe(OH)_3\downarrow + 3CaCl_2 + 6CO_2\uparrow$$

• Effective pH Range: Broad operating window ($4.0\text{ to }11.0$).
• Alkalinity Consumption: $1.0\text{ mg/L}$ of $FeCl_3$ consumes $0.92\text{ mg/L}$ of alkalinity as $CaCO_3$.
• Operational Characteristics: Ferric floc is denser and settles faster than alum floc; highly effective in cold water ($< 4^\circ\text{C}$); excellent for heavy metals and arsenic removal; solutions are extremely acidic ($pH < 2$) and corrosive to chemical feed lines.

3. Polyaluminum Chloride (PACl) & Aluminum Chlorohydrate (ACH)

Pre-polymerized aluminum salts ($Al_n(OH)_mCl_{3n-m}$) are engineered with pre-hydrolyzed high-charge polymeric species:

• Consume $50\%$ to $80\%$ less natural alkalinity than alum.
• Perform exceptionally well in cold raw waters without requiring pH adjustment.
• Generate smaller, denser sludge volumes with lower residual dissolved aluminum carryover.

4. Coagulant Aids & Flocculant Polymers

• Cationic Polymers (e.g., PolyDADMAC): High positive charge density, low-to-medium molecular weight; used as primary coagulants or coagulant aids for charge neutralization, reducing required metal coagulant dose.
• Anionic Polymers (hydrolyzed polyacrylamides): High molecular weight, negative charge; used in the flocculation stage to form broad inter-particle bridges in moderate-to-high turbidity waters.
• Nonionic Polymers: Neutral polyacrylamides used as filter aids to increase floc shear resistance across granular media beds.

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Flash (Rapid) Mixing & Flocculation Dynamics

  Raw Water + Coagulant
  ========================> [ FLASH MIX ] ================> [ FLOC CHAMBER 1 ] ===>
                            G > 700 s^-1                    G = 50-70 s^-1
                            Time = 10-30 sec                (Rapid Collisions)
                                                                   |
  ===> [ FLOC CHAMBER 2 ] ===> [ FLOC CHAMBER 3 ] ================> [ SEDIMENTATION BASIN ]
       G = 30-40 s^-1          G = 15-25 s^-1                         Quiescent Settling
       (Floc Growth)           (Prevent Floc Shear)                   SOR: 500-1000 gpd/sq ft

Rapid Flash Mixing Mechanics

Because charge neutralization reactions occur in less than $0.1\text{ second}$, the coagulant chemical must be dispersed instantaneously throughout the raw water stream before metal hydrolysis precipitates form.

• Mechanisms: In-line static mixers, high-speed mechanical turbine impellers, pumped chemical diffusion quills, or hydraulic jumps in flumes.
• Velocity Gradient ($G$): The mathematical measure of mixing intensity (shear rate in $\text{s}^{-1}$):

$$G = \sqrt{\frac{P}{\mu \cdot V}}$$

Where $P$ is power dissipated in the fluid ($\text{ft}\cdot\text{lb/s}$ or $\text{Watts}$), $\mu$ is dynamic fluid viscosity ($\text{lb}\cdot\text{s/ft}^2$ or $\text{Pa}\cdot\text{s}$), and $V$ is basin volume ($\text{ft}^3$ or $\text{m}^3$).

• Flash Mix Design Standards:
  • Velocity Gradient: $G > 700\text{ to }1000\text{ s}^{-1}$
  • Detention Time ($t$): $10\text{ to }30\text{ seconds}$
  • Mixing Product ($Gt$): $10,000\text{ to }30,000$ (dimensionless)

Tapered Flocculation Design

Flocculation provides gentle, prolonged agitation to promote collisions among destabilized microflocs, agglomerating them into large, dense, settleable macroflocs (pinfloc growing to $1-3\text{ mm}$ flocs).

If mixing intensity is too low, particles will not collide; if mixing intensity is too high, the hydraulic shear forces exceed the structural tensile strength of the floc, causing floc shear (breakup).

To optimize kinetics, plants utilize Tapered Flocculation across a minimum of 3 compartmentalized stages:

• Stage 1: $G = 50\text{ to }70\text{ s}^{-1}$ (High initial collision frequency)
• Stage 2: $G = 30\text{ to }40\text{ s}^{-1}$ (Floc aggregation and densification)
• Stage 3: $G = 15\text{ to }25\text{ s}^{-1}$ (Gentle transport preventing shear)
• Detention Time: $20\text{ to }40\text{ minutes}$ total retention time.
• Camp Number ($Gt$): $20,000\text{ to }100,000$.
• Equipment: Horizontal paddle-wheel flocculators with variable frequency drives (VFDs) or vertical hydrofoil axial turbines separated by baffled dividing walls (orifice velocity $0.5\text{ to }1.5\text{ fps}$) to eliminate hydraulic short-circuiting.

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Sedimentation Basin Hydraulics & Clarifier Typologies

Sedimentation is the physical separation process where aggregated floc settles to the basin floor under gravitational acceleration, producing a clarified supernatant for filtration.

Hazen Theory & Hydraulic Loading Metrics

According to Hazen's sedimentation theory, the removal of unhindered settling particles in a horizontal flow clarifier depends entirely on the basin surface area ($A_s$) and volumetric flow rate ($Q$), completely independent of water depth or detention time. A particle is completely removed if its settling velocity ($v_s$) equals or exceeds the basin's Surface Overflow Rate ($SOR$):

$$SOR = \frac{\text{Plant Flow Rate } (Q)}{\text{Basin Surface Area } (A_s)} = \frac{\text{gal/day}}{\text{ft}^2} \quad \left(\text{or } \frac{\text{gpm}}{\text{ft}^2}\right)$$ $$\text{Weir Overflow Rate } (WOR) = \frac{\text{Plant Flow Rate } (Q)}{\text{Total Effluent Weir Length } (L_{\text{weir}})} = \frac{\text{gal/day}}{\text{linear ft}}$$ $$\text{Detention Time } (DT) = \frac{\text{Basin Volume } (V)}{\text{Flow Rate } (Q)} = \frac{\text{Gallons} \times 24\text{ hr/day}}{\text{Flow (gpd)}}$$

Clarifier Classifications

1. Conventional Rectangular Basins: Long basins with length-to-width ratios $\ge 4:1$ and depths of $10-15\text{ ft}$. Feature 4 functional zones: Inlet (perforated target baffle to distribute flow evenly), Settling zone, Sludge collection zone (bottom flight scrapers), and Outlet zone (submerged launders with adjustable V-notch weir plates). Detention time: $2-4\text{ hours}$; $SOR: 500-1000\text{ gpd/sq ft}$.
2. Circular Center-Feed Clarifiers: Radial flow outwardly directed from a central energy-dissipating feed well toward a peripheral effluent launder. Equipped with rotating bottom rake scrapers.
3. Upflow Solids-Contact Clarifiers: Single compact vessels integrating rapid mix, reaction flocculation, and high-density sludge blanket filtration. Influent raw water is forced upward through a dynamic suspended bed of previously formed sludge flocs, accelerating particle contact and achieving $SOR$ values of $1000-1500\text{ gpd/sq ft}$.
4. High-Rate Inclined Settlers (Tube & Plate Settlers): Modules of PVC tubes inclined at a $60^\circ$ angle (or parallel Lamella plates). The $60^\circ$ inclination makes the surfaces self-cleaning (sludge slides down continuously into the hopper). The effective settling depth is reduced from $12\text{ feet}$ to $2\text{ inches}$, drastically shrinking required basin footprint and allowing $SOR$ loading rates of $1500\text{ to }3000\text{ gpd/sq ft}$.

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Jar Testing Protocol & Coagulation Optimization

The laboratory Jar Test is the standard operational procedure for establishing optimal coagulant type, chemical dose, coagulant aid concentration, and target coagulation pH.

  [Jar 1: 10 mg/L]  [Jar 2: 20 mg/L]  [Jar 3: 30 mg/L]  [Jar 4: 40 mg/L]  [Jar 5: 50 mg/L]  [Jar 6: Control]
  ------------------------------------------------------------------------------------------------------
  1. Rapid Mix:    100-300 RPM for 1.0 minute (Simulates Flash Mix)
  2. Flocculation: Tapered 40 -> 25 -> 15 RPM for 20 minutes (Simulates 3-Stage Floc)
  3. Settle:       0 RPM for 15-30 minutes (Simulates Clarifier)
  4. Evaluate:     Measure Supernatant Turbidity (NTU), Final pH, TOC/UV-254, and Floc Size/Rate

Step-by-Step Jar Test Procedure

1. Collect a fresh representative raw water sample and immediately measure temperature, pH, turbidity, and alkalinity.
2. Fill six 2-liter square B-Ker (anti-vortex) jars with $2000\text{ mL}$ of sample each.
3. Add variable, graduated doses of primary coagulant (e.g., $10, 20, 30, 40, 50\text{ mg/L}$) across the jars simultaneously while running.
4. Flash Mix: Run gang stirrers at high speed ($100\text{ to }300\text{ rpm}$) for $1.0\text{ minute}$.
5. Flocculation: Reduce stirrer speeds to simulate plant hydraulics: $40\text{ rpm}$ for $10\text{ min}$, $25\text{ rpm}$ for $10\text{ min}$, and $15\text{ rpm}$ for $5\text{ min}$. Record time to initial visible pinfloc formation.
6. Settling: Stop stirrers and allow quiescent settling for $15\text{ to }30\text{ minutes}$. Record floc settling velocity ($\%\text{ settled per minute}$) and sludge compaction volume.
7. Analysis: Extract supernatant samples from the sampling ports ($2\text{ inches}$ below surface) and analyze for: residual turbidity (NTU), true color (PCU), UV-254 absorbance / TOC, residual dissolved aluminum/iron, and final pH.
8. Selection: The optimal dose is the lowest chemical quantity that achieves target turbidity removal, maximum TOC/UV-254 reduction, robust settling velocity, and acceptable final pH without chemical overdosing.