Permeability & De‑aeration Rates of Common Bulk Powders

Including portland cement, coal, iron powder, PVC, wheat flour

Follow us on Twitter
Question, remark ? Contact us at contact@myengineeringtools.com

1. Introduction
2. Fundamental Theory

3. Factors That Influence Permeability

4. Measurement Methods

5. Data table

6. Sample Calculations

7. Case Studies (Brief)

8. Frequently‑Asked Questions

Author’s note: This article consolidates publicly‑available data, standard test methods and practical calculations for engineers dealing with bulk‑solid handling. All numbers are order‑of‑magnitude values; actual figures depend on particle size distribution, moisture content and compaction level.

1. Introduction

When a powder is stored, conveyed or discharged, air must move through the inter‑particle voids. The ease of that movement is described by permeability (k) – a material‑specific property that directly influences pressure drop, silo vent sizing, fluidised‑bed stability and the speed at which trapped air is expelled (deaeration rate).

Low‑permeability powders can cause pulsating flow, silo arching, or incomplete filling, while highly permeable powders may fluidise unintentionally, leading to dust emissions. Understanding and quantifying these properties is therefore essential for reliable plant design.

2. Fundamental Theory

2.1 Darcy’s Law for Gases

$ \displaystyle \Delta P = \frac{\mu \, L \, v}{k} $

$\Delta P$ – pressure drop (Pa)
$\mu$ – dynamic viscosity of air (≈ 1.85 × 10⁻⁵ Pa·s at 20 °C)
$L$ – thickness of the powder bed (m)
$v$ – superficial air velocity (m s⁻¹)
$k$ – permeability (m²)

2.2 Kozeny‑Carman Equation

$ \displaystyle k = \frac{\varepsilon^{3}}{F\,(1-\varepsilon)^{2}} \; \frac{d_{p}^{2}}{180} $

$\varepsilon$ – porosity (void fraction)
$F$ – shape factor (≈ 1 for spherical particles, > 1 for irregular shapes)
$d_{p}$ – mean particle diameter (m)

This semi‑empirical relation lets you estimate k from basic particle data when laboratory measurements are unavailable.

2.3 De‑aeration Rate

$ \displaystyle v_{a} = \frac{k \, \Delta P}{\mu \, L} $

The time to deaerate a layer of thickness L is roughly t = L / vₐ.

(v_{a}) stands for the average air‑release velocity through the powder bed.

What it represents

Symbol	Meaning	Units
(v_{a})	Average linear speed of the air that escapes from the pores of the consolidated powder. It tells you how fast the trapped air moves upward (or downward) per unit cross‑section of the bed.	meters per second (m s⁻¹)

In practice, (v_{a}) is the effective superficial velocity of the gas that is driven by the pressure difference (\Delta P) across the powder layer of thickness (L).

Where it fits in a design calculation

Set the pressure drop you expect (or can tolerate) across the powder column – this is often dictated by the vent size or the fan curve.
Insert the material’s permeability (k) (from measurements or tables).
Use the air viscosity (\mu) (≈ 1.85 × 10⁻⁵ Pa·s at 20 °C for dry air).
Divide by the layer thickness (L) (the height of the powder column you want to deaerate).

The result (v_{a}) tells you how quickly the air will be expelled.

Converting (v_{a}) to a practical metric

Often you care about the time needed to deaerate a given thickness. That is simply

[ t_{\text{deaeration}} = \frac{L}{v_{a}} ]

where (t) is in seconds if you keep (L) in metres and (v_{a}) in m s⁻¹.

Example (quick recap)

Powder: wheat flour, (k = 1.3 \times 10^{-6},\text{m}^2)
Layer thickness: (L = 0.5) m
Allowed pressure drop: (\Delta P = 2) kPa
Air viscosity: (\mu = 1.85 \times 10^{-5}) Pa·s

[ v_{a}= \frac{1.3\times10^{-6}\times 2000}{1.85\times10^{-5}\times0.5} \approx 0.028;\text{m s}^{-1} ]

[ t = \frac{0.5}{0.028}\approx 18;\text{s} ]

So the air will leave the 0.5 m flour bed in roughly 18 seconds under those conditions.

Bottom line: (v_{a}) is the air‑release speed that results from the interplay of permeability, pressure drop, air viscosity, and bed thickness. Knowing it lets you size vents, choose fans, and predict how long a batch will need to “settle out” its trapped air before processing.

3. Factors That Influence Permeability

Factor	Effect on k	Typical Range
Particle size (dₚ)	k ∝ dₚ² (larger particles → higher k)	10 µm – 5 mm
Particle shape	Irregular shapes increase tortuosity → lower k	F ≈ 1–3
Size distribution	Broad distributions can pack tighter → lower k	–
Bulk density / Compaction %	Higher compaction → lower porosity → lower k	10 % – 50 %
Moisture / Cohesion	Capillary bridges reduce pore connectivity → lower k	–
Temperature	Viscosity μ decreases with T → apparent k rises	–

Permeability is “a measure of how easily a powder is crossed by an air flow” – a definition repeated across industry resources.

4. Measurement Methods

Method	Standard / Reference	Typical Sample Size	What It Gives
Steady‑state pressure‑drop cell	ASTM D8327‑24 (Freeman FT4)	100 g – 500 g	Direct k (m²) at chosen consolidation
Gas pycnometer + Kozeny‑Carman	NIST‑recommended	10 g	True density → porosity → estimated k
Dynamic flow tester (GranuPack)	Research papers (ScienceDirect)	200 g	k vs. packing fraction, useful for process‑condition mapping
Air‑permeability probe (single‑point)	IEC 60404‑9	Small plug	Quick screening, less precise

5. Data Table

Note : orders of magnitude only, of course variying depending on the actual specification of materials

Material	Compaction %	Porosity ε	True ρ (kg m⁻³)	Bulk ρ (kg m⁻³)	Permeability k (×10⁻⁶ m²)	De‑aeration vₐ (×10⁻³ m s⁻¹)
Alumina – sandy	17	0.62	3950	3270	0.42	19
Barytes	43	0.48	4500	2340	0.48	3.9
Ordinary Portland Cement	40	0.55	3150	1418	0.71	3
Coal – granular (as‑supplied)	14	0.70	1400	980	42	24
Coal – degraded	36	0.58	1400	620	1	2.9
Coal – pulverised	31	0.61	1400	730	0.53	4.3
Copper concentrate	30	0.57	3500	1505	0.33	9.8
Fly ash – fine	49	0.45	2300	1265	0.6	2
Iron powder	34	0.52	7800	4050	0.34	7
Magnesium sulphate	29	0.68	1700	550	6.3	17
Polyethylene – pellets	5	0.92	950	86	420	60
Potassium chloride	16	0.63	1910	714	11	26
PVC – powder	22	0.59	1400	574	1.2	8
Silica sand	12	0.66	2650	1760	3.9	34
Wheat flour	37	0.51	1500	735	1.3	6.2
Zircon sand	15	0.60	4700		1.3	10

6. Sample Calculations

6.1 Pressure Drop in a Cement Silo

Given:

Height L = 2 m
Compaction = 40 % → bulk density ≈ 1418 kg m⁻³
Permeability k = 0.71 × 10⁻⁶ m²
Air viscosity μ = 1.85 × 10⁻⁵ Pa·s
Superficial air velocity v = 0.2 m s⁻¹

$$\Delta P = \frac{1.85\times10^{-5}\times 2 \times 0.2}{0.71\times10^{-6}} \approx 5.2\times10^{3}\,\text{Pa}\;(5.2\text{ kPa})$$

Interpretation: a vent rated for ≈ 6 kPa will comfortably handle the required airflow.

6.2 De‑aeration Time for Wheat Flour

Assume a 0.5 m thick flour layer, ΔP = 2 kPa.

$$v_a = \frac{k\,\Delta P}{\mu L} = \frac{1.3\times10^{-6}\times 2000}{1.85\times10^{-5}\times0.5} \approx 0.028\;\text{m s}^{-1}$$

Time to purge the layer:

$$t = \frac{L}{v_a}= \frac{0.5}{0.028}\approx 18\;\text{s}$$

Only a few seconds of venting clear most trapped air – valuable for rapid batch changes.

6.3 Designing a Pneumatic Conveyor for Coal

Target mass flow = 5 kg s⁻¹, bulk density ≈ 800 kg m⁻³ (degraded coal).

Volumetric flow:

$$Q = \frac{\dot{m}}{\rho_b}= \frac{5}{800}=6.25\times10^{-3}\,\text{m}^3\!\!/\text{s}$$

Keeping pressure drop ≤ 10 kPa and using Darcy’s law, an iterative solution gives a pipe diameter of ≈ 80 mm.

7. Case Studies (Brief)

Portland cement: Water‑cement ratio strongly affects porosity; a 0.45 ratio drops k by ~40 % compared with dry cement.
Coal (granular vs. pulverised): Fine grinding reduces k dramatically; designers must increase vent area or use higher‑pressure fans.
Iron powder: High density and irregular shape give low k (≈ 0.34 × 10⁻⁶ m²); suitable for compacted feedstock in metal‑additive manufacturing.
PVC powder: Binder additives create micro‑channels, raising k to ~1.2 × 10⁻⁶ m² despite moderate compaction.
Wheat flour: Moisture content (12 % vs. 8 %) shifts k by ±30 %; critical for food‑industry silo design.

8. Frequently‑Asked Questions

What is the typical permeability of wheat flour?: ≈ 1.3 × 10⁻⁶ m² at 37 % compaction (values taken from the public data table)

How does compaction percentage affect deaeration rate?: Deaeration velocity is roughly inversely proportional to the square of the porosity; higher compaction → lower porosity → slower air release.

Which standard covers permeability testing?: ASTM D8327‑24 – “Standard Test Method for Measuring the Permeability of Powders as a Function of Consolidation Using the Freeman Technology FT4 Powder Rheometer.”

Can I estimate permeability from particle size alone?: Yes, using the Kozeny‑Carman equation, but shape factor and packing density must also be considered for reasonable accuracy.

Source : Pneumatic conveying design guide, Mills
https://powderprocess.net/Tools_html/Data_Diagrams/Permeability_Aeration.html