Particle Size Distribution (PSD) & Mesh Conversion – Theory and Testing Methods
A material’s particle-size distribution (PSD) tells you how much of the sample lies at each size, from its coarsest fragments to its finest dust. Because different industries quote size in different ways (microns, “mesh,” percent retained, D-values, etc.), it is essential to understand both the test method and the statistical descriptors used.
1. Why PSD Matters
Performance. Finer talc improves opacity in paint, but coarser grades reinforce plastic better.
Flow & packing. A broad PSD fills voids and lowers bulk density; a narrow PSD gives free-flowing powders.
Quality control. Consistent PSD = reproducible end-product properties.
2. Measurement Techniques
| Method | Typical size range (μm) | What it actually measures | Key pros | Key limitations |
|---|---|---|---|---|
| Sieving (dry or wet) | ~20 μm to 100 mm | Mass retained on woven wire screens (ASTM E11) | Simple, direct “mesh” values; cheap QC | Slow below 75 μm; assumes near-spherical, non-agglomerated particles |
| Air-jet sieve | 20 – 200 μm | Same principle, but an air jet disperses fines | Faster, better de-agglomeration | Still unusable for sub-20 μm |
| Laser diffraction (e.g. Malvern Mastersizer, CILAS, Microtrac) | 0.02 – 3 000 μm | Scattering angle of a laser beam → equivalent spherical diameter via Mie or Fraunhofer theory | Wide dynamic range, rapid, full cumulative curve | Needs correct refractive index; treats particles as spheres |
| Dynamic Light Scattering (DLS) | 0.003 – 1 μm (colloids) | Brownian motion → hydrodynamic diameter | Nanoparticles, liquids | Generates intensity-weighted distribution; not useful for ≥1 μm |
| Sedimentation (Stokes, Andreasen pipette, ASTM C958) | 0.5 – 100 μm | Settling velocity in liquid column | Good for platelike talcs that misbehave in laser diffraction | Slow; temperature & density sensitive |
| Electrical pulse/Coulter counter | 0.4 – 1 200 μm (discrete particles) | Change in electrolyte resistance as each particle passes an aperture | True number distribution; no optical assumptions | Requires complete dispersion in electrolyte |
| Image analysis (optical or SEM) | 1 μm – several mm | Real projected area or Feret diameters | Shape metrics (aspect, roundness) | Small sample ⇢ statistical noise; tedious >200 μm² |
Rule of thumb: use sieving for products sold in mesh terms (e.g., 325-mesh talc). Use laser diffraction when customers ask for D10/D50/D90/D97 or a full PSD curve.
3. Statistical Descriptors
| Symbol | Meaning | Interpretation |
|---|---|---|
| D₁₀, D₅₀, D₉₀ … | Diameter below which 10 %, 50 %, 90 % of the sample lies (by mass) | Median (D₅₀) splits the sample in half; span = (D₉₀ – D₁₀)/D₅₀ gauges width |
| D₉₇ | 97 % passing | Useful “top-cut” spec; stricter than a single-mesh retain |
| % Retained on n-mesh | Mass that does not pass the sieve opening (e.g., “Ret. on 500 mesh 0.3 %”) | 0.3 % of sample is coarser than 25 µm (500-mesh) |
| % Passing (or “through”) | Complement of retention (= 100 % – %Ret.) | Often logged cumulatively |
| PSD span | (D90−D10)/D50(D_{90} – D_{10})/D_{50} | Low span ≈ narrow distribution |
4. Cumulative vs. Differential Curves
Cumulative curve, Q(x): fraction ≤ x. Sieve data and D-values live here.
Differential curve, q(x): fraction between sizes. Laser-diffraction software often displays this histogram for troubleshooting fines vs coarses.
5. Mathematical Fits
Real PSDs often follow empirical laws that help interpolate or compare batches.
Log-normal distribution
Appropriate for grinding products whose breakage is multiplicative.
Rosin–Rammler–Sperling–Bennett (RRSB)
A log-log plot yields slope n (distribution breadth) and scale X₀ (the size where 63.2 % passes).
Power-law tail for comminution fines
Useful for estimating the weight fraction below a micron when direct measurement is noisy.
6. “Mesh” versus Microns (Why Conversion Is Never Exact)
Mesh size is the count of openings per inch in a US standard sieve. Wire diameter reduces the free opening, so a “325-mesh” sieve has an average aperture of 44 µm, not 78 µm.
Conversion tables (linked) assume ASTM E11 nominal openings; ISO 565 differs slightly.
Shape factor: A flaky talc platelet may fit through a 44 µm square even if its longest axis is 100 µm. Hence a PSD reported as “≤ 325 mesh” is not the same as D₉₇ ≤ 44 µm.
Rule: quote mesh specs only when tested by sieve; quote D-values only when tested by laser/sedimentation. Never “convert” one customer’s laser spec to another customer’s mesh spec without new lab data.
7. Practical Tips for Reliable PSD Data
Dispersion matters. Ultrasonics with 0.1 % sodium pyrophosphate break talc agglomerates without delamination.
Refractive index entry: For laser diffraction, use n = 1.59 + 0.0i for pure talc; incorrect n skews sub-5 µm volume.
Replicates: At least three runs; report average ± 1 σ for D-values.
Blend control: Use real-time online laser probes (e.g., Malvern Insitec) on mills to keep D₉₇ drift < 2 µm.
Specify the full trio: “D₅₀ = 12 µm, D₉₀ = 38 µm, D₉₇ = 45 µm (Malvern Mastersizer 3000, dry, 3 bar, RI 1.59/1.0)” leaves no ambiguity.
8. Key Takeaways
Choose the method that matches both material and customer spec: sieve for mesh, laser for D-values.
D-values (D₁₀/D₅₀/D₉₇) describe cumulative passing; retention describes cumulative failing.
Mathematical models (log-normal, RRSB) help compare batches or extrapolate beyond test range.
Mesh conversion is a convenience, not an equivalence—always validate with the correct test.
Link to the Mesh ↔ Micron Conversion Table → [see next page] for quick numeric look-ups.