Question 2 of 5: Settling regimes and the mechanisms of coagulation

Question 2: Settling regimes and the mechanisms of coagulation (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Discrete versus flocculent settling (10 marks)

Discrete settling — conventionally Type I — is the sedimentation of particles in a suspension dilute enough that each particle settles independently of its neighbours, and stable enough that no particle changes its size, shape or density during descent. Because nothing about the particle changes, its settling velocity is established within a fraction of a second of release and stays constant for the whole depth of the tank. Grit removal, plain presedimentation of a silty river water, and the settling of sand in a stilling basin are the practical examples.

Flocculent settling — Type II — is the sedimentation of a suspension in which particles collide, adhere and coalesce as they fall. Each coalescence produces a larger, faster-falling aggregate, so the settling velocity increases with time and with depth of fall, and the trajectory of a particle is curved rather than straight. Coagulated and flocculated water in a conventional clarifier, primary sedimentation of raw municipal wastewater, and the upper region of a secondary clarifier are the practical examples.

The engineering consequence of the difference is the one worth stating explicitly, because it recurs in Question 4. Discrete settling can be analysed entirely from first principles, so the removal of a given particle depends only on whether its settling velocity exceeds the overflow rate, and tank depth is irrelevant. Flocculent settling has no closed-form theory, because the collision rate depends on the local particle concentration and velocity gradient; it must be characterised by a settling-column test in which samples are drawn at several depths and times and the results plotted as contours of equal percentage removal. And because more depth means more time for collisions to occur, flocculent removal genuinely does improve with depth — the one case where a deeper tank helps.

Factors that affect discrete settling. All of them can be read off Stokesʹ law, which applies in the laminar regime (particle Reynolds number below about 1) that covers grit and most inorganic solids of interest:

• Particle diameter, d. The dominant variable, because the settling velocity varies with the square of diameter. Halving the particle size cuts the settling velocity by a factor of four, which is why fine colloids are untreatable by sedimentation alone and must first be coagulated into something larger.
• Particle density, ρ_p. Only the excess density over water does work, so the driving term is (ρ_p − ρ). Grit at about 2650 kg/m³ has an excess density of some 1650 kg/m³ and settles readily; an organic floc at 1010 to 1050 kg/m³ has an excess density fifty times smaller and settles a hundred times more slowly at the same size. This is why grit chambers can be small and clarifiers cannot.
• Liquid viscosity, μ, and hence temperature. The settling velocity is inversely proportional to viscosity, and the dynamic viscosity of water rises from about 0.80 mPa·s at 30 °C to about 1.79 mPa·s at 0 °C. Cold water therefore settles solids at less than half the rate of warm water, which for Canadian plants is a governing design condition rather than a footnote: the winter overflow rate, not the summer one, sizes the tank.
• Liquid density, ρ. A secondary effect through the same buoyancy term, significant only where salinity or temperature stratification is strong — for example in a coastal outfall or a thermally stratified reservoir intake.
• Particle shape and sphericity. Stokesʹ law assumes a sphere. A plate-like clay particle or a filamentous fragment presents more drag area per unit mass and settles more slowly than a sphere of the same volume, an effect handled through a shape factor or by using an equivalent Stokes diameter derived from a settling test rather than a sieve.
• Surface overflow rate, SOR = Q/A. Not a property of the particle but the design variable it is compared against: in an ideal basin every particle whose settling velocity equals or exceeds the overflow rate is completely removed regardless of where it enters, and particles slower than that are removed in the ratio v_s/SOR.
• Suspension concentration. Independent settling is only valid while the suspension is dilute. Above a few grams per litre the upward displacement of water by descending particles retards them all — hindered or zone settling — and Stokesʹ law no longer applies, which is the regime that governs the sludge blanket of a secondary clarifier.
• Hydraulic short-circuiting and currents. Real tanks are not ideal. Inlet jetting, wind-driven surface currents, density currents caused by a colder or more concentrated influent, and thermal stratification all cause part of the flow to reach the outlet faster than the nominal detention time, so measured removal falls below the ideal-basin prediction. Inlet baffling, well-designed launders and adequate weir loading exist to control exactly this.

(b) Mechanisms of destabilisation in coagulation–flocculation (15 marks)

Coagulation is the chemical destabilisation of a colloidal suspension; flocculation is the subsequent transport step in which destabilised particles are brought into contact and grown into settleable aggregates. All three mechanisms named in the question are ways of defeating the same obstacle, so the obstacle is worth stating first. Colloids in natural water — clays, silica, algal cells, humic and fulvic acids — carry a net negative surface charge, arising from isomorphic substitution within the clay lattice and from ionisation of carboxyl and hydroxyl groups on natural organic matter. That surface charge attracts a cloud of counter-ions, forming an electrical double layer: a tightly bound Stern layer and, beyond it, a diffuse Gouy–Chapman layer whose potential decays with distance. When two such particles approach, their diffuse layers overlap and repel, and the resulting repulsion opposes the ever-present van der Waals attraction. The sum of the two, in DLVO theory, produces an energy barrier that Brownian motion cannot surmount — which is precisely why a colloidal suspension is stable for months and cannot be settled or filtered as it stands.

Ionic-layer compression (double-layer compression). The thickness of the diffuse layer — the Debye length κ⁻¹ — varies inversely with the square root of the ionic strength I of the solution:

Adding an indifferent electrolyte, one whose ions do not react specifically with the particle surface, raises the ionic strength and so compresses the diffuse layer against the particle. The surface charge itself is unchanged, but the repulsive potential now decays over a much shorter distance, so it falls away before the particles are close enough for the barrier to matter; van der Waals attraction then dominates at all separations and collisions succeed. Counter-ion valence is decisive here, because the ionic strength depends on the square of the charge and the critical coagulation concentration falls roughly with the inverse sixth power of it — the Schulze–Hardy rule — so a trivalent ion is some hundreds of times more effective per mole than a monovalent one. Two features distinguish this mechanism in practice: it is non-stoichiometric, so there is no overdose penalty, and it requires salt concentrations far too high to be economic in a treatment plant. Its real importance is as the natural mechanism that deposits river sediment where fresh water meets the sea in an estuary, and as the theoretical baseline against which the other two mechanisms are understood.

Adsorption and charge neutralisation. This is the mechanism that a hydrolysing metal salt exploits at low dose. When aluminium sulphate or ferric chloride is dispersed into water it hydrolyses within milliseconds into a series of positively charged mononuclear and polynuclear species — Al(OH)²⁺, Al(OH)₂⁺ and polymeric forms such as Al₁₃O₄(OH)₂₄⁷⁺ — and these adsorb specifically onto the negative colloid surfaces rather than merely crowding around them. Adsorption lowers the effective surface charge and drives the zeta potential toward zero; with the electrostatic repulsion removed, van der Waals attraction can act and collisions become productive. Two properties follow directly and are heavily examined. First, the mechanism is stoichiometric: the required dose is proportional to the surface area of colloid present, so a higher-turbidity water needs more coagulant, and the optimum is found by jar test or tracked continuously with a streaming-current detector. Second, and unlike double-layer compression, it can be overdosed: continued adsorption of cationic species past the neutral point reverses the surface charge to net positive and the suspension restabilises, so the removal-versus-dose curve has a minimum and then rises again. The operating regime is low coagulant dose at a pH of roughly 5 to 6, and it is the regime used for enhanced coagulation aimed at natural organic matter, where the metal must bind the organics rather than merely precipitate.

Sweep coagulation (enmeshment in a precipitate). When the coagulant dose is raised well beyond the solubility limit of the metal hydroxide at the operating pH — aluminium hydroxide has its solubility minimum near pH 6 to 7, ferric hydroxide near pH 7 to 9 — the water becomes supersaturated and an amorphous, highly hydrated metal hydroxide precipitates rapidly throughout the volume. The colloids are then physically enmeshed in, and swept down by, this growing precipitate; they also serve as nucleation sites, which produces the initially counter-intuitive result that a more turbid water requires less coagulant per unit of turbidity, because nucleation is easier. Because the mechanism is physical capture rather than charge interaction, it is not charge-sensitive and there is no restabilisation on overdose, and it produces a large, robust, readily settled floc. Its penalty is chemical sludge: sweep floc generates far more solids to thicken, dewater and dispose of than charge neutralisation does. Sweep coagulation is nevertheless the dominant mechanism in most conventional Canadian surface-water plants, because it is forgiving of the cold, low-turbidity, highly coloured raw waters typical of the Canadian Shield and of variable source quality generally.

The three mechanisms are not alternatives to be chosen once at the design stage; they overlap in dose–pH space, and a real plant may move between charge neutralisation and sweep floc seasonally. What the plant cannot do is separate coagulation from the transport step that follows: destabilisation must be achieved during a brief, intense rapid mix — a velocity gradient of order 600 to 1000 s⁻¹ for under a minute, because metal hydrolysis is complete in well under a second — and the resulting particles must then be grown in a tapered flocculation basin at a much gentler 20 to 70 s⁻¹ for 20 to 30 minutes. Too much energy in flocculation shears the floc apart again; too little leaves the collisions to Brownian motion alone, which is far too slow for particles above about a micrometre.