Filtration, sedimentation and fluidisation

In short

This topic covers the three mechanical ways solids and fluids are separated or contacted in a process plant: pushing a suspension through a porous medium (filtration), letting gravity or a centrifugal field pull particles down through the liquid (sedimentation), and blowing fluid up through a bed until the particles are suspended (fluidisation). All three are rate processes - the engineer's job is to predict a volume-time curve, a settling velocity or a minimum velocity, and then size an equipment and a cycle around it. It is heavily examined in GATE (CH), in the mechanical-operations paper of every Indian university, and in the Fluid and Particle Mechanics lab (leaf filter, batch sedimentation, fluidised bed pressure-drop). On the job it decides effluent-treatment plant design (to meet CPCB consent limits), catalyst and ash handling in FCC and CFBC boilers, and dewatering in pharma, sugar, alumina and mineral plants.

Explained

Filtration - principles and the rate equation

• Filtration: separation of solids from a fluid by forcing the suspension through a filter medium (cloth, wire mesh, ceramic, membrane) that retains the solids as a cake.
• Cake filtration (solids build a growing layer, most industrial cases) versus depth/clarifying filtration (particles trapped inside the medium, dilute feeds) versus crossflow filtration (feed flows parallel to the medium, cake kept thin - microfiltration/ultrafiltration).
• Resistance is in series: cake resistance (grows with filtrate volume) + medium resistance Rm (constant). Flow through the cake is laminar creeping flow, so Darcy's law applies.
• Driving force classifies the equipment: gravity (sand filter), vacuum (≤ ~80 kPa, rotary drum, Nutsche), pressure (plate-and-frame press, 3-10 bar; pressure leaf), centrifugal (basket centrifuge).
• Specific cake resistance α (m/kg) measures how hard the cake is to push filtrate through - fine, slimy, compressible cakes have α orders of magnitude higher than coarse crystals.
• Compressible cake: α rises with pressure, α = α₀(Δp)^s, s = compressibility index (0 for rigid cakes such as sand or coarse crystals; 0.2-0.8 for alum sludge, clays, biomass). For a highly compressible cake, increasing pressure gives less than proportional gain in rate - sometimes none.
• Two classic modes: constant-pressure filtration (pump at fixed Δp, rate falls with time - most common; linear t/V vs V plot gives α and Rm) and constant-rate filtration (positive-displacement pump, Δp rises with time).
• Filter aids (diatomaceous earth/kieselguhr, perlite, cellulose) are used either as a precoat on the medium or as body feed mixed into the slurry, to keep a slimy cake permeable. Not used when the cake is the product.
• Cycle steps: filtration → cake washing (displacement washing, wash ratio) → dewatering/air blowing → cake discharge → medium cleaning. Optimum cycle time balances filtration time against fixed downtime per cycle.

Filtration equipment

• Plate-and-frame filter press: batch, cheap, high pressure, very dry cake, labour-intensive discharge; still the workhorse in Indian bulk-drug, dyes and intermediates plants.
• Pressure leaf filter / Sparkler filter: leaves in a pressure shell, good for polishing with filter aid, closed operation for solvents.
• Rotary drum vacuum filter: continuous; drum part-submerged in a trough, zones for pickup, drying, washing, discharge (scraper/string/belt). Used for gypsum, sugar mud, pulp.
• Rotary disc and horizontal belt (pan) filters: large continuous areas; belt filters allow good countercurrent washing - alumina, phosphoric acid.
• Nutsche filter / filter-dryer (agitated): batch, closed, inertable - standard in API manufacture because the same vessel filters, washes and dries.
• Centrifugal filters: basket (batch, perforated), pusher and peeler centrifuges (continuous) - used where cake must be very dry.
• Bag and cartridge filters: polishing of liquids; candle/ceramic filters for hot gas; baghouses and ESPs for dust from flue gas (a gas-solid separation cousin).
• Selection logic: particle size and compressibility → medium; required cake dryness → pressure or centrifugal; batch size and sterility → closed Nutsche; tonnage → continuous vacuum.

Sedimentation (gravity settling)

• Sedimentation: removal of particles from a liquid by gravity. Called clarification when a clear liquid is the product (low solids) and thickening when a concentrated sludge is the product.
• Free settling: particle settles alone, unaffected by neighbours or walls (dilute, < ~0.5 vol%). Hindered settling: concentrated suspension - upward displaced liquid and particle interaction slow everything down; the whole suspension settles with a sharp interface.
• Three force balance: gravity − buoyancy − drag = 0 at steady state gives the terminal settling velocity ut.
• Regimes by Reynolds number Rep = dp ut ρ/μ: Stokes (Rep < ~0.3, viscous, ut ∝ dp²), intermediate/Allen (0.3-1,000, empirical or CD = 18.5/Rep^0.6), Newton's law (10³-2×10⁵, CD ≈ 0.44, ut ∝ √dp). Above Rep ≈ 2×10⁵, boundary-layer transition drops CD (drag crisis).
• Hindered settling correction: Richardson-Zaki, u/ut = εⁿ with n ≈ 4.65 in the Stokes regime (ε = liquid volume fraction, voidage); so a 40 vol% solids suspension settles roughly 0.6^4.65 ≈ 0.1 times the free-settling rate.
• Batch settling test (cylinder test): interface height versus time gives four zones - clear liquid A, uniform suspension B, transition C, compression/sediment D; the constant-rate first portion gives the settling velocity, the curve then bends at the critical settling point and ends in slow compression.
• Kynch theory: settling is a function of local concentration only; a tangent construction on the H-t curve gives the settling velocity and concentration of each layer, used in the Coe-Clevenger and Talmage-Fitch methods of sizing a thickener.
• Thickener area is fixed by the slowest-settling (rate-limiting) layer; depth is fixed by the compression-zone residence time needed to reach the discharge solids.
• Equipment: rectangular horizontal-flow clarifier, circular centre-feed clarifier with rake, Dorr-Oliver thickener, high-rate lamella/tube settler (inclined plates multiply effective area in a small footprint - common in Indian ETPs and water works), sedimentation with coagulation (alum, ferric chloride, polyelectrolyte) to make flocs that settle fast.
• Centrifugal sedimentation when gravity is too slow: tubular bowl, disc-stack (milk, oil clarification), decanter/scroll centrifuge (sludge dewatering), hydrocyclone (classification by size/density, no moving parts).
• Indian practice: sewage and effluent treatment plants are designed by surface overflow rate (typically ~20-40 m³/m²·day for primary clarifiers; check the current CPHEEO manual and the relevant IS codes for the design value) and must meet CPCB/State Pollution Control Board consent limits under the Water (Prevention and Control of Pollution) Act, 1974 and the Environment (Protection) Act, 1986; the Environment (Protection) Rules give the general effluent standards for TSS, BOD, COD and pH.

Fluidisation

• Pass fluid upward through a bed of particles: at low velocity it is a fixed bed (Δp ∝ u, Ergun/Kozeny-Carman); at minimum fluidisation velocity umf the pressure drop equals the buoyant weight of the bed per unit area and the particles become suspended; beyond that, Δp stays essentially constant while the bed expands.
• Pressure-drop curve: rising branch (fixed bed) → small hump (breaking of interlocking/packing) → flat plateau (fluidised); on reducing velocity the curve retraces the plateau and comes down along a looser-bed line, so umf is best read from the decreasing-velocity run.
• Types: particulate (smooth) fluidisation - typical of liquid-solid systems, bed expands uniformly; aggregative (bubbling) fluidisation - typical of gas-solid, bubbles rise through a dense "emulsion" phase; slugging in narrow deep beds (bubbles span the tube); channelling and spouting (defluidised, poor contact); turbulent and finally fast/pneumatic transport above the terminal velocity.
• Geldart classification (gas-solid): A - fine, aerated (FCC catalyst, 30-100 µm), bed expands before bubbling; B - sand-like (100-800 µm), bubbles at umf; C - cohesive (< ~30 µm, flour, fines), channels and is hard to fluidise; D - large, spoutable (> ~1 mm, grains, coal).
• Upper limit: the bed carries over when u approaches the particle terminal velocity ut; for fine particles ut/umf can be ~70-90 (wide operating window), for coarse particles only ~8-10 (narrow). Elutriation is the preferential carry-over of fines; cyclones return them.
• Operating features: excellent gas-solid heat and mass transfer, near-isothermal bed, solids can be circulated like a fluid, high bed-to-wall heat transfer coefficients (hundreds of W/m²·K).
• Limitations: erosion and attrition of particles and internals, gas bypassing in bubbles (lower conversion than plug flow), particle entrainment needing cyclones/filters, backmixing of solids, higher pumping cost, difficult scale-up.
• Industrial uses: FCC riser-regenerator (IOCL, BPCL, HPCL, RIL refineries), CFBC and bubbling FBC boilers burning high-ash Indian coal, lignite and biomass, fluid-bed dryers and granulators (pharma), roasting of sulphide ores, fluid-bed coating, calcination.
• Distributor design (perforated plate, bubble caps, sintered plate) controls uniformity; a bad distributor gives dead zones and channelling.

Comparing and choosing a solid-liquid separation

• Order of preference by concentration: thicken first (cheap, gravity), then filter (removes most liquid), then dry thermally (most expensive per kg of water removed).
• Fine particles (< ~10 µm) settle very slowly in the Stokes regime - flocculate, use a centrifuge, or use filtration with a filter aid.
• Density difference drives sedimentation; if Δρ is small the only practical route is filtration or membranes.
• Filtration gives the driest cake; centrifugation is faster and continuous; sedimentation is cheapest but needs area.

Standards, codes and safety context

• Pressure filters and centrifuge housings that are pressure vessels fall under the Static and Mobile Pressure Vessels (Unfired) Rules, 1981 where applicable, and are designed to IS 2825 (code for unfired pressure vessels) or ASME Section VIII; the current edition should be confirmed before quoting a clause.
• Water and wastewater: IS 10500 (drinking-water specification) sets the quality a treatment train including sedimentation and filtration must reach; CPHEEO manuals on water supply and sewerage give Indian design practice.
• Occupational safety: since 21 November 2025 the four Labour Codes are in force - the Occupational Safety, Health and Working Conditions Code, 2020 replaced the Factories Act, 1948, and its provisions on guarding of machinery, dust control and confined spaces apply to centrifuges, filter presses and fluid-bed dryers.
• Dust explosion risk in fluid-bed dryers and granulators handling organic powders - inerting, earthing, explosion relief; relevant where solvents are present (petroleum/solvent handling rules also apply).

Key points

• Cake filtration - solids form a growing permeable layer; its resistance increases with filtrate volume, so rate falls at constant pressure.
• Specific cake resistance α (m/kg) - cake permeability expressed per unit dry mass; obtained from the slope of t/V versus V.
• Medium resistance Rm (1/m) - constant resistance of cloth plus any precoat; from the intercept of the same plot.
• Compressibility index s - exponent in α = α₀Δp^s; s = 0 incompressible, s → 1 means extra pressure gives almost no extra rate.
• Constant-pressure filtration - t/V = KcV/2 + 1/q₀, a straight line; constant-rate filtration gives Δp rising linearly with V.
• Filter aid - precoat or body feed that keeps slimy cakes permeable; never used when the cake is the product.
• Optimum cycle time - filtration time that maximises filtrate per total cycle including fixed downtime; for Rm ≈ 0 it equals the downtime.
• Terminal settling velocity ut - velocity at which drag balances net gravity; Stokes ut ∝ dp²Δρ/μ, Newton ut ∝ √(dpΔρ/ρ).
• Free versus hindered settling - hindered settling applies above ~0.5 vol% solids; Richardson-Zaki u = ut εⁿ, n ≈ 4.65 in Stokes flow.
• Batch settling curve - constant-rate zone, critical settling point, then compression; the basis of Coe-Clevenger and Talmage-Fitch thickener sizing.
• Kynch theory - settling rate is a function of local solids concentration alone; tangent construction gives layer velocities.
• Clarifier versus thickener - clear overflow is the product in a clarifier, thick underflow in a thickener; same unit, different design basis.
• Lamella settler - inclined plates multiply projected settling area, cutting footprint by 5-10 times.
• Minimum fluidisation velocity umf - from Ergun equation set equal to buoyant bed weight; Δp constant beyond umf.
• Δp at fluidisation = (1 − εmf)(ρs − ρ)g·L - independent of velocity, the plateau in the pressure-drop curve.
• Geldart groups A/B/C/D - aeratable, sand-like, cohesive, spoutable; decides whether a powder will fluidise at all.
• ut/umf ratio - the operating window; wide for fine Group A powders, narrow (~8-10) for coarse particles.
• Fluidised bed trade-off - superb heat and mass transfer and isothermal operation, against bubble bypassing, attrition, erosion and entrainment.

Formulas and examples

Example 1 - constant-pressure filtration, α and Rm from lab data. A leaf filter of area 0.1 m² is run at Δp = 2 × 10⁵ Pa on a slurry with μ = 1 × 10⁻³ Pa·s and w = 20 kg/m³ dry cake per m³ filtrate. Data: V = 0.002 m³ at t = 20 s; V = 0.004 m³ at t = 60 s.

• t/V values: 20/0.002 = 10,000 s/m³; 60/0.004 = 15,000 s/m³.
• Slope = (15,000 − 10,000)/(0.004 − 0.002) = 2.5 × 10⁶ s/m⁶ = Kc/2 → Kc = 5 × 10⁶ s/m⁶.
• Intercept 1/q₀ = 10,000 − 2.5 × 10⁶ × 0.002 = 5,000 s/m³.
• α = Kc A² Δp/(μ w) = 5 × 10⁶ × 0.01 × 2 × 10⁵ / (1 × 10⁻³ × 20) = 5 × 10¹¹ m/kg.
• Rm = (1/q₀)·A·Δp/μ = 5,000 × 0.1 × 2 × 10⁵/1 × 10⁻³ = 1 × 10¹¹ 1/m.
• Time for 0.01 m³: t = (Kc/2)V² + V/q₀ = 2.5 × 10⁶ × 10⁻⁴ + 5,000 × 0.01 = 250 + 50 = 300 s.

Example 2 - scale-up and cycle optimisation. Same slurry, same Δp, on a plant filter of A = 10 m² (100 × the lab area). Kc scales as 1/A²; intercept as 1/A.

• Kc,plant = 5 × 10⁶/10⁴ = 500 s/m⁶; 1/q₀,plant = 5,000/100 = 50 s/m³.
• Filtrate in 1 hour (3,600 s): 250V² + 50V = 3,600 → V = [−50 + √(2,500 + 4 × 250 × 3,600)]/(2 × 250) = (−50 + √3,602,500)/500 = (−50 + 1,898.0)/500 = 3.70 m³.
• If discharge and cleaning take 1,800 s, optimum filtration time ≈ 1,800 s (Rm small): V = solve 250V² + 50V = 1,800 → V = (−50 + √(2,500 + 1,800,000))/500 = (−50 + 1,342.6)/500 = 2.585 m³.
• Cycle output = 2.585 m³ per 3,600 s = 2.59 m³/h, against 3.70/(3,600 + 1,800) × 3,600 = 2.47 m³/h for the 1-hour run - the shorter cycle wins.

Example 3 - terminal settling velocity and regime check. A silica particle, dp = 80 µm, ρs = 2,650 kg/m³, settling in water at 30 °C (ρ = 996 kg/m³, μ = 0.8 × 10⁻³ Pa·s).

• Assume Stokes: ut = (80 × 10⁻⁶)² × (2,650 − 996) × 9.81/(18 × 0.8 × 10⁻³).
• Numerator = 6.4 × 10⁻⁹ × 1,654 × 9.81 = 1.0385 × 10⁻⁴; denominator = 0.0144 → ut = 7.2 × 10⁻³ m/s (7.2 mm/s).
• Check Rep = 80 × 10⁻⁶ × 7.2 × 10⁻³ × 996/(0.8 × 10⁻³) = 0.72 - slightly above 0.3, so Stokes over-predicts by roughly 5-10%; use an intermediate-regime correlation for design.
• In a 25 vol% suspension (ε = 0.75): u = 7.2 × 0.75^4.65 = 7.2 × 0.2624 = 1.9 mm/s.

Example 4 - clarifier area. A plant discharges 1,200 m³/day of effluent; the smallest floc to be removed settles at 1.5 mm/s.

• Q = 1,200/86,400 = 0.01389 m³/s. A = Q/ut = 0.01389/0.0015 = 9.26 m² (diameter ≈ 3.4 m) - theoretical minimum; apply a factor (short-circuiting, inlet turbulence) and check against the overflow-rate limit in the design manual.
• Overflow rate check: 1,200/9.26 = 130 m³/m²·day - far above typical primary-clarifier practice (~20-40 m³/m²·day), so area is set by the code, not by ut: A ≈ 1,200/30 = 40 m² (≈ 7.1 m diameter).

Example 5 - minimum fluidisation and bed expansion. Catalyst spheres, dp = 300 µm, ρs = 1,500 kg/m³, εmf = 0.45, φs = 1, fluidised by air at 20 °C (ρ = 1.2 kg/m³, μ = 1.8 × 10⁻⁵ Pa·s), bed height at rest 0.5 m with ε = 0.40.

• umf = (300 × 10⁻⁶)² × (1,500 − 1.2) × 9.81 × 0.45³/[150 × 1.8 × 10⁻⁵ × (1 − 0.45)].
• Numerator = 9 × 10⁻⁸ × 1,498.8 × 9.81 × 0.0911 = 1.206 × 10⁻⁴; denominator = 1.485 × 10⁻³ → umf = 0.081 m/s.
• Δp at fluidisation (using εmf) = L(1 − ε)(ρs − ρ)g; bed at umf expands to L = 0.5 × (1 − 0.40)/(1 − 0.45) = 0.545 m → Δp = 0.545 × 0.55 × 1,498.8 × 9.81 = 4,407 Pa ≈ 4.4 kPa (equal to the buoyant weight per unit area, 0.5 × 0.60 × 1,498.8 × 9.81 = 4,409 Pa - unchanged by expansion, as expected).
• Terminal velocity (Stokes): ut = 9 × 10⁻⁸ × 1,498.8 × 9.81/(18 × 1.8 × 10⁻⁵) = 1.3235 × 10⁻³/3.24 × 10⁻⁴ = 4.08 m/s; Rep = 300 × 10⁻⁶ × 4.08 × 1.2/1.8 × 10⁻⁵ = 81.6, so Stokes is invalid and the true ut is lower (intermediate regime, roughly 1.5-2 m/s) - still ut/umf of order 20, a comfortable window.

Where it is used

• Refining and petrochemicals: FCC catalyst circulation and regeneration, catalyst fines removal, slurry settlers - IOCL, BPCL, HPCL, Reliance, Nayara.
• Power and cement: CFBC and AFBC boilers for high-ash Indian coal, lignite and biomass; ash-water settling ponds; ESPs and baghouses for dust - NTPC, BHEL-supplied units.
• Pharma and fine chemicals: agitated Nutsche filter-dryers, basket centrifuges, fluid-bed dryers and granulators for API and formulation plants - roles in production, tech transfer and validation.
• Mineral, alumina and sugar processing: thickeners and belt filters for red mud and bauxite slurry, rotary vacuum filters for sugar mud, hydrocyclones in coal washeries - Hindalco, Vedanta, Tata Steel, sugar co-operatives.
• Water and effluent treatment: clarifloculators, lamella settlers, rapid sand filters, sludge dewatering by filter press or decanter centrifuge in every CETP and STP, designed to meet CPCB/SPCB consent conditions.
• Job roles: process design engineer (equipment sizing and datasheets), plant/production engineer (filter cycle and centrifuge throughput), utilities and ETP engineer, equipment sales and application engineering for filter and centrifuge makers.

Interview questions

• Q: Why does the filtration rate fall with time at constant pressure? A: The cake thickens as filtrate passes, so its resistance grows in proportion to the volume collected while the driving force stays the same.
• Q: What do the slope and intercept of a t/V versus V plot give you? A: The slope gives the specific cake resistance α and the intercept gives the filter-medium resistance Rm, for the known area, pressure, viscosity and cake-to-filtrate mass ratio.
• Q: A cake is highly compressible. Will doubling the pressure double the rate? A: No - α rises as Δp^s, so the net gain is proportional to Δp^1−s; at s close to 1 the gain is almost nothing and the cake may blind the cloth.
• Q: When would you use a filter aid, and when must you not? A: Use it as precoat or body feed for slimy, compressible or very fine solids; never when the cake itself is the product, since the aid contaminates it.
• Q: What is the difference between a clarifier and a thickener? A: Mechanically they are similar; a clarifier is designed for a clear overflow (area set by the settling velocity of the finest particle), a thickener for a concentrated underflow (area set by the rate-limiting layer, depth by compression time).
• Q: Why does a suspension settle more slowly than a single particle? A: In hindered settling the upward flow of displaced liquid, higher effective suspension viscosity and particle interaction reduce the velocity, roughly as ut·ε^4.65 in the Stokes regime.
• Q: What happens to the pressure drop across a bed as gas velocity rises past umf? A: It rises linearly up to umf, then stays essentially constant at the buoyant weight of the bed per unit area while the bed expands.
• Q: How do you find umf? A: Equate the Ergun pressure drop to the buoyant bed weight per unit area and solve for u, or read it from the intersection of the fixed-bed and plateau lines of a measured Δp-u curve (decreasing-velocity run).
• Q: Why is FCC catalyst made at 60-80 µm rather than a few millimetres? A: Group A powders of that size fluidise smoothly, expand before bubbling, circulate readily between riser and regenerator, and give a very wide ut/umf operating window.
• Q: Why do very fine cohesive powders fluidise badly? A: Interparticle van der Waals and electrostatic forces exceed the drag and weight forces, so Geldart Group C powders channel or lift as a plug rather than fluidise; agitation, vibration or coarse additives are needed.
• Q: Name two disadvantages of a fluidised-bed reactor compared with a fixed bed. A: Gas bypassing through bubbles lowers conversion against plug-flow behaviour, and attrition and erosion of catalyst and internals cause fines loss and maintenance.
• Q: Effluent contains 5 µm particles with a density close to water. How will you separate them? A: Gravity settling is hopeless (Stokes velocity is microns per second with a small Δρ) - coagulate/flocculate to build larger flocs, or use a filter press with filter aid, a membrane, or a decanter centrifuge.

Common mistakes

• Applying Stokes' law without checking Rep - it is only valid up to about 0.3, and students routinely use it for millimetre particles in air, where it is wildly wrong.
• Using the free-settling velocity for a concentrated suspension, or the hindered velocity for a dilute clarifier feed.
• Scaling filtration data wrongly: the slope term varies as 1/A² and the intercept as 1/A, not both the same way.
• Mixing up w (mass of dry cake per unit volume of filtrate) with the slurry concentration, and ignoring the wash-liquid retained in the cake.
• Assuming pressure drop keeps rising above umf, or reading umf from the increasing-velocity branch where the packing hump distorts it.
• Forgetting that the fluidised-bed Δp is independent of velocity and of bed expansion, but the blower duty still rises with flow.
• Quoting a thickener area from the initial settling rate alone instead of the rate-limiting layer from the Talmage-Fitch or Coe-Clevenger construction.

Related topics

• Flow through packed and fluidised beds · Fluid flow and pumps in process plants · Size reduction and screening · Conveying and storage of solids · Dimensional analysis and similitude · Heat transfer in fluidised beds and dryers.