3.3 Coagulation Chemistry & Rapid Mixing

3.3 Coagulation Chemistry & Rapid Mixing

Coagulation is the chemical process of destabilizing colloidal particles in raw water so that they can aggregate into settleable and filterable flocs. While gravity alone cannot settle microscopic colloids within realistic timeframes, understanding colloidal physics, hydrolyzing coagulants, alkalinity stoichiometry, and rapid mixing hydraulics allows operators to achieve crystal-clear finished water.

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Nature of Colloidal Particles & The Electrical Double Layer

Water contaminants span a broad size spectrum. Understanding particle dimensions determines which treatment unit process governs their removal:

Particle Size Spectrum in Water Treatment
┌─────────────────┬────────────────────┬────────────────────┬─────────────────┐
│ Dissolved Ions  │ Colloidal Particles│ Suspended Solids   │ Settleable Solid│
│ <0.001 µm (<1nm)│ 0.001 µm to 1.0 µm │ 1.0 µm to 100 µm   │ >100 µm         │
│ Dissolved salts,│ Clays, silts, NOM, │ Algae, Giardia,    │ Sand, grit,     │
│ metal ions,     │ viruses, humic     │ Cryptosporidium,   │ heavy flocs     │
│ small organics  │ acids, color       │ large bacteria     │                 │
│                 │                    │                    │ Gravity settles │
│ Membrane/RO     │ Requires Chemical  │ Gravity/Media      │ in <10 minutes  │
│ or Adsorption   │ Coagulation        │ Filtration         │                 │
└─────────────────┴────────────────────┴────────────────────┴─────────────────┘

Why Colloids Will Not Settle: Brownian Motion and Surface Charge

Colloidal particles (0.001 to 1.0 µm) have an extraordinarily large surface-area-to-mass ratio. Consequently, surface physical-chemical forces completely overpower gravitational forces. Two primary phenomena maintain colloidal stability:

1. Brownian Motion: Continuous, random thermal kinetic bombardment by surrounding water molecules keeps colloids perpetually agitated in suspension. A 0.1 µm clay colloid would take hundreds of years to settle 1 foot under gravity alone.
2. Primary Negative Surface Charge: In natural surface waters (pH 6.0 to 8.5), colloids carry a net negative electrical surface charge. The origins of this negative charge include:
   • Isomorphous Substitution: In clay crystal lattices, higher-valence metal cations are replaced by lower-valence cations (e.g., $\text{Al}^{3+}$ replacing $\text{Si}^{4+}$, or $\text{Mg}^{2+}$ replacing $\text{Al}^{3+}$), creating a permanent structural negative lattice deficit.
   • Ionization of Surface Functional Groups: Natural Organic Matter (NOM, consisting of humic and fulvic macromolecules) contains carboxyl (–COOH) and phenolic hydroxyl (–OH) groups that dissociate at natural pH into negatively charged carboxylate (–COO⁻) and phenolate (–O⁻) sites.
   • Preferential Anion Adsorption: Hydroxyl ions ($\text{OH}^-$) and other anions adsorb onto mineral surfaces.

The Electrical Double Layer & Zeta Potential

To balance its negative surface charge and maintain electrical neutrality, each colloidal particle attracts an surrounding cloud of positive ions (counter-ions) from the bulk water, creating the electrical double layer:

Electrical Double Layer & Potential Gradient

  Negatively Charged    Stern Layer    Diffuse (Gouy-Chapman)    Bulk Solution
   Colloid Surface    (Fixed Cations)          Layer              (Neutral)
 ┌─────────────────┐ ┌───────────────┐ ┌──────────────────────┐ ┌─────────────┐
 │                 │ │    +     +    │ │   +     -    +   -   │ │  +   -   +  │
 │        -        │ │  (Tightly     │ │ (Counter-ions in     │ │ (Equal      │
 │                 │ │   bound       │ │  thermal dynamic     │ │  cations &  │
 │        -        │ │   cations)    │ │  equilibrium)        │ │  anions)    │
 │                 │ │    +     +    │ │   -     +    -   +   │ │  -   +   -  │
 └─────────────────┘ └───────────────┘ └──────────────────────┘ └─────────────┘
 ▲                                   ▲
 │                                   │ Slipping Plane (Plane of Shear)
 │                                   └─── Electrical Potential = ZETA POTENTIAL
 └─ Surface Potential (Ψ₀)

 Potential (mV)
   0 ┼──────────────────────────────────────────────────────── (Bulk Liquid)
     │                                              ·········
     │                                  ············
 -10 ┼                      ············   ◄── Target Zeta Potential (-5 to +5 mV)
     │             ·········
 -20 ┼  ··········· ◄── Raw Water Zeta Potential (-15 to -30 mV)
     │
 -30 ┼── Stern Layer Drop

• Stern Layer (Fixed Layer): An inner, rigid layer of dehydrated or partially hydrated cations held tightly to the colloid surface by strong electrostatic and chemical forces. The electrical potential drops sharply across this layer.
• Diffuse Layer (Gouy-Chapman Layer): An outer, dynamic zone containing an excess of cations and a deficit of anions. Cation concentration decays exponentially with radial distance until bulk liquid electroneutrality is reached.
• Slipping Plane (Shear Plane): The boundary separating fluid moving along with the migrating particle from the bulk water.
• Zeta Potential ($\zeta$): The electrical potential (in millivolts, mV) measured precisely at the slipping plane. In natural untreated surface waters, the zeta potential typically measures −15 mV to −30 mV.

The Electrostatic Barrier: According to DLVO theory (Derjaguin, Landau, Verwey, and Overbeek), the net interaction between colloids is the sum of attractive van der Waals forces and repulsive electrostatic forces. When the zeta potential is strongly negative ($< -15\text{ mV}$), the repulsive energy barrier prevents particles from approaching closely enough for van der Waals attraction to take hold. Coagulation aims to reduce the zeta potential to near zero (−5 to +5 mV), extinguishing electrostatic repulsion and allowing collision and agglomeration.

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The Four Coagulation Mechanisms

Chemical coagulants destabilize colloidal particles through four distinct mechanisms:

Coagulation Destabilization Mechanisms
├── 1. Charge Neutralization (Adsorption-Destabilization)
│   └── Cationic metal hydroxy-polymers adsorb directly onto negative colloid surfaces
├── 2. Double Layer Compression
│   └── High ionic strength shrinks diffuse layer thickness (Schulze-Hardy Rule: z⁶)
├── 3. Sweep Flocculation (Enmeshment)
│   └── Overdosing metal salts precipitates a voluminous hydroxide "snowstorm"
└── 4. Interparticle Bridging
    └── Long-chain polymers adsorb onto multiple colloids simultaneously

1. Charge Neutralization (Adsorption-Destabilization)

When metal coagulants dissolve, their trivalent cations immediately form positively charged poly-nuclear hydroxy complexes (e.g., $\text{Al(OH)}^{2+}$, $\text{Al}7(\text{OH}){17}^{4+}$, $\text{Al}_{13}\text{O}4(\text{OH}){24}^{7+}$, $\text{Fe(OH)}^{2+}$). These cationic complexes adsorb strongly onto the negatively charged colloidal surfaces, neutralizing surface charge and driving the zeta potential to zero.

• Stoichiometric: Required coagulant dosage is directly proportional to colloidal concentration and NOM surface area.
• Overdosing Hazard (Restabilization): If an operator overdoses coagulant under charge neutralization conditions, excess cationic polymers saturate the surface, reversing the particle charge from negative to strongly positive ($> +10\text{ mV}$). The particles restabilize with positive charges, repelling one another and causing finished water turbidity to spike.

2. Double Layer Compression

Adding high concentrations of indifferent electrolytes increases the ionic strength of the solution, which forces counter-ions into the diffuse layer and compresses its physical thickness. As the diffuse layer contracts, particles can approach closely enough for short-range van der Waals attractive forces to dominate.

• Schulze-Hardy Rule: The coagulating power of an indifferent ion increases with the sixth power of its valence ($z^6$): $\text{Coagulating Effectiveness} \propto z^6$
  • Monovalent ion ($\text{Na}^+, z=1$): $1^6 = 1$
  • Divalent ion ($\text{Ca}^{2+}, z=2$): $2^6 = 64$ (~50 to 60 times more effective than $\text{Na}^+$)
  • Trivalent ion ($\text{Al}^{3+}$ or $\text{Fe}^{3+}, z=3$): $3^6 = 729$ (~700 to 1,000 times more effective than $\text{Na}^+$)

3. Sweep Flocculation (Enmeshment)

When metal coagulants are dosed in excess of the solubility limit of amorphous aluminum hydroxide ($\text{Al(OH)}_3\text{(s)}$) or ferric hydroxide ($\text{Fe(OH)}_3\text{(s)}$), rapid chemical precipitation occurs. A dense, voluminous, sticky hydroxide precipitate forms—resembling a falling snowstorm. As these heavy hydroxide flocs settle through the basin, they physically collide with, entrap, enmesh, and sweep down colloids.

• Non-Stoichiometric: Sweep flocculation is the primary mechanism in low-turbidity, low-NOM waters (where colloid collision frequency is too sparse for charge neutralization alone). It requires higher coagulant doses than charge neutralization.

4. Interparticle Bridging

Occurs when high-molecular-weight synthetic polymers or long-chain hydrolyzed metal polymers are introduced. A single polymer chain adsorbs onto the surface of one colloidal particle while its free ends extend into the bulk solution and attach to other colloids, forming a polymer-colloid-polymer "bridge." This binds microflocs into large, dense aggregates.

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Primary Coagulants & Chemical Properties

Selecting the proper primary coagulant depends on raw water pH, alkalinity, temperature, and organics content.

Aluminum Sulfate Hydrolysis and pH Sensitivity

Commercial dry alum has the approximate formula $\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O}$ with a molecular weight of ~594 g/mol. In solution, $\text{Al}^{3+}$ hydrolyzes through stepwise reactions:

$\text{Al}^{3+} + \text{H}_2\text{O} \rightleftharpoons \text{Al(OH)}^{2+} + \text{H}^+$ $\text{Al(OH)}^{2+} + \text{H}_2\text{O} \rightleftharpoons \text{Al(OH)}_2^+ + \text{H}^+$ $\text{Al(OH)}_2^+ + \text{H}_2\text{O} \rightleftharpoons \text{Al(OH)}_3\text{(s)} \downarrow + \text{H}^+$

The Critical Alum pH Windows:

• Optimum Precipitation (pH 5.8 to 7.5): Amorphous $\text{Al(OH)}_3\text{(s)}$ precipitate achieves minimum solubility near pH 6.0 to 6.8.
• Low pH Hazard (pH < 5.5): The equilibrium shifts toward soluble $\text{Al}^{3+}$ and $\text{Al(OH)}^{2+}$ cations. Insoluble floc fails to form, raw water turbidity passes through filters, and finished water contains elevated dissolved aluminum.
• High pH Hazard (pH > 7.8): Insoluble aluminum hydroxide dissolves back into solution as the soluble aluminate anion: $\text{Al(OH)}_3\text{(s)} + \text{OH}^- \rightleftharpoons \text{Al(OH)}_4^- \quad (\text{or } \text{AlO}_2^- + 2\text{H}_2\text{O})$ Soluble aluminate passes cleanly through sand filters and subsequently post-precipitates inside distribution system storage tanks and consumer plumbing as a milky white aluminum hydroxide precipitate, causing widespread complaints and violating water quality standards.

Iron Salts vs Pre-Hydrolyzed Polyaluminum Chloride (PAC)

1. Iron Salts (Ferric Chloride and Ferric Sulfate): Iron forms ferric hydroxide ($\text{Fe(OH)}_3\text{(s)}$) flocs that are significantly denser, tougher, and faster-settling than aluminum flocs. Ferric works over a remarkably wide pH window (4.0 to 11.0). In water systems subject to the Disinfection Byproducts Rule (DBPR), Enhanced Coagulation requires depressing pH to 5.0–5.5 to maximize Total Organic Carbon (TOC) removal; ferric chloride excels under these acidic conditions without dissolving.
2. Polyaluminum Chloride (PAC) & Aluminum Chlorohydrate (ACH): PAC products are manufactured by pre-hydrolyzing aluminum chloride with base under factory-controlled conditions, locking aluminum into highly charged polynuclear structures such as the $\text{Al}_{13}$ Keggin complex ($\text{Al}_{13}\text{O}4(\text{OH}){24}^{7+}$). Because hydrolysis has already partially taken place, PAC consumes 50% to 80% less alkalinity than alum and suppresses pH far less. Most importantly, PAC is far less sensitive to cold water; while alum hydrolysis slows dramatically below 4°C, PAC maintains high performance in winter waters.

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Alkalinity Relationship & Supplemental Base Addition

Coagulation is an acid-producing reaction that consumes natural bicarbonate alkalinity. When alum reacts with natural calcium bicarbonate ($\text{Ca(HCO}_3)_2$) alkalinity, the chemical reaction is:

$\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O} + 3\text{Ca(HCO}_3)_2 \rightarrow 2\text{Al(OH)}_3\downarrow + 3\text{CaSO}_4 + 14\text{H}_2\text{O} + 6\text{CO}_2\uparrow$

Stoichiometric Consumption Rule of Thumb

Coagulant Alkalinity Depletion Rules:
├── 1.0 mg/L commercial alum consumes ~0.45 to 0.50 mg/L natural alkalinity as CaCO₃
└── 1.0 mg/L anhydrous ferric chloride consumes ~0.92 mg/L natural alkalinity as CaCO₃

The Alkalinity Depletion Crisis

Many surface waters in northern New Jersey (such as the Highlands reservoirs and Passaic tributaries) have naturally low alkalinity, often between 20 and 45 mg/L as $\text{CaCO}_3$.

Scenario: A plant treats raw water having an alkalinity of 24 mg/L as $\text{CaCO}_3$ and adds an alum dose of 35 mg/L:

$\text{Alkalinity Consumed} = 35\text{ mg/L alum} \times 0.50\text{ mg/L CaCO}_3\text{ per mg/L alum} = 17.5\text{ mg/L as CaCO}_3$ $\text{Residual Alkalinity} = 24.0 - 17.5 = 6.5\text{ mg/L as CaCO}_3$

With nearly all buffering capacity stripped and free carbonic acid ($CO_2$) released, the raw water pH plunges from 7.2 down to 4.8. At pH 4.8, alum cannot precipitate into $\text{Al(OH)}_3$ floc. The coagulation process completely collapses, corrosive acidic water enters the filters, and soluble aluminum breaks through into the distribution network. Operators must maintain a minimum residual alkalinity of 20 to 30 mg/L as $\text{CaCO}_3$ in coagulated water.

Supplemental Alkalinity Chemicals

When natural raw water alkalinity is deficient, operators must feed a supplemental base:

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Rapid Mixing (Flash Mixing) Principles & Hydraulics

The sole objective of rapid mixing (flash mixing) is to disperse the chemical coagulant instantaneously and completely throughout the raw water stream before hydrolysis species can polymerize.

Rapid Mixing Timeline:
├── 0.0 to 0.1 sec: Metal coagulant dissolves and coordinates with water molecules
├── 0.1 to 1.0 sec: Hydrolysis produces short-lived cationic polynuclear complexes
├── <1.0 second: Charge neutralization destabilizes negative colloids
└── >1.0 second: Insoluble amorphous Al(OH)₃ / Fe(OH)₃ precipitates begin to form

If chemical dispersion takes 10 to 15 seconds, coagulant molecules in the center of the plume will react with themselves rather than raw water colloids, causing localized overdosing, wasted chemical, and un-coagulated water carryover.

Velocity Gradient (Camp & Stein G Value)

Mixing intensity is quantified by the velocity gradient ($G$ value), expressed in units of reciprocal seconds ($\text{s}^{-1}$):

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

Where:

• $P = \text{power dissipated into the fluid (Watts in metric, or ft-lb/s in US customary: } 1\text{ HP} = 550\text{ ft-lb/s})$
• $\mu = \text{dynamic fluid viscosity (Pa}\cdot\text{s in metric, or lb}\cdot\text{s/ft}^2\text{ in US customary)}$
• $V = \text{mixing basin volume (m}^3\text{ or ft}^3)$

Engineering Design Standards for Rapid Mix

• Velocity Gradient ($G$): $700\text{ to }1,000+\text{ s}^{-1}$ (violent, turbulent mixing).
• Detention Time ($t$): 1 to 5 seconds for in-line mechanical/static mixers; 10 to 30 seconds (maximum 60 seconds) for mechanical rapid mix tanks.

Rapid Mixer Configurations

1. In-Line Mechanical Mixer        2. Static (Motionless) Mixer      3. Hydraulic Jump Mixer
┌────────────────────────────┐    ┌───────────────────────────┐    ┌──────────────────────┐
│ Raw Water ──► [Motor] ──►  │    │ Raw Water ──►             │    │ Raw Water  Flow ──►  │
│                 │          │    │ ┌───┐ ┌───┐ ┌───┐         │    │ ───────┐             │
│               [Shaft]      │    │ │ / │ │ \ │ │ / │ ──►     │    │        │  Hydraulic  │
│                 │          │    │ └───┘ └───┘ └───┘         │    │   Weir │    Jump     │
│ Coagulant ──► [Impeller]   │    │ Internal Fixed Vanes      │    │   Drop │  ████████   │
│ Instantaneous Dispersion   │    │ Headloss drives mixing    │    │        ▼  ████████   │
└────────────────────────────┘    └───────────────────────────┘    └──────────────────────┘

• In-Line Mechanical Mixers: High-speed impellers (800 to 1,800 rpm) mounted directly within a pipe spool piece. Coagulant is injected directly into the eye of the impeller, achieving complete dispersion in <1 second with low headloss.
• Static (Motionless) In-Line Mixers: Fixed geometric helical vanes set inside a pipe section. Fluid splits, shears, and recombines as it passes through the vanes. Zero moving parts and minimal maintenance; however, mixing intensity depends on flow velocity (at low plant flows, $G$ drops and mixing degrades).
• Hydraulic Jump: Coagulant is injected across the width of a flume (such as a Parshall flume throat or steep weir drop) immediately upstream of a standing hydraulic jump. Kinetic energy dissipation creates intense turbulence ($G > 800\text{ s}^{-1}$) without mechanical drives.

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Operational Troubleshooting & Exam Traps

[!IMPORTANT] Exam Trap: Chemical Injection Point Separation Never inject primary coagulants (alum) and alkaline chemicals (lime or caustic soda) at the exact same physical location. Feeding lime into the alum injection zone creates an immediate alkaline plume (pH > 9.0) where alum dissolves into soluble aluminate ($\text{Al(OH)}_4^-$) before it can destabilize colloids. Chemical feed points must be separated by at least 10 to 30 seconds of flow travel time.

[!TIP] Operational Rule: Cold Water Coagulation Adjustments In winter, water temperatures often drop below 4°C (39°F). Cold water increases viscosity, slowing particle motion, and severely retards alum hydrolysis kinetics. Operators should: (1) increase rapid mix energy; (2) switch coagulants from alum to pre-hydrolyzed polyaluminum chloride (PAC); or (3) dose a cationic polymer coagulant aid to accelerate microfloc formation.