2.2 Coagulation Chemistry, Coagulants & Rapid Mixing Mechanics

2.2 Coagulation Chemistry, Coagulants & Rapid Mixing Mechanics

Quick Answer: Coagulation is the chemical process of destabilizing finely divided colloidal particles so they can agglomerate into settleable flocs. Natural raw water colloids carry negative electrical surface charges that prevent them from colliding, quantified by a negative zeta potential (typically $-15\text{ to }-30\text{ mV}$). Primary coagulants carrying multi-valent positive charges ($\text{Al}^{3+}$, $\text{Fe}^{3+}$) are injected into a high-energy rapid mixer ($G = 700-1000\text{ s}^{-1}$, 1-30 seconds) to neutralize surface charges, collapse the electrical double layer, and form sweep flocs.

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Colloidal Physics & The Electrical Double Layer

Waterborne impurities fall into three broad physical size categories:

1. Suspended Solids: Particles $> 1.0\text{ }\mu\text{m}$ (silt, fine sand, large bacteria) that settle under gravity if given sufficient quiescent settling time.
2. Colloidal Solutes: Particles ranging from $0.001\text{ }\mu\text{m}$ to $1.0\text{ }\mu\text{m}$ (clays, color-causing humic acids, viruses, protein macromolecules).
3. Dissolved Matter: Solutes $< 0.001\text{ }\mu\text{m}$ (salts, simple sugars, small organic molecules).

Why Colloids Do Not Settle

Colloids cannot settle under gravity in conventional treatment timeframes. A fine clay colloid ($0.1\text{ }\mu\text{m}$) would require an estimated 20 to 200 years to settle 1 foot in still water. Instead, colloids remain suspended indefinitely due to two interacting physical phenomena:

• Brownian Motion: Continuous, random bombardment of sub-micron colloids by thermal kinetic movement of surrounding water molecules.
• Electrostatic Repulsion: Natural colloids carry a net negative surface charge resulting from isomorphic substitution within clay mineral crystal lattices (e.g., $\text{Al}^{3+}$ substituting for $\text{Si}^{4+}$) and ionization of functional carboxyl ($\text{-COOH}$) and phenolic hydroxyl ($\text{-OH}$) groups on humic matter.

The Electrical Double Layer (EDL) & Zeta Potential

Because the colloid has a negative surface charge, it attracts dissolved cations from the surrounding bulk solution, creating an Electrical Double Layer (EDL):

• Stern Layer (Fixed Layer): A rigid, dense layer of positive counter-ions held tightly against the colloid surface by electrostatic attraction.
• Diffuse Layer: A secondary, looser zone extending into the bulk water where positive cations outnumber negative anions, with ion concentration tapering off to bulk solution levels.
• Plane of Shear (Slipping Plane): The boundary separating ions that move along with the colloid through the water from the bulk fluid.
• Zeta Potential ($ZP$): The electrical potential (voltage) measured at the slipping plane, expressed in millivolts ($\text{mV}$).

Natural raw surface waters typically display a zeta potential of $-15\text{ mV to }-30\text{ mV}$. Electrostatic repulsion prevents colloids from approaching closely enough for short-range attractive van der Waals forces to take effect.

$\text{Coagulation Objective: Reduce Zeta Potential to between } -5\text{ mV and } +3\text{ mV}$

When the zeta potential approaches zero, the electrostatic repulsive energy barrier collapses, allowing van der Waals forces to pull particles together upon contact.

+------------------------------------------------------------------------+
|                   ELECTRICAL DOUBLE LAYER DIAGRAM                      |
|                                                                        |
|   [ Colloidal Particle ]  |  Stern Layer  |       Diffuse Layer        |
|    Negative Surface       | Rigid Cations |   Cations & Anions Graded  |
|        ( - - - - )        | ( + + + + + ) |  ( +  -  +  +  -  +  - )   |
|                           |               |                            |
|                           |               |-> Plane of Shear           |
|                                               (Zeta Potential Point)   |
|                                                                        |
|   Repulsive Energy Barrier collapses as ZP moves from -30 mV toward 0  |
+------------------------------------------------------------------------+

The Four Coagulation Mechanisms

1. Double-Layer Compression: High concentrations of inert electrolytes increase the ionic strength of the water, compressing the diffuse layer and reducing the distance over which repulsive forces act.
2. Charge Neutralization: Positively charged coagulant hydrolysis species (e.g., $\text{Al(OH)}^{2+}$, $\text{Al}_8\text{(OH)}_{20}^{4+}$, $\text{Fe(OH)}_2^+$) adsorb directly onto the negatively charged colloid surface, neutralizing the zeta potential.
3. Sweep Flocculation (Enmeshment): When metal coagulants are added in quantities exceeding the solubility limit of the metal hydroxide at operating pH, rapid precipitation of amorphous gelatinous metal hydroxides ($\text{Al(OH)}_3\text{(s)}$ or $\text{Fe(OH)}_3\text{(s)}$) occurs. The expanding "sponge-like" hydroxide precipitate enmeshes and sweeps colloids out of suspension.
4. Interparticle Bridging: High-molecular-weight synthetic polymers bind to multiple colloids simultaneously, forming physical chemical bridges that span the electrostatic gap.

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Primary Chemical Coagulants

1. Aluminum Sulfate (Alum)

Alum ($\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O}$, molecular weight $\approx 594\text{ g/mol}$) is the most widely utilized municipal coagulant. It is supplied as dry crystalline powder or as a liquid solution (typically $48\%\text{ to }50\%$ dry alum equivalent by weight, specific gravity $1.32\text{ to }1.34$, providing $\approx 5.4\text{ lbs dry alum/gal}$).

• Effective pH Range: $5.8\text{ to }7.5$ (minimum aluminum solubility occurs at $\text{pH } 6.0\text{ to }6.2$). At $\text{pH} < 5.5$ or $\text{pH} > 8.0$, aluminum remains dissolved as free $\text{Al}^{3+}$ or aluminate ions ($\text{Al(OH)}_4^-$), escaping filters and causing post-precipitation in the distribution network.
• Hydrolysis Reaction: $\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O} + 6\text{H}_2\text{O} \rightleftharpoons 2\text{Al(OH)}_3\text{(s)} \downarrow + 3\text{H}_2\text{SO}_4 + 14\text{H}_2\text{O}$

Alkalinity Consumption by Alum

Alum requires alkalinity in the raw water to react and form aluminum hydroxide floc. It reacts with natural calcium bicarbonate alkalinity:

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

$\mathbf{1.0\text{ mg/L of commercial alum consumes } \approx 0.50\text{ mg/L of alkalinity (as }\text{CaCO}_3\mathbf{)}}$

If raw water natural alkalinity is insufficient ($< 30\text{ to }45\text{ mg/L}$ as $\text{CaCO}_3$), alum addition depresses pH below the optimum coagulation zone. This leads to incomplete flocculation, elevated settled water turbidity, dissolved aluminum breakthrough into finished water, and highly corrosive water.

2. Iron Salts (Ferric Coagulants)

• Ferric Chloride ($\text{FeCl}_3$): Available as a dark brown, highly corrosive, acidic liquid ($35\%\text{ to }45\%$, $\text{pH} < 2$). Effective across a broad pH range of $4.0\text{ to }11.0$. It consumes approximately $0.92\text{ mg/L of alkalinity as }\text{CaCO}_3\text{ per }1.0\text{ mg/L of dry }\text{FeCl}_3$.
• Ferric Sulfate ($\text{Fe}_2(\text{SO}_4)_3$): Available in dry or liquid form. Like ferric chloride, it produces dense, heavy ferric hydroxide ($\text{Fe(OH)}_3$) flocs that settle more rapidly than alum flocs, particularly in cold water ($< 4^\circ\text{C}$). Effective for raw waters with high organic color.

3. Polyaluminum Chloride (PACl) & Pre-Hydrolyzed Salts

Polyaluminum Chloride ($\text{Al}_n\text{Cl}_{(3n-m)}(\text{OH})_m$) and Aluminum Chlorohydrate (ACH) are pre-polymerized aluminum salts with controlled basicity ($50\%\text{ to }83\%$). Because the aluminum is already partially hydrolyzed into complex polymers:

• They consume significantly less natural alkalinity than alum (often $50\%\text{ to }80\%$ less).
• They cause minimal pH depression, frequently eliminating the need for lime or caustic soda.
• They perform reliably in cold water where alum hydrolysis kinetics slow down.
• They produce less chemical sludge volume by weight.

Supplemental Alkalinity & pH Conditioning Chemicals

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Worked Engineering Problem: Alum Feed & Alkalinity Balance

Problem: A water plant treats a flow rate of $6.0\text{ MGD}$ with an alum dose of $34.0\text{ mg/L}$. The raw water natural alkalinity is $28.0\text{ mg/L}$ as $\text{CaCO}_3$. The target finished water alkalinity entering the distribution system must be maintained at a minimum of $25.0\text{ mg/L}$ as $\text{CaCO}_3$ to prevent corrosion.

1. Calculate the daily dry alum requirement in pounds per day.
2. Determine the alkalinity consumed by the alum.
3. Calculate the required supplemental hydrated lime dosage ($\text{mg/L}$) and the total pounds of lime needed per day, assuming hydrated lime provides $1.35\text{ mg/L of alkalinity as }\text{CaCO}_3\text{ per }1.0\text{ mg/L of commercial lime}$.

Step 1: Calculate Daily Alum Feed (Pounds Formula): $\text{Feed (lbs/day)} = \text{Flow (MGD)} \times \text{Dosage (mg/L)} \times 8.34\text{ lbs/gal}$ $\text{Alum (lbs/day)} = 6.0\text{ MGD} \times 34.0\text{ mg/L} \times 8.34 = 1,701.36\text{ lbs/day}$

Step 2: Calculate Alkalinity Consumed by Alum: $\text{Alkalinity Consumed} = 34.0\text{ mg/L alum} \times 0.50\text{ mg/L alk / mg/L alum} = 17.0\text{ mg/L as CaCO}_3$

Step 3: Determine Residual Alkalinity Without Lime: $\text{Remaining Alkalinity} = 28.0\text{ mg/L (raw)} - 17.0\text{ mg/L (consumed)} = 11.0\text{ mg/L as CaCO}_3$

Step 4: Calculate Supplemental Alkalinity Deficit: $\text{Alkalinity Deficit} = 25.0\text{ mg/L (target)} - 11.0\text{ mg/L (remaining)} = 14.0\text{ mg/L as CaCO}_3$

Step 5: Calculate Lime Dose and Daily Pounds: $\text{Lime Dose (mg/L)} = \frac{14.0\text{ mg/L alkalinity}}{1.35\text{ mg/L alk / mg/L lime}} = 10.37\text{ mg/L hydrated lime}$ $\text{Lime (lbs/day)} = 6.0\text{ MGD} \times 10.37\text{ mg/L} \times 8.34 = 518.91\text{ lbs/day}$

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Rapid Mixing Hydraulics & Mechanics

The primary function of rapid mixing (flash mixing) is to instantaneously disperse the coagulant chemical throughout the entire raw water stream.

The Kinetics of Coagulant Hydrolysis

Hydrolysis reactions occur in fractions of a second:

• Positively charged monomeric and polymeric intermediate aluminum species form within $0.01\text{ to }0.1\text{ seconds}$.
• Charge neutralization of colloids occurs within $0.1\text{ to }1.0\text{ seconds}$.
• If the coagulant is not dispersed into the raw water within this brief window, the intermediate species polymerize into neutral $\text{Al(OH)}_3\text{(s)}$ precipitates without contacting colloids, wasting chemical.

Rapid Mixing Design Parameters

• Detention Time ($t$): Extremely short, typically 1 to 30 seconds (never exceeding 60 seconds).
• Velocity Gradient ($G$): A measure of hydraulic shear and mixing intensity: $G = \sqrt{\frac{P}{\mu V}}$ where $P$ is power dissipated ($\text{ft}\cdot\text{lb/s}$ or Watts), $\mu$ is dynamic viscosity of water, and $V$ is basin volume. For rapid mixing, design standards require: $G = 700\text{ s}^{-1} \text{ to } 1,000+\text{ s}^{-1}$

Types of Rapid Mixers

• Mechanical Impeller Mixers: High-speed vertical shaft mixers equipped with radial or axial flow turbines installed in small mixing chambers. Provide controllable mixing intensity but consume electrical power and require shaft seal maintenance.
• In-Line Static Mixers: Fixed, twisted helical geometric elements fitted directly inside the raw water pipeline. As water flows through the elements, turbulent vortices continuously divide and recombine the stream. Extremely rapid ($< 2\text{ seconds}$), zero moving parts, but head loss increases with the square of the flow rate.
• Hydraulic Mixers (Hydraulic Jumps): Coagulant injected directly into the turbulent standing wave of a Parshall flume or open channel weir drop. Energy is supplied entirely by gravitational head loss; mixing intensity varies with flow rate.

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Coagulant Aids & Synthetic Polymers

Polyelectrolytes (polymers) are long-chain synthetic or natural organic macromolecules made of repeating monomer subunits. They serve three operational roles:

1. Primary Coagulant: High-charge-density, low-molecular-weight cationic polymers (e.g., polyDADMAC, Epi-DMA). They neutralize negative colloidal charges at low dosages ($0.5\text{ to }2.0\text{ mg/L}$) without consuming alkalinity or altering pH.
2. Flocculant Aids (Coagulant Aids): High-molecular-weight, low-charge anionic or nonionic polymers. Added downstream of the primary coagulant (often at the end of rapid mix or in stage 1 flocculation) to bind micro-flocs into tough, dense macro-flocs via bridging.
3. Filter Aids: Ultra-low dosages ($0.01\text{ to }0.05\text{ mg/L}$) added directly to filter influent to toughen floc against hydraulic shearing in the media bed.

Caution — Polymer Overdosing & Restabilization: Overdosing cationic polymer can flip the colloidal surface charge from negative to positive. The particles become positively charged, repel one another again, and undergo charge reversal restabilization. Water turns milky, floc formation ceases, settled turbidity spikes, and filters blind rapidly.

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Process Control: Jar Testing Protocol

The Jar Test is the standard laboratory method used to determine the optimal coagulant type, chemical dosage, rapid mix intensity, and coagulation pH.

+------------------------------------------------------------------------+
|                         JAR TEST PROCEDURE                             |
|                                                                        |
|   1. Fill six 1-liter (or 2-liter) Gator beakers with fresh raw water  |
|   2. Dose varying coagulant concentrations (e.g., 10, 20, 30, 40, 50)  |
|   3. Flash Mix: 100 to 150 rpm for 1 minute (Simulate Rapid Mix)       |
|   4. Flocculation: 30 rpm for 20 minutes (Tapered shear simulation)    |
|   5. Settling: 0 rpm for 15 to 30 minutes (Observe floc settling rate) |
|   6. Withdraw supernatant 2 inches below surface; measure NTU and pH   |
|   7. Select dosage yielding lowest turbidity with lowest chemical cost |
+------------------------------------------------------------------------+

Operational Troubleshooting Matrix: Coagulation Anomalies