Drying, humidification and crystallisation

In short

These three unit operations all involve simultaneous heat and mass transfer across a gas-liquid or liquid-solid interface. Drying removes small amounts of liquid (usually water) from a solid by vaporising it into a gas stream; humidification/dehumidification adjusts the moisture content of a gas and underlies cooling towers and air conditioning; crystallisation produces a pure solid phase from a supersaturated solution. They are examined in GATE-CH (drying rate curves, psychrometry, crystal yield by mass balance), in university Mass Transfer-II papers, and in interviews for bulk drugs, agrochemicals, fertilisers, salt, sugar, dairy and food processing. Indian employers who test these directly include Sun Pharma, Cipla, Dr Reddy's, Aarti Industries, UPL, Coromandel International, Tata Chemicals, Amul/GCMMF, Nestlé India, Hindustan Unilever and engineering firms such as L&T, Thermax, Praj and GMM Pfaudler.

Explained

Moisture in solids and the drying rate curve

• Free moisture (X): moisture above the equilibrium value - the only part that can be removed by a given air condition. X = total moisture − equilibrium moisture X*, on a dry-solid basis (kg water / kg bone-dry solid). Always convert from wet basis before using drying equations.
• Bound moisture: held in cell walls, capillaries or as a solution, exerting a vapour pressure below that of pure water at the same temperature. Unbound moisture: excess above the saturation value, exerting the full vapour pressure of pure water.
• Hygroscopic solid: one with appreciable bound moisture (wood, leather, paper, grain, starch, pharma powders). Non-hygroscopic solids (sand, many crystals) have X* ≈ 0.
• Equilibrium moisture curve (sorption isotherm): X* versus relative humidity at fixed temperature; shows hysteresis between adsorption and desorption branches. A solid can never be dried below X* for the air used - lower the air humidity (or heat the air) to lower X*.
• Drying rate curve: plot N = −(Ls/A)(dX/dθ) against X. Four regions: initial adjustment (A-B), constant rate period (B-C), first falling rate (C-D) and second falling rate (D-E).
• Constant rate period: the surface stays fully wetted, like a free liquid surface. Rate is controlled entirely by external heat/mass transfer; the surface sits at the wet-bulb temperature of the air. Nc = ky(Ys − Y) = h(Tg − Tw)/λw.
• Critical moisture content (Xc): the X at the end of the constant rate period, when liquid can no longer reach the whole surface. Not a material constant - it rises with thickness, with drying rate and with coarse particle packing.
• First falling rate (unsaturated surface drying): the wetted fraction of the surface shrinks; rate falls roughly linearly with X. Second falling rate: the evaporation plane recedes inside the solid and internal diffusion/capillary flow controls; rate becomes independent of air velocity and strongly dependent on thickness.
• Case hardening: too-rapid surface drying forms an impermeable skin, trapping moisture and cracking the product - common in ceramics, pasta and granules.
• Through-circulation drying (air passes through a bed) dries far faster than cross-circulation (air over the surface), because the transfer area per unit volume is much larger.

Dryer types, selection and energy

• Batch, direct (convective): tray/truck dryer (cheap, labour-intensive, 4-24 h cycles, pharma and dyes); through-circulation tray dryer; batch fluidised bed dryer (FBD - standard in Indian formulation plants after wet granulation, 20-40 min).
• Continuous, direct: rotary dryer (fertiliser, sand, minerals; counter-current for high ΔT, with flights to lift and shower the solid); tunnel/belt dryer (bricks, tea, vegetables); continuous fluid bed and flash/pneumatic dryer (seconds, for surface-moist crystals); spray dryer (slurry/solution atomised into hot air; milk powder, detergent, instant coffee, spray-dried pharma excipients); spouted bed.
• Indirect (conducted) dryers: heat through a wall, no air carrying solvent away - drum dryer, vacuum shelf/tray dryer, rotary vacuum dryer (RVD), agitated thin-film dryer, agitated nutsche filter dryer (ANFD) - preferred for heat-sensitive, toxic, flammable or solvent-wet APIs because solvent vapour is condensed and recovered.
• Special: freeze dryer (lyophiliser) - frozen water removed by sublimation under vacuum (below the 611 Pa triple point); gives maximum retention of activity, used for vaccines, injectables and probiotics, but is slow and expensive. Microwave/RF, infrared and superheated-steam drying heat volumetrically or from inside out.
• Selection logic: solid form (slurry, paste, crumb, granule, sheet) → heat sensitivity → solvent (aqueous vs organic) → scale and batch vs continuous → dust/explosion and containment requirement → product specification (particle size, bulk density, no fines).
• Energy: the latent heat of water (~2,260 kJ/kg at 100 °C, ~2,440 kJ/kg at 25 °C) dominates. Reduce the duty by mechanical dewatering first (filter press, centrifuge, decanter) - removing water mechanically costs roughly 1-2% of the thermal cost. Then recover with air recirculation, exhaust-to-inlet heat exchange and higher inlet temperature.
• Safety and statutes: dryers handling organic solvents are Class I hazardous area equipment - nitrogen inerting, oxygen monitoring, earthing, flameproof motors, explosion vents or suppression. Dust explosion hazards in spray and fluid bed dryers (MIE, Kst). Occupational safety, dust exposure and pressure-vessel requirements now fall under the Occupational Safety, Health and Working Conditions Code, 2020, in force from 21 November 2025, which replaced the Factories Act, 1948. Unfired pressure parts are designed to IS 2825 (code for unfired pressure vessels) or ASME Section VIII Div 1. Pharma dryers must satisfy Schedule M of the Drugs and Cosmetics Rules (revised Schedule M for GMP) and, for exports, cGMP. Emissions to air from dryer stacks are regulated by the CPCB/State PCBs under the Air (Prevention and Control of Pollution) Act, 1981.

Humidification: psychrometry and its definitions

• Absolute (specific) humidity Y: kg water vapour per kg dry air. Molal humidity: mol water / mol dry air. These, not wet-basis fractions, are used in balances because the dry air is the invariant carrier.
• Saturation humidity Ys: Y when the vapour pressure equals the saturation pressure at the gas temperature.
• Relative humidity (RH): 100 × pA/pA,sat at the gas temperature. Percentage (absolute) humidity: 100 × Y/Ys - these two are not equal except at 0% and 100%.
• Dry-bulb temperature (Tg): the actual gas temperature. Dew point (Td): temperature at which the gas becomes saturated on cooling at constant Y - the first condensation point and the target in dehumidification.
• Wet-bulb temperature (Tw): steady temperature reached by a small wet surface in a large stream of the gas; it is a dynamic, mass-transfer equilibrium, not a thermodynamic property of the gas alone.
• Adiabatic saturation temperature (Tas): temperature reached if the gas is saturated by contact with recirculating water with no heat added. For air-water only, the Lewis relation h/(ky cs) ≈ 1 makes Tw ≈ Tas; for organic vapours (toluene, methanol in air) h/(ky cs) ≈ 1.6-2.0, so Tw > Tas and the two must be distinguished.
• Humid heat cs = 1.005 + 1.88 Y kJ/(kg dry air·K). Humid volume and enthalpy are referenced to liquid water at 0 °C.
• Psychrometric (humidity) chart: Y on the y-axis against Tg; carries the saturation curve, constant-RH curves, adiabatic saturation (≈ constant wet-bulb) lines, humid volume and enthalpy. Reading it is a standard exam question: fix any two independent properties and read the rest.
• Processes on the chart: sensible heating (horizontal right - RH falls, Y constant), sensible cooling (horizontal left), adiabatic humidification (along the wet-bulb line, up and left - an air washer or a desert cooler), dehumidification by cooling below dew point then reheating (window/split AC), chemical dehumidification (silica gel, molecular sieve, LiCl - moves up in temperature as adsorption heat is released).
• Water-cooling tower: water is cooled by evaporating 1-2% of itself; limited by the wet-bulb temperature of the air, never the dry-bulb. Approach = outlet water temperature − inlet air wet-bulb (typically 3-6 K); range = water inlet − outlet temperature; make-up = evaporation + drift + blowdown. Types: natural draught hyperbolic (large thermal power stations), mechanical induced-draught and forced-draught counterflow or crossflow, with film or splash fill, drift eliminators and a basin. Cycles of concentration controlled by blowdown; Legionella and biofouling controlled by dosing.
• Design relation: towers and humidifiers are sized by an enthalpy-driving-force integral (Merkel method) giving NTU and then packing height - the gas-phase analogue of HTU-NTU in absorption.

Crystallisation: driving force, nucleation and growth

• Purpose: produce a solid of defined purity, crystal size distribution (CSD), habit and polymorph; it is simultaneously a separation and a particle-formation step, and often the purity-defining step in an API process.
• Solubility curve: solubility versus temperature. Normal solubility (KNO₃, KCl, sucrose) rises with temperature → cool to crystallise. Inverted/retrograde (Na₂SO₄ above 32.4 °C, CaSO₄) → heat or evaporate.
• Supersaturation is the only driving force: Δc = c − c*, ratio S = c/c*, or relative σ = (c − c*)/c*. Created by (i) cooling, (ii) evaporation, (iii) vacuum/flash cooling (adiabatic - both at once), (iv) drowning-out/anti-solvent (adding water to an alcoholic solution), (v) reaction (precipitation), (vi) pH swing or salt formation.
• Metastable zone: between the solubility curve and the spontaneous-nucleation (supersolubility) curve. Operating inside this zone gives controlled growth on seeds and large crystals; crossing it gives a burst of nuclei and fine, filter-blocking product. The Ostwald-Miers diagram shows both curves.
• Nucleation: primary homogeneous (spontaneous, needs high σ), primary heterogeneous (on dust or vessel walls, lower σ), and secondary (crystal-crystal, crystal-impeller and crystal-wall contact) - the dominant mechanism in industrial crystallisers; B⁰ = k ΔC^b Mt^j N^r.
• Growth: two steps in series - diffusion of solute through the boundary layer, then surface integration into the lattice. ΔL law (McCabe): all geometrically similar crystals of the same material in the same solution grow at the same linear rate G = dL/dθ, independent of size - the basis of most exam problems.
• Seeding: adding a controlled mass of sized seed in the metastable zone fixes the number of crystals, so final size is set by mass balance rather than chance. Cooling-profile control (slow at first, faster later) keeps σ constant and avoids secondary nucleation.
• Related phenomena: crystal habit (needles vs plates vs prisms) changes with solvent, σ and impurities and controls filtration and flow; polymorphism (different lattices, different solubility and bioavailability - critical and patent-sensitive in pharma); hydrates/solvates; inclusions and mother-liquor occlusion (the main purity loss, cured by slower growth and washing); agglomeration; caking; Ostwald ripening; chiral resolution by diastereomeric salt crystallisation.
• Kelvin (Gibbs-Thomson) effect: very small crystals have a higher solubility, so nuclei below the critical size redissolve - why fines dissolve on gentle heating ("fines destruction").

Crystallisers, yield and operation

• Equipment: tank/batch agitated crystalliser with jacket or internal coils (most Indian API and specialty plants - cheap, flexible); Swenson-Walker (open, jacketed, scraped-trough, continuous cooling); forced-circulation (FC) evaporative crystalliser (high capacity, smaller crystals - ammonium sulphate, sodium chloride); draft-tube baffle (DTB) crystalliser (internal circulation + settling zone for fines destruction - large uniform crystals); Oslo/Krystal growth-type (supersaturated liquor fed under a fluidised bed of growing crystals - the largest, most uniform crystals); scraped-surface and DTB vacuum units; continuous oscillatory baffled and MSMPR cascades for continuous pharma.
• MSMPR (mixed-suspension mixed-product-removal) theory: with size-independent growth and an ideally mixed, clear-feed vessel, the population balance gives n = n⁰ exp(−L/Gτ). The dominant (mode) size L_d = 3Gτ and the mass-mean is 3.67 Gτ - a standard GATE result.
• Magma/slurry: the mixture of crystals and mother liquor; downstream are thickening, filtration or centrifugation, washing (fresh solvent displaces impure liquor), drying and sizing. Mother-liquor recycle raises yield but accumulates impurities, so a purge is required.
• Yield follows from a mass balance on solute and solvent between the feed and the saturated final mother liquor, allowing for the water of crystallisation in the crystal and any evaporation.
• Heat effects: heat of crystallisation ≈ −(heat of solution); evaporative crystallisers also need latent heat, usually met by multiple-effect or MVR arrangements (common in Indian salt and sugar works).
• Common troubles: encrustation/scaling on heat-transfer surfaces (reduce ΔT, use high circulation, periodic wash-out), fines carryover, oiling-out (liquid-liquid phase split before crystals form), and bimodal CSD from uncontrolled nucleation.
• Indian practice: solar salt works in Gujarat and Tamil Nadu; sugar boiling in vacuum pans with seeding (massecuite A, B, C) under BIS specifications for plantation white sugar; soda ash and sodium bicarbonate at Tata Chemicals Mithapur; ammonium sulphate and urea prilling/granulation under the Fertiliser (Control) Order; borax and boric acid; API crystallisation under revised Schedule M GMP, where CSD and polymorph are registered specifications.

Key points

• Free moisture X - moisture above equilibrium, on a dry-solid basis; only this is removable.
• Bound vs unbound moisture - bound exerts less than pure-water vapour pressure; unbound exerts the full value.
• Equilibrium moisture X\* - the floor set by the air's relative humidity; cannot be beaten by longer drying, only by drier/hotter air.
• Constant rate period - fully wet surface at the wet-bulb temperature, rate set by external h and ky, proportional to roughly u^0.8 for parallel flow.
• Critical moisture content Xc - end of the constant rate period; depends on thickness and drying rate, not a pure material property.
• Falling rate period - internal moisture movement controls; rate independent of air velocity, strongly dependent on thickness (≈ thickness² for diffusion control).
• Indirect vs direct dryers - indirect is chosen for solvents, toxics and vacuum service because vapour is condensed and recovered.
• Freeze drying - sublimation below the triple point (611 Pa, 0.01 °C); best quality retention, highest cost.
• Absolute humidity Y - kg vapour per kg dry air; the invariant basis for all psychrometric balances.
• RH ≠ percentage humidity - RH uses partial pressures, percentage humidity uses humidity ratios.
• Dew point - saturation temperature on cooling at constant Y; the condensation target in dehumidification.
• Wet-bulb ≈ adiabatic saturation for air-water only, because the Lewis number ≈ 1; not true for organic vapours.
• Cooling-tower limit - outlet water temperature can approach, but never go below, the inlet-air wet-bulb temperature.
• Supersaturation - the sole driving force for crystallisation; too much gives nucleation, a controlled little gives growth.
• Metastable zone - operate between the solubility and supersolubility curves, with seeds, for large crystals.
• ΔL law - all similar crystals grow at the same linear rate, independent of size.
• MSMPR - n = n⁰ e^−L/Gτ, dominant size = 3Gτ, mass-mean = 3.67 Gτ.
• Yield - set by a solute/solvent balance to the saturated mother liquor, corrected for hydrate water and evaporation.

Formulas and examples

Example 1 - Moisture basis and free moisture. A filter cake is 30% water on a wet basis; equilibrium moisture with the dryer air is 0.02 kg/kg dry solid; the product must leave at 5% water on a wet basis.

• X1 = 0.30/0.70 = 0.4286 kg/kg dry solid; X2 = 0.05/0.95 = 0.05263 kg/kg.
• Free moisture: X1f = 0.4286 − 0.02 = 0.4086; X2f = 0.05263 − 0.02 = 0.03263 kg/kg.
• Per 100 kg wet cake: dry solid = 70 kg, water = 30 kg. Final water = 70 × 0.05263 = 3.68 kg → water evaporated = 26.3 kg; product mass = 73.7 kg.

Example 2 - Drying time with constant and falling rate periods. 2,000 kg (dry basis) of solid, drying area 0.05 m² per kg dry solid (so A = 100 m²). Free moisture falls from 0.40 to 0.05 kg/kg; Xc = 0.20 kg/kg; Nc = 0.0008 kg/(m²·s). In the falling rate period the rate is proportional to X.

• Constant rate, 0.40 → 0.20: θc = 2,000 × (0.40 − 0.20)/(100 × 0.0008) = 400/0.08 = 5,000 s = 1.39 h.
• Falling rate, 0.20 → 0.05: θf = (2,000 × 0.20/(100 × 0.0008)) × ln(0.20/0.05) = 5,000 × ln 4 = 5,000 × 1.3863 = 6,931 s = 1.93 h.
• Total ≈ 11,931 s = 3.31 h. Note the last 0.15 kg/kg takes longer than the first 0.20 - the usual exam point.

Example 3 - Psychrometry from partial pressure. Air at 40 °C, 101.3 kPa, with water-vapour partial pressure 3.0 kPa. Saturation pressure of water at 40 °C ≈ 7.38 kPa.

• Y = (18/29) × 3.0/(101.3 − 3.0) = 0.6207 × 3.0/98.3 = 0.01894 kg/kg dry air.
• Ys at 40 °C = 0.6207 × 7.38/(101.3 − 7.38) = 0.6207 × 7.38/93.92 = 0.04877 kg/kg.
• RH = 100 × 3.0/7.38 = 40.7%; percentage humidity = 100 × 0.01894/0.04877 = 38.8% - the two differ, as expected.
• Dew point = saturation temperature at 3.0 kPa ≈ 24 °C (from steam tables).
• Humid heat cs = 1.005 + 1.88 × 0.01894 = 1.0406 kJ/(kg dry air·K); enthalpy H ≈ 1.0406 × 40 + 2,501 × 0.01894 ≈ 41.6 + 47.4 = 89.0 kJ/kg dry air.

Example 4 - Crystal yield with water of crystallisation. 1,000 kg of a 30 wt% Na₂CO₃ solution is cooled to 20 °C, where the solubility is 21.5 g anhydrous Na₂CO₃ per 100 g water and the stable solid is Na₂CO₃·10H₂O. No evaporation. (M: Na₂CO₃ = 106, decahydrate = 286.)

• Feed: solute 300 kg, water 700 kg.
• Let C = kg of decahydrate crystals. Anhydrous in crystals = 106C/286 = 0.3706C; water in crystals = 180C/286 = 0.6294C.
• Mother liquor: solute = 300 − 0.3706C; water = 700 − 0.6294C. Saturation: (300 − 0.3706C) = 0.215 × (700 − 0.6294C).
• 300 − 0.3706C = 150.5 − 0.1353C → 149.5 = 0.2353C → C = 635.4 kg of Na₂CO₃·10H₂O.
• Check: solute left = 300 − 235.5 = 64.5 kg; water left = 700 − 400.0 = 300.0 kg; ratio = 21.5/100 ✔.
• Yield on anhydrous solute = 235.5/300 = 78.5%. Mother liquor = 1,000 − 635.4 = 364.6 kg.
• Exam trap: reporting 635 kg as "the yield of sodium carbonate". It is the yield of the decahydrate; only 235.5 kg of it is Na₂CO₃.

Example 5 - MSMPR crystalliser. A 4 m³ continuous MSMPR crystalliser is fed at 0.5 m³/h with growth rate G = 2 × 10⁻⁸ m/s.

• τ = 4/0.5 = 8 h = 28,800 s.
• Gτ = 2 × 10⁻⁸ × 28,800 = 5.76 × 10⁻⁴ m = 0.576 mm.
• Dominant size L_d = 3Gτ = 1.73 mm; mass-mean = 3.67Gτ = 2.11 mm.
• Halving the feed rate doubles τ and doubles the dominant size - the standard "how do I get bigger crystals" answer, along with seeding and lower supersaturation.

Where it is used

• Pharmaceuticals and APIs: cooling and anti-solvent crystallisation to fix polymorph and CSD, then ANFD/RVD or vacuum tray drying and FBD after granulation - Sun Pharma, Cipla, Dr Reddy's, Divi's, Aurobindo; roles as production, process-development and QA engineer, with Schedule M and cGMP documentation.
• Food and dairy: spray drying of milk powder, whey and instant coffee (Amul/GCMMF, Nestlé India, Hindustan Unilever); sugar crystallisation in vacuum pans; freeze-dried coffee and vegetables; grain and spice drying.
• Inorganic chemicals and fertilisers: salt, soda ash and bicarbonate at Tata Chemicals Mithapur; ammonium sulphate, urea and complex fertilisers at Coromandel, IFFCO and RCF, with rotary and fluid bed dryers and prilling towers.
• Cooling-water systems: induced-draught cooling towers in every refinery, power plant and large chemical complex (IOCL, BPCL, NTPC); roles in utilities/energy engineering, water-treatment chemistry and performance testing against design approach.
• HVAC and process air conditioning: dehumidification by cooling coils or desiccant wheels for pharma clean rooms, electronics assembly and cold stores - designers follow ISHRAE/ASHRAE practice and the Energy Conservation Building Code.
• Equipment manufacturing and consultancy: dryer, crystalliser and cooling-tower vendors and EPCs - GMM Pfaudler, Thermax, Praj Industries, L&T, Paharpur and Bry-Air - where sizing, pilot trials and scale-up are the core work.

Interview questions

• Q: Why does the solid surface sit at the wet-bulb temperature during the constant rate period? A: All the heat arriving at the fully wetted surface is used as latent heat of vaporisation, so the surface reaches the same dynamic balance of heat in and mass out that defines the wet-bulb temperature.
• Q: Will increasing air velocity shorten the falling rate period? A: Barely - the falling rate period is controlled by internal moisture movement, so velocity mainly shortens the constant rate period; reducing thickness or raising temperature helps instead.
• Q: Is the critical moisture content a property of the material? A: No. It depends on sample thickness, packing and the drying rate, so it must be measured under conditions close to the plant's.
• Q: Why is an ANFD or vacuum dryer used for a solvent-wet API rather than a fluid bed dryer? A: The solvent vapour is condensed and recovered instead of being diluted in a large air stream, the product is contained, and vacuum lets drying proceed at a low temperature.
• Q: How low can a cooling tower cool the water? A: In theory to the inlet-air wet-bulb temperature; in practice 3-6 K above it, that gap being the approach.
• Q: Relative humidity is 50%. Is the percentage humidity also 50%? A: No - relative humidity is a ratio of partial pressures and percentage humidity a ratio of humidity ratios; percentage humidity is slightly lower.
• Q: Why is the wet-bulb temperature equal to the adiabatic saturation temperature for air-water but not for air-toluene? A: Because the Lewis relation h/(ky·cs) ≈ 1 holds for air-water; for organic vapours it is about 1.6-2.0, so the two temperatures separate.
• Q: What single variable controls crystal size, and how do you get bigger crystals? A: Supersaturation. Keep it low and inside the metastable zone - seed, cool slowly on a controlled profile, raise residence time, and destroy fines.
• Q: What is the ΔL law and where does it fail? A: All geometrically similar crystals grow at the same linear rate regardless of size; it fails with size-dependent growth, growth-rate dispersion, agglomeration or when diffusion limits very large crystals.
• Q: Why does the same compound crystallised from two solvents behave differently on the filter? A: The solvent changes habit and polymorph - needles from one solvent give a compressible, slow-filtering cake, prisms from another filter and wash easily.
• Q: A product fails its assay even though the crystal looks pure. Why? A: Mother liquor is occluded as inclusions or retained in the cake; cure by slower growth at lower supersaturation and proper displacement washing.
• Q: Why dewater mechanically before drying? A: Removing a kilogram of water by centrifuge or filter press costs a tiny fraction of the energy needed to evaporate it, so mechanical dewatering is always the cheapest first stage.
• Q: What is flash (vacuum) cooling crystallisation? A: The hot solution is flashed into a vessel at reduced pressure, so part of the solvent evaporates and the liquor cools adiabatically - supersaturation is generated by cooling and concentration together, with no heat-transfer surface to foul.

Common mistakes

• Using wet-basis moisture in the drying-time equations - every rate equation needs X on a dry-solid basis, and free moisture (X − X*), not total moisture.
• Forgetting to subtract the equilibrium moisture, which makes the computed falling-rate time infinite as X → 0.
• Treating relative humidity and percentage humidity as the same quantity, or confusing dew point with wet-bulb temperature.
• Assuming wet-bulb equals adiabatic saturation for any gas-vapour pair - it is an air-water coincidence.
• Reporting the mass of hydrated crystals as the yield of the anhydrous salt, or ignoring the water of crystallisation that leaves the mother liquor with the crystals.
• Ignoring evaporation in a vacuum or evaporative crystalliser mass balance, which understates the yield.
• Claiming high supersaturation gives more product quickly - it gives a nucleation burst, fine crystals, poor filtration and occluded impurities.
• Quoting a drying time scaled from a lab tray without accounting for thickness: diffusion-controlled falling-rate time scales roughly with the square of thickness.

Related topics

Mass transfer: diffusion · Evaporation and heat transfer equipment · Particle technology: filtration, centrifugation and size reduction · Adsorption and ion exchange · Absorption and stripping · Process utilities: cooling water and steam systems