3.1 Coagulation Principles & Chemical Additives

Colloidal Stability and Surface Physics in Raw Water

Surface water sources contain suspended solids and natural organic matter that create turbidity, color, and microbiological risk. In water treatment engineering, particulate matter is categorized by particle diameter into three distinct classes:

1. Suspended solids ($> 1.0\text{ }\mu\text{m}$): Coarse silt, fine sand, and large algae that settle readily under quiescent conditions.
2. Colloidal solids ($0.001\text{ to }1.0\text{ }\mu\text{m}$): Clays, colloidal silica, humic and fulvic acids, viruses, and cellular fragments that remain suspended indefinitely in water without chemical treatment.
3. Dissolved solids ($< 0.001\text{ }\mu\text{m}$ / dissolved ionic species): Dissolved minerals, salts, and small organic molecules.

The Electrical Double Layer and Zeta Potential

Colloidal stability is governed by surface electrical charges and interparticle forces. Natural colloids in water acquire a net negative surface charge through three primary mechanisms:

• Isomorphic substitution: Mineral lattice substitutions (e.g., $Al^{3+}$ replacing $Si^{4+}$ in clay crystal structures).
• Ionization of surface functional groups: Dissociation of carboxyl ($-COOH \rightarrow -COO^- + H^+$) and phenolic hydroxyl groups on organic macromolecules.
• Specific ion adsorption: Preferential adsorption of natural anions (such as humic substances or hydroxyl ions) onto particle surfaces.

To balance this negative surface charge, waterborne cations are drawn toward the colloid, establishing an electrical double layer consisting of:

• The Stern Layer: A compact, fixed inner boundary of tightly bound, positively charged counter-ions moving synchronously with the particle.
• The Gouy-Chapman Diffuse Layer: An outer, dynamic zone where counter-ion concentration gradually decreases outward until reaching the bulk solution ionic equilibrium.

When a colloid moves through water, it carries a boundary layer of water molecules with it. The electrical potential at this shear plane (the slipping plane) is defined as the zeta potential (typically $-15\text{ to }-30\text{ mV}$ in natural raw surface waters). As long as the zeta potential remains strongly negative, mutual electrostatic repulsion (like charges repelling) prevents colloids from approaching each other.

Repulsive Electrostatic Force (Zeta Potential) > Attractive van der Waals Force ---> Stable Suspension (No Settling)

Opposing this repulsion are van der Waals forces—short-range, attractive intermolecular London-dispersion forces. Because van der Waals attraction decays rapidly with distance ($F \propto 1/r^6$), colloids cannot agglomerate unless their electrostatic repulsive barrier is neutralized or compressed, allowing them to approach within nanometer proximity.

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Mechanisms of Coagulation

Coagulation is the chemical process of adding specialized metal salts or polymers to destabilize colloidal particles, eliminating the repulsive energy barrier so particles can aggregate. Coagulation occurs through four distinct physical-chemical mechanisms:

[!IMPORTANT] Restabilization Warning: In charge neutralization, applying an excessive coagulant dose can reverse particle charge from negative to positive (positive zeta potential), re-stabilizing the colloidal dispersion and causing post-treatment turbidity spikes.

Primary Coagulants and Alkalinity Stoichiometry

Water treatment plants utilize trivalent metal coagulants ($Al^{3+}$ and $Fe^{3+}$) because the trivalent ion is up to 700 to 1,000 times more effective at colloidal destabilization than monovalent ions ($Na^+$), a principle known as the Schulze-Hardy Rule.

1. Aluminum Sulfate (Commercial Alum)

Commercial alum is delivered as dry hydrate or liquid solution with the typical chemical formula $\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O}$ (molecular weight approximately $594\text{ g/mol}$). Liquid alum typically contains approximately $48.5%\text{ dry alum}$ by weight, with a specific gravity of $1.32\text{ to }1.34$.

When alum is dosed into water, it reacts with natural bicarbonate alkalinity to form insoluble aluminum hydroxide precipitate: $\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O} + 3\text{Ca}(\text{HCO}_3)_2 \longrightarrow 2\text{Al}(\text{OH})_3\downarrow + 3\text{CaSO}_4 + 6\text{CO}_2 + 14\text{H}_2\text{O}$

Alkalinity Consumption Rule of Thumb

• 1.0 mg/L of commercial alum consumes ~0.50 mg/L of natural alkalinity (expressed as $\text{CaCO}_3$).
• Optimum Coagulation pH Window: $5.5\text{ to }7.5$ (minimum aluminum solubility occurs between $\text{pH }6.0\text{ and }6.2$).

If raw water alkalinity is insufficient ($< 30\text{--}40\text{ mg/L as }\text{CaCO}_3$), the hydrogen ions liberated by alum hydrolysis will drive raw water pH below $5.5$. In this acidic range, aluminum cannot precipitate as $\text{Al}(\text{OH})_3(s)$ and remains in soluble ionic forms ($Al^{3+}, AlOH^{2+}$), causing high filtered water turbidity, severe filter breakthrough, and elevated dissolved aluminum carryover into the distribution system. Operators must feed supplemental base:

• Hydrated Lime ($\text{Ca}(\text{OH})_2$): $1.0\text{ mg/L}$ commercial alum requires $\approx 0.38\text{ mg/L}$ hydrated lime.
• Soda Ash ($\text{Na}_2\text{CO}_3$): $1.0\text{ mg/L}$ commercial alum requires $\approx 0.54\text{ mg/L}$ soda ash.
• Caustic Soda ($50%\text{ NaOH}$): $1.0\text{ mg/L}$ commercial alum requires $\approx 0.40\text{ mg/L}$ caustic soda.

2. Ferric Salts (Ferric Chloride and Ferric Sulfate)

• Ferric Chloride ($\text{FeCl}_3$) and Ferric Sulfate ($\text{Fe}_2(\text{SO}_4)_3$): $\text{FeCl}_3 + 3\text{HCO}_3^- \longrightarrow \text{Fe}(\text{OH})_3\downarrow + 3\text{Cl}^- + 3\text{CO}_2$
• Alkalinity Consumption: $1.0\text{ mg/L }\text{FeCl}_3$ consumes approximately $0.92\text{ mg/L}$ of alkalinity as $\text{CaCO}_3$.
• Operating Characteristics: Ferric hydroxide flocs are heavier, denser, and settle faster than alum flocs. Ferric operates across a much broader pH window ($4.0\text{ to }11.0$) and performs reliably in cold water ($< 4^\circ\text{C}$), where alum kinetics degrade. However, ferric solutions are highly corrosive and stain concrete and equipment.

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

PACl coagulants are pre-hydrolyzed, engineered polymeric aluminum formulations with the empirical formula $\text{Al}_n(\text{OH})m\text{Cl}{3n-m}$.

• Advantages: Because PACl is partially pre-neutralized (basicity $50%\text{ to }83%$), it consumes $50%\text{ to }80%$ less natural alkalinity than alum, produces significantly lower chemical sludge volume, forms rapidly settling flocs in cold water, and operates effectively across wide pH ranges ($6.0\text{ to }8.5$).

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Coagulant Aids and Synthetic Polymers

Coagulant aids are auxiliary chemicals added to strengthen fragile microflocs, expand operational pH tolerances, accelerate settling velocities, or reduce primary coagulant dosage:

1. Cationic Polymers (poly-DADMAC, epi-DMA): Positively charged, medium-molecular-weight polymers that act as secondary coagulants or primary coagulants in direct filtration plants, requiring zero alkalinity consumption.
2. Anionic Polymers (hydrolyzed polyacrylamides): Negatively charged, high-molecular-weight long chains ($10^6\text{ to }10^7\text{ Da}$) that bridge neutralized microflocs in the presence of divalent cations like $Ca^{2+}$. Dosed downstream of the flash mixer ($0.05\text{ to }0.25\text{ mg/L}$).
3. Non-ionic Polymers (pure polyacrylamides): Electrically neutral polymers that aggregate flocs via hydrogen bonding and physical entanglement.
4. Activated Silica: Sodium silicate activated with acid or chlorine to produce polysilicic acid micro-gels, strengthening alum flocs in cold, low-turbidity waters.
5. Weighting Agents: Bentonite clay or powdered activated carbon (PAC) dosed into clean, low-turbidity raw waters to provide ballast and nucleation sites for sweep flocculation.

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Rapid (Flash) Mixing Hydraulics and Velocity Gradients

Primary coagulant hydrolysis reactions and charge-neutralization adsorption occur in fractions of a second ($< 0.1\text{ to }1.0\text{ second}$). If coagulants are not dispersed instantaneously throughout the entire process stream, localized over-dosing occurs, resulting in chemical waste, poor flocculation, and coagulant carryover.

The Velocity Gradient ($G$)

The intensity of hydraulic mixing is quantified by the velocity gradient ($G$), expressed in reciprocal seconds ($s^{-1}$): $G = \sqrt{\frac{P}{\mu V}}$ Where:

• $P$ = Power dissipated into the fluid (Watts or $\text{ft}\cdot\text{lb/s}$)
• $\mu$ = Dynamic viscosity of water ($Pa\cdot s$ or $\text{lb}\cdot\text{s/ft}^2$)
• $V$ = Volume of the mixing zone ($m^3$ or $\text{ft}^3$)

Flash Mix Design Criteria

Rapid-mix intensity and time are paired design variables. In-line or pump-injection devices may disperse chemical in only a few seconds at high $G$; mechanical basins often use a longer detention period. Operators verify the approved design, mixer power, flow, and chemical dispersion rather than applying one universal $G$ and one universal detention time.

Rapid Mix Configurations

• In-Line Static Mixers: Fixed internal elements inside a pipe generating extreme turbulent shear with no moving parts.
• Mechanical Flash Mix Chambers: High-speed vertical impellers (radial turbines or marine propellers) in small baffled compartments.
• Hydraulic Jumps: Supercritical-to-subcritical flow transitions downstream of Parshall flumes or weir drops that harness gravity dissipation.

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Jar Testing Protocol and Operational Optimization

The standard operational laboratory tool for evaluating coagulation-flocculation chemistry is the multi-station jar tester (standard 6-station gang stirrer using 2-liter square B-Ker2 or circular jars with illuminated base).

Jar Test Protocol Sequence:
[1. Collect Fresh Raw Sample] ---> [2. Fill 6 Jars & Dose Varied Coagulants]
   ---> [3. Rapid Flash Mix: 100-300 RPM (1 min)]
   ---> [4. Slow Flocculation: Tapered 50 -> 30 -> 15 RPM (20 min)]
   ---> [5. Quiescent Settling (15-30 min)]
   ---> [6. Sample Supernatant: Turbidity, pH, Settleability, Residual Al/Fe]

Standard Laboratory Procedure

1. Measure baseline raw water quality: Temperature, pH, turbidity (NTU), total alkalinity, and color.
2. Dose increasing coagulant increments across jars (e.g., $10, 15, 20, 25, 30, 35\text{ mg/L}$).
3. Rapid Mix: Spin paddles at $100\text{ to }300\text{ RPM}$ ($G \approx 300\text{--}400\text{ s}^{-1}$) for $1\text{ minute}$ while injecting coagulants simultaneously.
4. Flocculation Mix: Drop paddle speeds to simulate plant hydraulics (e.g., $50\text{ RPM}$ for $5\text{ min}$, $30\text{ RPM}$ for $10\text{ min}$, $15\text{ RPM}$ for $5\text{ min}$).
5. Settling: Stop paddles and record floc settling velocity, noting the time required for flocs to settle $10\text{ cm}$.
6. Supernatant Analysis: Pipette settled supernatant from sampling ports located $2\text{ inches}$ below surface; analyze settled turbidity, final pH, UV-254 absorbance (for TOC removal), and residual dissolved coagulant.

Interpreting Jar Test Data for Plant Control

• Optimal Dose: The lowest coagulant dose that produces clear supernatant with settled turbidity $< 1.0\text{--}2.0\text{ NTU}$, rapid floc settling ($> 1\text{ ft/min}$), and acceptable final pH.
• Cold Water Inversion: In winter ($< 4^\circ\text{C}$), water viscosity doubles, slowing ion transport. Jar tests reveal whether elevating pH, adding $0.1\text{ mg/L}$ cationic polymer aid, or switching to PACl restores settling performance.