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Drying & particle engineering Published equations Educational models Planned capability

A dried powder stays stable only while it stays dry and glassy, and the dryer, carrier and package decide whether it does

How spray drying and freeze-drying make a powder, why powders take up water and cake, how packaging sets the clock, and how to read stability data.

Status. EUTECNIQ owns no dryer, laboratory or stability data. Laboratory drying is planned for Phase I and pilot spray, freeze and fluid-bed drying for Phase II (facility plan, October 2026).

Academy and related: carriers for spray-dried extracts (Course 12) · scale-up and tech transfer

0.345measured critical water activity of a 20 : 80 mango–maltodextrin blend, against 0.074 for mango solids alone
0 of 3published powders stay below their critical humidity, unpackaged, at any ICH storage condition
59.4%spray-dryer thermal efficiency at 180 °C inlet and 85 °C outlet (model)
24 monthslongest shelf life ICH Q1E allows from 12 months of long-term data

Kashiwakura et al., J Appl Glycosci 2024; ICH Q1A(R2) and Q1E (2003), drug guidance; efficiency = (inlet − outlet)/(inlet − ambient), 20 °C ambient (Masters, Spray Drying Handbook).

What this page answers

A powder fails by taking up water, passing its glass transition or losing its active in the dryer, and each failure is measurable

Three failure routes, each traced to the variable that controls it and the test that would catch itPublished mechanisms
Three ways a dried botanical powder fails, what happens physically or chemically, the variable that controls each, and the measurement that would detect itFailureWhat happensControlled byMeasured byTakes up waterWater crosses the package film and isabsorbed along the sorption isotherm, sowater activity risesPackage WVTR and area,storage humidity, the powder'scritical water activityWater content (Karl Fischer,USP <921>); water activity(USP <922>); sorptionisothermWarms past its glasstransitionAbsorbed water lowers Tg​; above Tg​ theamorphous glass becomes a stickyrubber that cakes, collapses orcrystallizesA carrier that raises Tg​; dryeroutlet temperature; storagehumidity and temperatureTg​ by DSC (USP <891>);crystallinity by X-ray powderdiffraction (USP <941>)Loses its active in thedryerHeat, oxygen and time degrade heat- oroxygen-sensitive constituentsDrying route; inlet and outlettemperatures; inert gasValidated assay before andafter drying, on a dry-solidsbasisRows 1 and 2 are physical changes; row 3 is chemical degradation. A powder can cake without losing any active, and lose active without caking.Three ways a dried botanical powder fails, what happens, the variable that controls each, and the measurement that would detect itTakes up waterwhat happensWater crosses the package film and is absorbedalong the sorption isotherm, so water activity risescontrolled byPackage WVTR and area, storage humidity, thepowder's critical water activitymeasured byWater content (Karl Fischer, USP <921>); wateractivity (USP <922>); sorption isothermWarms past its glass transitionwhat happensAbsorbed water lowers Tg​; above Tg​ theamorphous glass becomes a sticky rubber thatcakes, collapses or crystallizescontrolled byA carrier that raises Tg​; dryer outlet temperature;storage humidity and temperaturemeasured byTg​ by DSC (USP <891>); crystallinity by X-raypowder diffraction (USP <941>)Loses its active in the dryerwhat happensHeat, oxygen and time degrade heat- oroxygen-sensitive constituentscontrolled byDrying route; inlet and outlet temperatures; inertgasmeasured byValidated assay before and after drying, on adry-solids basisRows 1 and 2 are physical changes; row 3 is chemicaldegradation.
Glass transition and stickiness, collapse and recrystallization: Roos Y, Karel M. Food Technol. 1991;45(12). Wall deposition of sugar-rich extracts: Bhandari et al. 1997. Water activity: FDA Inspection Technical Guide No. 39 (1984). USP general chapters ⟨891⟩, ⟨921⟩, ⟨922⟩ and ⟨941⟩. Each row is developed further down the page.
Text version of the three failure routes
  • Takes up water. Water crosses the package film and is absorbed along the sorption isotherm, so water activity rises. Controlled by the film's WVTR, the package area, the storage humidity and the powder's critical water activity. Measured as water content (Karl Fischer, USP ⟨921⟩), water activity (USP ⟨922⟩) and the sorption isotherm.
  • Warms past its glass transition. Absorbed water lowers Tg; above Tg the amorphous glass becomes a sticky rubber that cakes, collapses or crystallizes. Controlled by a carrier that raises Tg, the dryer outlet temperature and the storage humidity and temperature. Measured by DSC (USP ⟨891⟩) and X-ray powder diffraction (USP ⟨941⟩).
  • Loses its active in the dryer. Heat, oxygen and time degrade heat- or oxygen-sensitive constituents. Controlled by the drying route, inlet and outlet temperatures and inert gas. Measured by a validated assay before and after drying, on a dry-solids basis.
  • Stability testing≠a validated shelf life
  • Moisture content≠water activity
  • Physical change (caking, collapse)≠chemical degradation of the active
  • Accelerated-condition results≠long-term behavior, when storage crosses the glass transition
  • Laboratory dryer feasibility≠commercial demonstration
Explanation, details and sources
EUTECNIQ would
  • Choose route, carrier and conditions for a defined extract
  • Measure moisture, water activity, Tg and crystallinity
  • Match packaging to the critical water activity
  • Design and interpret stability studies
Proposed
Qualified partners would
  • Run drying trials and tests before EUTECNIQ's laboratory exists
  • Run specialist tests such as X-ray powder diffraction
  • Supply commercial drying capacity
External partner
EUTECNIQ does not claim
  • Any dried product, yield or stability result
  • A validated shelf life for any material
  • That drying, by itself, improves absorption in people
Limits
Drying routes

Spray drying trades a short exposure to hot air for evaporative cooling; freeze-drying trades time and cost for cold

Hot air and spray enter together; by the bottom of the chamber the water has gone and powder flows to the cyclone

How it works

Pick an atomizer to see how it makes droplets. Hover or tab to any part for what it does.

Co-current spray dryer, cutawayIllustrative schematic

Rotary disk. A disk spinning at high speed flings the feed off its rim, so the spray leaves almost sideways.

Four atomizer types (rotary, pressure nozzle, two-fluid nozzle, ultrasonic) and the typical droplet range (below 10 µm to above 100 µm, giving dry particles of about 0.5–50 µm): Vehring R. Pharm Res. 2008;25(5):999–1022. Layout and part names follow standard spray-dryer practice; no equipment has been selected.
At the calculator's defaults, half the heater duty evaporates water and two fifths leaves with the exhaust airModel output, default inputs
Spray-dryer energy balance at the calculator's defaults: 94.8 kW heater duty, of which 50% evaporates 70 kg/h of water and 43% leaves in the exhaustControl volumeH-101 air heater1Ambient airD-10123Feed4Exhaust air to cyclone5Powder (via cyclone)Wall lossQ = 94.8 kWheater dutyWall depositparticles touching thewall above their Tg​stick; recovery =powder collected ÷solids fedStreamFlowState1Ambient air2,089 kg dry air/h20 °C, 8 g water/kg2Hot air2,089 kg dry air/h180 °C3Feed120 kg/h40% solids, 20 °C4Exhaust air2,089 kg dry air/h85 °C, 41.5 g water/kg5Powder50.0 kg/h4% moisture, 85 °CWhere the 94.8 kW goesevaporation: 47.7 kW (50%)evaporation 47.7 kW50%exhaust air: 38.5 kW (41%)exhaust air 38.5 kW41%vapor superheat: 2.4 kW (2%)wall loss: 4.7 kW (5%)powder: 1.5 kW (2%)vapor superheat 2.4 kW; wall loss 4.7 kW; powder 1.5 kWBalance: G cH​[(1 − f)ΔTin​ − ΔTout​] = E(λ0​ + cv​ΔTout​) + P cp​ΔTout​, with E = 70.0kg/h of water evaporated and f = 5% wall lossThermal efficiency (Tin​ − Tout​)/(Tin​ − T0​) = 59%; 4.87 MJ per kg of waterevaporated
Steady-state chamber balance of the spray-dryer calculator on the process engineering page, at its defaults: 120 kg/h feed at 40% solids, 4% powder moisture, 180 °C inlet and 85 °C outlet air, 20 °C ambient air at 8 g water per kg dry air, wall loss 5% of heater duty; humid heat cH = 1.006 + 1.86W, λ0 = 2,501 − 2.324T0 kJ/kg, dry-solids cp 1.5 kJ/(kg·K) (illustrative). ASHRAE Handbook—Fundamentals (2017), ch. 1; Masters K. Spray Drying Handbook, 4th ed. (1985); NIST Chemistry WebBook. Wall deposition: Bhandari et al. 1997. Not a design for any dryer.
Text version of the energy balance, wall deposition and recovery

Streams per hour: ambient air, 2,089 kg dry air at 20 °C and 8 g water/kg, heated in H-101 to 180 °C; feed, 120 kg at 40% solids and 20 °C; exhaust air, 2,089 kg dry air at 85 °C carrying 41.5 g water/kg; powder, 50.0 kg at 4% moisture and 85 °C. Water evaporated: 70.0 kg/h. Heater duty 94.8 kW: evaporation 47.7 kW (50%), exhaust air 38.5 kW (41%), vapor superheat 2.4 kW, wall loss 4.7 kW, powder 1.5 kW. Thermal efficiency (Tin − Tout)/(Tin − T0) = 59%; 4.87 MJ per kg of water.

Wall deposition. Particles that touch the wall while above their glass transition stick there. Sugar-rich extracts are prone to this, because their glass-transition temperature is low (Bhandari et al. 1997). Deposits lower yield and stay exposed to hot air for longer. Carriers that raise the glass transition, and lower outlet temperatures, reduce deposition.

Powder recovery. Recovery is the powder collected divided by the solids fed. The difference is wall deposit, fines that escape the cyclone to the bag filter, and material lost at start-up and shutdown. Recovery is measured by a mass balance on each run, not assumed from the dryer's specification.

A hotter inlet and a cooler outlet raise a spray dryer's thermal efficiency, and the outlet also sets residual water and stickinessModel output
Overall thermal efficiency = (inlet − outlet) ÷ (inlet − ambient), ambient 20 °C (Masters K. Spray Drying Handbook. 4th ed. 1985). The marked point uses the energy-balance defaults on the process engineering page. Stickiness at the outlet: scale-up page. Drag to rotate.
Data table: efficiency, %
Inlet50 °C out70 °C out90 °C out110 °C out

One droplet passes through five stages, and the shell that forms in the middle decides the particle's shape and density

How it works

Durations depend on droplet size, air temperature, humidity and feed solids, so no single time applies to every dryer.

While its surface is wet the droplet stays near the wet-bulb temperature; once a crust forms it warms toward the outlet airSchematic, not to scale
One spray-dried droplet through five stages: atomization, first drying stage near the wet-bulb temperature, skin formation, second drying stage through the crust, and separation, with the shape of its temperature history1 Atomization2 First drying stage3 Skin formation4 Second drying stage5 Separation and recoveryFeed breaks into droplets;their size distribution setseverything that followsshrinksSurface stays wet; thedroplet sits near thewet-bulb temperature; d²falls linearly in timeDissolved solids crowd thereceding surface; once theylock up, a shell or crustformsWater diffuses through thecrust; drying slows and theparticle warms toward theoutlet-air temperatureCyclone and bag filtercollect the powder; stickyparticles deposit on thechamber wall insteadTtime →inlet airoutlet airdroplet then particle temperature, schematicnear the wet-bulb temperature while the surface is wetwarms toward the outlet air
Stages and the d² law after Vehring R. Pharm Res. 2008;25(5):999–1022. The temperature trace shows shape only; it is not computed for any dryer.
Text version of the five stages
  1. AtomizationThe feed breaks into droplets; their size distribution sets everything that follows.
  2. First drying stageThe surface stays wet, the droplet sits near the wet-bulb temperature, and its area shrinks steadily.
  3. Skin formationDissolved solids crowd the receding surface; once they lock up, a shell or crust forms.
  4. Second drying stageWater must diffuse through the crust, so drying slows and the particle warms toward the outlet-air temperature.
  5. Separation and recoveryThe cyclone and bag filter collect powder; sticky particles deposit on the chamber wall instead.

Evaporation cools the droplet, so while it is still wet the product feels far less heat than the inlet air.

The Péclet number says whether a droplet dries into a dense bead or a hollow shell

How it works

If the surface recedes faster than dissolved molecules can diffuse inward, they pile up at the surface and form a shell early.

Droplet drying (Vehring 2008)d²(t) = d0² − κ t  τD = d0²κ
Pe = κ8 D  D = kBT6πη r
First-stage drying time τD
Diffusion coefficient D
Péclet number Pe
Surface enrichment E
Droplet size over its first drying stage, and how much solute crowds the surfaceModel output

Small molecules dried gently stay evenly spread and make dense particles; large molecules dried fast form a shell first.

Equations 4, 5, 7 and 8 and the low- and high-Péclet formation mechanisms: Vehring R. Pharmaceutical particle engineering via spray drying. Pharm Res. 2008;25(5):999–1022 (a glycoprotein dried at Pe 2.7, 5.6 and 16.8 became increasingly wrinkled). Stokes–Einstein: Einstein A. Ann Phys. 1905;17:549–560. Water viscosity: Pátek J, et al. J Phys Chem Ref Data. 2009;38:21–29.
Method, assumptions and limits
What it calculates
The first-stage drying time of one droplet, the diffusion coefficient of a dissolved molecule, the Péclet number and the surface enrichment of that solute.
Equations
τD = d0²/κ; D = kBT/(6πηr); Pe = κ/(8D); E = 1 + Pe/5 + Pe²/100 − Pe³/4000 (Vehring 2008, eq. 8).
Variables and units
d0 in µm; κ in µm²/ms (1 µm²/ms = 10⁻⁹ m²/s), on a logarithmic slider from 1 to 20; r in nm, logarithmic from 0.3 to 5; T = 298.15 K; η = 0.890 mPa·s. Pe is dimensionless: (m²/s)/(m²/s).
Assumptions
Constant evaporation rate; no interaction between solutes; diffusion coefficient of a sphere in water at 25 °C. A real drying droplet is warmer and more concentrated, so D is a first estimate.
Valid range
The enrichment formula is accurate to about ±1% for Pe below 20 (Vehring 2008); above that the readout says so instead of extrapolating.
What it does not establish
τD covers only the first drying stage, before the shell locks up; the second stage through the crust is slower. The model does not predict particle morphology for a real extract, which is checked by electron microscopy and density measurements.
Verification
Independent Python reference cases in tests/numerics/ref/technologies-drying-particle-engineering.py.

A freeze-dryer is three things: cold shelves that hold the product, a colder condenser that traps vapor, and a vacuum pump

How it works

Hover or tab to any part for what it does.

Freeze-dryer, cutawayIllustrative schematic
Three stages (freezing; primary drying by sublimation under vacuum; secondary drying by desorption): Bhatta S, Stevanovic Janezic T, Ratti C. Freeze-drying of plant-based foods. Foods. 2020;9(1):87.
Water phase diagram and the freeze-drying pathComputed from published equations
Vapor pressure of ice and liquid water: Murphy DM, Koop T. Q J R Meteorol Soc. 2005;131:1539–1565 (both give 611.66 Pa at 273.16 K). Triple point 273.16 K (0.01 °C) and 611.657 Pa: IAPWS R14-08(2011), Revised Release on the Pressure along the Melting and Sublimation Curves of Ordinary Water Substance. Melting line drawn vertical on this scale.
The four steps of a freeze-drying cycle
  1. FreezeCool at normal pressure until all water is ice. Slow freezing grows bigger crystals, which sublime faster later.
  2. Pull vacuumDrop the pressure below the triple point, 611.657 Pa. Below it, liquid water cannot exist.
  3. Primary dryingWarm the shelves gently. Ice turns straight into vapor and freezes again on the condenser.
  4. Secondary dryingRaise the temperature to remove the bound water that never froze.

Freeze-drying works because ice can skip the liquid state entirely when the pressure is below the triple point.

Primary drying is a trade-off: a warmer product dries faster, until it crosses its collapse temperature

How it works

Sublimation is driven by the vapor pressure of ice at the product temperature minus the chamber pressure. Ten degrees warmer raises it 2.5 to 3.1 times between −45 and −10 °C (2.8 times from the default −32 °C). Above the collapse temperature the porous cake loses its structure.

Driving force for sublimationΔp = pice(Tproduct) − pchamber
Ice vapor pressure
Driving force Δp
Margin to collapse
Cake
An example cycle: temperatures (top) and chamber pressure (bottom)Illustrative cycle

Cycle shape after the stage descriptions in Bhatta et al. 2020; times and temperatures are invented for illustration. The product runs colder than the shelf during primary drying because sublimation absorbs heat.
Method, assumptions and limits
What it calculates
The vapor pressure of ice at the product temperature, the sublimation driving force against the chamber pressure, and the margin between product and collapse temperature.
Equations
ln pice = 9.550426 − 5723.265/T + 3.53068 ln T − 0.00728332 T (Murphy & Koop 2005, eq. 7; T in K, p in Pa); Δp = pice − pchamber.
Variables and units
Temperatures in °C on the sliders, converted to K; pressures in Pa.
Assumptions
Product temperature uniform at the sublimation front; practice cited by Bhatta et al. (2020): keep the product 2–3 °C below the collapse temperature, which can sit 2–20 °C above the glass transition of the freeze-concentrate. The flag turns amber within 2 °C of collapse.
Valid range
−45 to −10 °C and 2 to 30 Pa, inside the range of the Murphy–Koop equation (above 110 K).
What it does not establish
It does not compute sublimation rate, which also needs the dried-layer resistance and shelf heat transfer. Collapse temperatures are measured for each product, for example by freeze-drying microscopy. The cycle is illustrative, not a validated recipe.
Verification
Independent Python reference cases in tests/numerics/ref/technologies-drying-particle-engineering.py.
Why it matters

In one published comparison, freeze-dried guava powder kept 63% of its vitamin C versus 25% in a heat-pump dryer, but freeze-drying is slow and costly (Bhatta et al. 2020), so the cycle has to be engineered rather than guessed. Related: freeze-drying calculator in the science lab.

What each route does to a botanical active: heat, oxygen and time

How it works

Emulsification devices, which make droplets rather than remove water, are compared on the emulsions page.

A spray droplet's first drying stage lasts milliseconds to seconds; published freeze-drying runs take most of a day or twoPublished values and model range
Drying time scales: the first drying stage of a spray droplet lasts about a millisecond to ten seconds; published plant-food freeze-drying runs took 18 to 48 hours1 ms1 s1 min1 h1 daySpray dryingSpray drying, first stage of one droplet: 1.25 ms to 10 s1.25 ms to 10 s · first stage of one dropletFreeze-dryingFreeze-drying, published plant-food runs: 18–48 hpublished plant-food runs · 18–48 hSpray dryingHeat: near the wet-bulb temperature while wet, then toward the outlet-airtemperatureGas: air, or nitrogen in a closed cycleWatch: stickiness, wall deposits and shell formationFreeze-dryingHeat: the product stays below its collapse temperatureOxygen: very low during dryingWatch: cycle cost and collapse
Spray drying: first-stage time τD = d0²/κ over the Péclet explorer's range (5–100 µm droplets, κ 1–20 µm²/ms), after Vehring 2008; Bhandari et al. 1997. Freeze-drying: plant-food runs of 18–48 h, for example guava with 24 h freezing and then 24 h drying (Bhatta et al. 2020). Logarithmic time axis.
Text version of the comparison
Spray drying

A short exposure to hot air, but the droplet stays cool while it is wet

  • Heat: the droplet sits near the wet-bulb temperature while water evaporates, then warms toward the outlet-air temperature
  • Time: milliseconds to seconds for the first drying stage, depending on droplet size and air conditions
  • Gas: air, or nitrogen in a closed cycle
  • Watch: stickiness, wall deposits and shell formation
Vehring 2008; Bhandari et al. 1997
Freeze-drying

Cold and under vacuum, but slow

  • Heat: product stays below its collapse temperature
  • Time: hours to days; published plant-food runs took 18–48 h (guava: 24 h freezing, then 24 h drying)
  • Oxygen: very low during drying
  • Watch: cycle cost and collapse
Bhatta et al. 2020

Heat-sensitive actives point to freeze-drying or a carefully controlled spray dryer; oxygen-sensitive oils point to inert gas and to carriers that keep the powder glassy.

In an adiabatic spray dryer, 180 °C inlet air cools along a line of near-constant wet-bulb temperature, about 46 °C, as it picks up waterReference data; example path
Psychrometric chart of humid air at 101.325 kPa from 0 to 200 °C dry-bulb temperature and 0 to 0.10 kg of water per kg of dry air, with lines of relative humidity and of constant wet-bulb temperature. An example spray-drying path heats ambient air at 25 °C and 50% relative humidity to 180 °C, then cools it adiabatically to 80 °C as it evaporates water; along that path the wet-bulb temperature, which a wet droplet surface approaches, stays near 46 °C. Computed with CoolProp 8.0 humid-air properties.
CoolProp 8.0 HAPropsSI (Herrmann, Kretzschmar & Gatley 2009, ASHRAE RP-1485); ASHRAE Handbook—Fundamentals 2017, ch. 1. Inlet, outlet and ambient conditions are examples, not measurements. Generated illustration, EUTECNIQ. Full-size SVG
Water, glass and crystals

Water activity, not moisture content alone, decides when an amorphous powder turns sticky

Gordon–Taylor (glass transition) · GAB (moisture uptake)Tg = wsTgs + k wwTgwws + k ww
W = WmCKaw /
 [(1 − Kaw)(1 + (C − 1)Kaw)]

Published parameters for mango solids, maltodextrin and a 20 : 80 blend (Kashiwakura et al. 2024). Data, units and the measured-versus-computed critical water activities are in the methods panel.

Glass-transition temperature versus storage humidity, with the 25 °C linePublished parameters

Mango solids alone turn rubbery and sticky above about 8% relative humidity at 25 °C; blended 20 : 80 with maltodextrin they stay glassy up to about 40% in this model (34.5% measured).

Kashiwakura Y, Sogabe T, Anantawittayanon S, Mochizuki T, Kawai K. J Appl Glycosci. 2024;71(1):15–21, Table 1. Original data: Fongin S, et al. J Food Eng. 2017;210:91–97; Fongin S, et al. J Food Eng. 2019;247:95–103.
Water activity is measured as a dew point: a sample at 25 °C whose headspace dews at 16 °C has a water activity of 0.574Schematic · computed example
Isometric cutaway of a generic chilled-mirror dew-point cell for water activity. A sample cup sits in a sealed chamber; a small fan mixes the headspace; a mirror on a thermoelectric cooler, with a heat sink above, is cooled until dew forms, which a light source and photodetector sense; a thermocouple reads the mirror temperature and an infrared thermometer the sample temperature. A worked example computes water activity from a dew point of 16 degrees C and a sample at 25 degrees C.
Principle: Fontana AJ. Appendix D in Barbosa-Cánovas GV, et al., eds. Water Activity in Foods. Blackwell; 2007. Saturation pressures from IAPWS-95 via CoolProp; example temperatures chosen for illustration. Generated illustration, EUTECNIQ. Full-size SVG
Method, assumptions and limits
What it calculates
Equilibrium water content from the GAB isotherm at the chosen humidity, the glass-transition temperature of the wetted solid from the Gordon–Taylor equation, and the critical humidity at which Tg falls to 25 °C.
Equations
As shown above, with ws = 1/(1 + W/100) and ww = 1 − ws; the critical point is found by bisection.
Variables and units
W in g water per 100 g dry matter; Wm in the same units; C, K, k dimensionless; Tgs and Tgw in K, shown in °C.
Assumptions
Equilibrium at 25 °C; isotherm and Tg parameters exactly as tabulated by Kashiwakura et al. (2024, Table 1) for freeze-dried mango solids, maltodextrin and a 20 : 80 mango–maltodextrin blend (measurements by Fongin et al. 2017, 2019); Tgw = 136 K for water, as used by the authors. The glass-transition rule applies to any amorphous sugar-rich powder, spray-dried or freeze-dried. Relative humidity is the equilibrium water activity × 100; critical humidity is where Tg = 25 °C. The paper lists experimentally determined critical water activities of 0.074, 0.345 and 0.575; computed from its fitted parameters they are 0.076, 0.401 and 0.581, and the gap for the blend shows the uncertainty of chaining two fitted models.
Valid range
2–70% relative humidity, inside the measured range of the source data.
What it does not establish
Caking also depends on time above Tg, particle size and pressure in the pack. The values describe mango-based powders, not any EUTECNIQ material.
Verification
The script in src/modules/particles/compute/check_gt_gab.py reproduces the tabulated critical water contents (1.9, 5.8 and 9.4 g per 100 g) and compares the computed critical water activities with the measured ones (0.076 versus 0.074, 0.401 versus 0.345, 0.581 versus 0.575). Reference cases in tests/numerics/ref/technologies-drying-particle-engineering.py.

USP general chapters ⟨731⟩, ⟨891⟩, ⟨921⟩, ⟨922⟩ and ⟨941⟩ (USP–NF chapter list, accessed October 22, 2026). Water activity definition: FDA Inspection Technical Guide No. 39, Water Activity (aw) in Foods (1984). Roos Y, Karel M. Food Technol. 1991;45(12). Instrument principles are on the analytical page.

Academy: water activity and microbial growth limits (Course 7)

Explanation, details and sources

Moisture content is the mass of water in the powder. Water activity is its escaping tendency: the ratio of the powder's water vapor pressure to that of pure water at the same temperature (FDA Inspection Technical Guide 39). The sorption isotherm links the two; absorbed water lowers the glass-transition temperature (Tg).

Glass transition

Below Tg an amorphous powder is a hard glass; above it, a sticky rubber

Dried extracts are often amorphous, with no crystal lattice. Roos and Karel (1991) related Tg to stickiness, collapse and recrystallization.

Crystallization

Above Tg, amorphous sugars can crystallize

It changes structure, flow and solubility, and X-ray powder diffraction detects it. It is a physical change, possible with no chemical degradation.

Hygroscopicity

A steeper sorption isotherm means more water taken up per step in humidity

In the published isotherms below, mango solids hold about 8.7 g of water per 100 g at 30% relative humidity, against about 4.9 g for maltodextrin.

Computed from published parameters
PropertyWhat it tells youHow it is measuredCompendial chapter
Water contentTotal water, the input to a mass balance and to dry-basis calculationsKarl Fischer titrationUSP ⟨921⟩ Water Determination
Loss on dryingMass lost on heating: water plus any other volatilesOven or balance drying under set conditionsUSP ⟨731⟩ Loss on Drying
Water activityEscaping tendency of water; links to stickiness and microbial riskDew-point or capacitance sensor at controlled temperatureUSP ⟨922⟩ Water Activity
Glass transitionTemperature at which the amorphous solid softensDifferential scanning calorimetryUSP ⟨891⟩ Thermal Analysis
CrystallinityWhether the solid is amorphous or has crystallizedX-ray powder diffractionUSP ⟨941⟩
Sorption isothermWater taken up at each humidity: hygroscopicity and critical water activityEquilibration over controlled humidities or dynamic vapor sorptionMethod-specific
Packaging

Packaging sets how fast a powder reaches its critical water activity, so the film is chosen from the powder's isotherm

Moisture gain through the filmmdry100·dWdt
 = Π A psat(RH − aw)
Π = WVTR0.90 psat(38 °C)
Critical water activity (Tg = 25 °C)
Time to reach it
Initial water gain, whole pack
Water content at equilibrium with outside
Water activity of the packed powder over timeModel output

Isotherm and glass-transition parameters: Kashiwakura et al. 2024. Saturated vapor pressure of water: Murphy & Koop 2005. WVTR test method: ASTM F1249, one side of the film at controlled humidity (usually 90% or 100% RH) and the other swept with dry gas (AMETEK MOCON method summary). The calculator assumes the WVTR entered was measured at 38 °C and 90% RH; film values are inputs, not product data.
Method, assumptions and limits
What it calculates
How the water activity inside a sealed package rises over time, and when it reaches the powder's critical water activity at 25 °C.
Equations
Film permeance Π = WVTR/(0.90 psat(38 °C)); flux J = ΠApsat(25 °C)(RH − aw); time to critical t = (mdry/100)/(ΠApsat) ∫ (dW/daw)/(RH − aw) daw, integrated with Simpson's rule from the packed to the critical water activity.
Variables and units
WVTR in g/(m²·day), on a logarithmic slider from 0.01 to 20; A in m²; mdry in g; psat in Pa (3,170 Pa at 25 °C, 6,630 Pa at 38 °C); W in g per 100 g dry. ΠAp has units g/day.
Assumptions
The critical water activity is computed from the fitted isotherm and Gordon–Taylor parameters (0.401 for the blend; 0.345 was measured), so the time to reach it carries that model uncertainty. The film's permeance at 25 °C equals that at the 38 °C test condition (real films differ, so a WVTR measured at storage conditions is preferred); the headspace is always in equilibrium with the powder; no leaks through seals; constant 25 °C outside humidity.
Valid range
Outside humidity 40–85%; packed water activity 0.02–0.30; inside the GAB parameter range of the source data.
What it does not establish
It ignores oxygen ingress, light, chemical degradation, temperature cycling and seal failure. It predicts a physical limit, not a shelf life; that comes from stability testing in the final package.
Verification
An independent Python solution in tests/numerics/ref/technologies-drying-particle-engineering.py integrates the moisture balance in time (scipy) and is checked against the page.
Unpackaged, none of three published powders stays below its critical humidity at any ICH storage conditionICH conditions, published critical humidities
ICH Q1A(R2) (Step 4, February 6, 2003), section 2.2.7.1: long term 25 °C/60% RH or 30 °C/65% RH, intermediate 30 °C/65% RH, accelerated 40 °C/75% RH. Critical humidity at 25 °C, measured: Kashiwakura et al. 2024 (7.4, 34.5 and 57.5%). Cells: condition humidity minus critical humidity, in percentage points.
Data table (percentage points of relative humidity)
Powder (critical RH at 25 °C)25 °C/60%30 °C/65%40 °C/75%
Mango solids (7.4%)+52.6+57.6+67.6
Mango : maltodextrin 20 : 80 (34.5%)+25.5+30.5+40.5
Maltodextrin (57.5%)+2.5+7.5+17.5

At 30 and 40 °C the critical humidity is lower than at 25 °C, so those cells understate the excess.

Explanation, details and sources

Water vapor crosses a package film at a rate set by its water vapor transmission rate (WVTR), its area and the humidity difference across it. The powder inside soaks up that water along its sorption isotherm until its glass transition falls to the storage temperature.

Reading stability data

Stability data support a shelf life only while the lower confidence bound stays inside the specification, and only modestly beyond the data

With 12 months of long-term data, ICH Q1E allows a proposed shelf life of 24, 18, 15 or 12 months, depending on what the data showGuidance (drug products)
ICH Q1E extrapolation limits: with 12 months of long-term data a proposed shelf life can reach 24, 18, 15 or 12 months depending on the case012243648Maximum proposed shelf life Y, months061218243036Months of long-term data, Xup to 2X, not beyond X + 12: 12 months of data → 24 monthsup to 1.5X, not beyond X + 6: 12 months of data → 18 monthsup to X + 3: 12 months of data → 15 monthsno extrapolation: X: 12 months of data → 12 monthsup to 2X, but not more than 12 months beyond XNo significant change at the accelerated condition, andeither little change and variability or a statistical analysisperformed (2.4.1)up to 1.5X, but not more than 6 months beyond XChange or variability without statistical analysis; orsignificant accelerated change, no significant intermediatechange, with analysis (2.4.1.2, 2.4.2.1)up to 3 months beyond XSignificant accelerated change, no significant intermediatechange, data not amenable to statistics (2.4.2.1)no extrapolationSignificant change at the intermediate condition (2.4.2.2)Each case also needs relevant supporting data; refrigerated products have narrower limits (Q1E 2.5). Lines start at 6 months. The calculator below uses the 2X, X + 12 case.ICH Q1E extrapolation limits: with 12 months of long-term data a proposed shelf life can reach 24, 18, 15 or 12 months depending on the case012243648Maximum proposed shelf life Y, months0122436Months of long-term data, Xup to 2X, not beyond X + 12: 12 months of data → 24 monthsup to 1.5X, not beyond X + 6: 12 months of data → 18 monthsup to X + 3: 12 months of data → 15 monthsno extrapolation: X: 12 months of data → 12 monthsup to 2X, but not more than 12 months beyond XNo significant change at the accelerated condition, andeither little change and variability or a statisticalanalysis performed (2.4.1)up to 1.5X, but not more than 6 months beyond XChange or variability without statistical analysis; orsignificant accelerated change, no significantintermediate change, with analysis (2.4.1.2, 2.4.2.1)up to 3 months beyond XSignificant accelerated change, no significantintermediate change, data not amenable to statistics(2.4.2.1)no extrapolationSignificant change at the intermediate condition(2.4.2.2)Each case also needs relevant supporting data; refrigeratedproducts have narrower limits (Q1E 2.5). Lines start at 6months. The calculator below uses the 2X, X + 12 case.
ICH Q1E Evaluation of Stability Data (Step 4, February 6, 2003), sections 2.4.1.1, 2.4.1.2, 2.4.2.1, 2.4.2.2 and Appendix A (decision tree; Y = proposed period, X = period of long-term data). A drug-industry reference: dietary supplements have no federal expiration-date requirement.
Text version of the extrapolation limits
  • Up to 2X, but not more than 12 months beyond X: no significant change at the accelerated condition, and either little or no change and variability, or data amenable to statistical analysis with the analysis performed (Q1E 2.4.1.1, 2.4.1.2).
  • Up to 1.5X, but not more than 6 months beyond X: change or variability without statistical analysis (2.4.1.2); or significant change at the accelerated condition, no significant change at the intermediate condition, with statistical analysis (2.4.2.1).
  • Up to 3 months beyond X: significant change at the accelerated condition, no significant change at the intermediate condition, data not amenable to statistical analysis (2.4.2.1).
  • No extrapolation: significant change at the intermediate condition (2.4.2.2).

Each case also needs relevant supporting data. Refrigerated products have narrower limits (2.5).

Regression with a lower one-sided 95% confidence boundŷ(t) = a + b t
LCB(t) = ŷ(t) − t0.95, n−2 s ×
 √(1/n + (t − t̄)²/Stt)
Fitted slope
Lower bound meets 90%
Q1E extrapolation limit
Period these data could support
Illustrative assay results, trend and lower 95% confidence boundIllustrative data

Method: ICH Q1E Evaluation of Stability Data (Step 4, February 6, 2003), sections 2.4.1 and 2.6. Pull points 0, 3, 6, 9, 12, 18 and 24 months follow the testing frequency in ICH Q1A(R2). The data are generated from a straight line plus fixed scatter; they are not EUTECNIQ results.
Method, assumptions and limits
What it calculates
A least-squares line through illustrative assay results, its lower one-sided 95% confidence bound for the mean, the time at which that bound meets a 90% acceptance criterion, and the ICH Q1E cap on extrapolation.
Equations
As shown above. Stt = Σ(ti − t̄)²; s is the residual standard deviation with n − 2 degrees of freedom; cap = min(2tmax, tmax + 12 months). The supported period is the smaller of the crossing time and the cap, rounded down to whole months.
Variables and units
Assay in % of label claim; time in months; Student t quantiles 6.314, 2.920, 2.353, 2.132 and 2.015 for 1 to 5 degrees of freedom.
Assumptions
One batch, one result per pull point, starting at 101%; scatter = the chosen standard deviation times a fixed set of normal deviates; linear loss; the accelerated condition shows no significant change, so the twice-or-12-months rule applies.
Valid range
Loss rates 0.05–0.8% per month; scatter 0.2–2%; 6 to 24 months of data.
What it does not establish
A real program would test at least three batches (ICH Q1A(R2)) in the final package, check whether batches can be pooled (ICH Q1E), and track several attributes. For a multi-constituent botanical, the marker chosen may not represent the whole extract. Dietary supplements have no federal expiration-date requirement; FDA's Part 111 preamble says a firm that uses one should have data to support it.
Verification
Independent Python reference (numpy least squares, scipy Student t) in tests/numerics/ref/technologies-drying-particle-engineering.py.

ICH Q1A(R2) Stability Testing of New Drug Substances and Products (Step 4, February 6, 2003); ICH Q1E (Step 4, February 6, 2003); FDA draft guidance Q1 Stability Testing of Drug Substances and Drug Products, June 24, 2025 (Docket FDA-2025-D-1106); ICH Q1 EWG work plan, February 2026. Part 111 preamble (72 FR 34752, June 25, 2007), as summarized by the Consumer Healthcare Products Association (2015).

Explanation, details and sources

ICH Q1E sets the drug-industry reference method: fit the trend, and take the earliest time at which the one-sided 95% confidence limit for the mean meets the acceptance criterion. Extrapolation is limited: up to twice the period covered by long-term data, and not more than 12 months beyond it, when accelerated data show no significant change and the data support statistical analysis.

Accelerated conditions

40 °C and 75% RH can push an amorphous powder past its glass transition

A powder that cakes at 40/75 may never cake at 25/60. Extrapolating rates across a glass transition or any change of physical state is not valid; such results are a stress signal.

Engineering interpretation
Batches and package

Three batches, in the package the customer receives

ICH Q1A(R2) asks for at least three primary batches, with long-term data at 25 °C/60% RH (or 30/65) and accelerated data at 40 °C/75% RH. Packaging is part of the system being tested.

Guidance (drug products)
Status of the guidance

A consolidated ICH Q1 is still a draft

As of October 2026, the consolidated ICH Q1 guideline that would supersede Q1A–Q1F is a Step 2 draft (FDA draft guidance, June 2025); the ICH work plan targets Step 4 in November 2026. Q1A(R2) and Q1E remain the adopted texts.

Draft
Experimental validation

Every model on this page makes a prediction that a measurement would confirm or reject

Seven predictions from the models on this page, each with the measurement that would test itProposed test logic
Seven model predictions on this page, each with the measurement that would confirm or reject it and a typical acceptance logicMeasurement that would confirm itTypical acceptance logicModel predictionParticle shape from the PécletnumberScanning electron microscopy; bulk and tappeddensityDense versus hollow or wrinkled particles aspredictedCritical water activity fromGordon–Taylor and GABDSC on samples equilibrated at several humidities;sorption isothermMeasured Tg crosses 25 °C near the predictedhumidityPowder remains amorphousX-ray powder diffraction at release and afterstorageNo new crystalline peaksResidual moisture after dryingKarl Fischer water or loss on drying, with wateractivityInside the specification set from the isothermActive survives the dryerValidated assay before and after drying, on adry-solids basisRetention inside a pre-set limitPowder recoveryMass balance on solids fed and powder collected,per runLosses identified and trendedPackage keeps the powder belowcriticalFilm WVTR testing; water activity of packedsamples during stability storageWater activity stays below the critical valuethrough the proposed periodSeven model predictions on this page, each with the measurement that would confirm or reject it and a typical acceptance logicParticle shape from the Péclet numberMeasurement that would confirm it · Scanningelectron microscopy; bulk and tapped densityTypical acceptance logic · Dense versus hollowor wrinkled particles as predictedCritical water activity from Gordon–Taylor and GABMeasurement that would confirm it · DSC onsamples equilibrated at several humidities;sorption isothermTypical acceptance logic · Measured Tg crosses25 °C near the predicted humidityPowder remains amorphousMeasurement that would confirm it · X-raypowder diffraction at release and after storageTypical acceptance logic · No new crystallinepeaksResidual moisture after dryingMeasurement that would confirm it · Karl Fischerwater or loss on drying, with water activityTypical acceptance logic · Inside thespecification set from the isothermActive survives the dryerMeasurement that would confirm it · Validatedassay before and after drying, on a dry-solidsbasisTypical acceptance logic · Retention inside apre-set limitPowder recoveryMeasurement that would confirm it · Massbalance on solids fed and powder collected, perrunTypical acceptance logic · Losses identified andtrendedPackage keeps the powder below criticalMeasurement that would confirm it · Film WVTRtesting; water activity of packed samples duringstability storageTypical acceptance logic · Water activity staysbelow the critical value through the proposedperiod
Measurements are standard techniques named on this page and in the table below; acceptance logic is EUTECNIQ's proposal, not a specification.

The models choose what to test first; none of them replaces the measurement.

Show the table (7 rows)
Model predictionMeasurement that would confirm itTypical acceptance logic
Particle shape from the Péclet numberScanning electron microscopy; bulk and tapped densityDense versus hollow or wrinkled particles as predicted
Critical water activity from Gordon–Taylor and GABDSC on samples equilibrated at several humidities; sorption isothermMeasured Tg crosses 25 °C near the predicted humidity
Powder remains amorphousX-ray powder diffraction at release and after storageNo new crystalline peaks
Residual moisture after dryingKarl Fischer water or loss on drying, with water activityInside the specification set from the isotherm
Active survives the dryerValidated assay before and after drying, on a dry-solids basisRetention inside a pre-set limit
Powder recoveryMass balance on solids fed and powder collected, per runLosses identified and trended
Package keeps the powder below criticalFilm WVTR testing; water activity of packed samples during stability storageWater activity stays below the critical value through the proposed period

Discuss a powder or drying question

Partners with a sticky, unstable or hard-to-dry botanical extract can describe it; EUTECNIQ would respond with a proposed study plan and its limits.