Reference ID: MET-681A | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Sieve analysis is the oldest and still most widely used method for determining the particle size distribution (PSD) of granular solids. In process engineering it underpins the design and troubleshooting of any unit operation in which size matters: comminution circuits, fluidised-bed reactors, pneumatic conveying lines, crystallisers, cyclones, filters, hoppers and silos. The test separates a representative sample into discrete size fractions by mechanical shaking on a stack of woven-wire sieves. The resulting retained mass on each sieve is converted into a cumulative percentage, from which key descriptors such as d10, d50, d90 or the uniformity coefficient Cu = d60/d10 are interpolated. These descriptors feed directly to:
mass-balancing and population-balance models,
selection of mill type and closing screen,
prediction of pressure drop and heat/mass transfer coefficients,
assessment of flowability, segregation tendency and storage stability.
Methodology & Formulas
Total sample mass
The sum of all retained masses must equal the original test portion:
\[ M_{\text{tot}} = \sum_{i} m_{i} \]
where mi is the mass retained on sieve i (including the pan).
Cumulative retained mass
Starting with the coarsest sieve, add the retained masses successively:
\[ M_{i} = M_{i-1} + m_{i} \]
with M0 = 0 by definition.
Cumulative percentage retained
Convert each cumulative mass to a percentage of the total:
\[ C_{i} = \frac{M_{i}}{M_{\text{tot}}} \times 100\ \% \]
Validity criteria
Check
ISO 3310-1 threshold
Consequence if violated
Minimum total mass
\( M_{\text{tot}} \geq 50\ \text{g} \)
Excessive weighing error; repeat test with larger split.
Fine end poorly defined; interpolation of dx unreliable.
Interpolation of characteristic sizes
Plot Ci versus sieve opening di on a semi-log grid. Any percentile dx (where x is the percentage passing) is obtained by linear interpolation in log-space:
\[ \log d_{x} = \log d_{\text{upper}} - \frac{x - P_{\text{upper}}}{P_{\text{upper}} - P_{\text{lower}}} \left( \log d_{\text{upper}} - \log d_{\text{lower}} \right) \]
with P the cumulative percentage passing (= 100 − C).
The required mass depends on the nominal top sieve opening and the particle density. A quick field rule is:
For aggregates (2.36 – 37.5 mm) use 500 g – 3 kg
For sands (0.075 – 2.36 mm) use 100 – 300 g
Never drop below the value calculated by (0.5 × D³ × ρ) where D is the largest sieve opening in cm and ρ is particle density in g cm⁻³; this keeps weighing errors < 0.1 %.
Ten minutes is usually sufficient for dry sieving; wet sieving may need 5 min plus rinsing. Over-shaking causes particle degradation and skews the distribution. Verify endpoint by:
Weighing the retained material on the critical sieve at 1-min intervals
Stopping when the change is < 1 % of the previous mass
Sieve results are based on the second smallest dimension (the sieve aperture), whereas laser diffraction reports a volume-equivalent sphere diameter. For flaky or elongated particles the laser D50 is typically 10 – 30 % finer. Calibrate by running both methods on the same lot and applying a shape correction factor.
Start with the ASTM or ISO root-2 (1.41) progression to avoid blind spots. Example stack for 0 – 5 mm powder:
5.00 mm
3.35 mm
2.36 mm
1.70 mm
1.18 mm
850 µm
600 µm
425 µm
300 µm
212 µm
150 µm
Pan
After the first run, insert intermediate sieves where > 15 % is retained to improve resolution.
Inspect each sieve before use:
Reject frames when any aperture exceeds the nominal opening by > 5 %
Log serial numbers and inspection dates in your LIMS
Rotate a certified glass bead reference sample through the stack every 40 hours of use; if > 2 % of beads are retained on their target sieve, retire the sieve
Worked Example: Sieve Analysis for a 200 g Silica Feed to a Ball Mill
A process engineer needs to characterise the feed to a ball-mill circuit. A 200 g representative sample is withdrawn from the feed conveyor, dried at 105 °C for 2 h, and subjected to a standard ASTM C136 dry-sieve test. The retained masses on each sieve are recorded and must be converted to a cumulative particle-size distribution.
Mass retained on 40 mesh (0.425 mm): 8.0 g
Mass retained on 60 mesh (0.250 mm): 42.0 g
Mass retained on 80 mesh (0.180 mm): 78.0 g
Mass retained on 120 mesh (0.125 mm): 52.0 g
Mass in pan (<0.125 mm): 20.0 g
Total sample mass, Mtot: 200.0 g
Calculate the cumulative mass retained, Mi, on each sieve starting with the coarsest:
M40 = 8.0 g
M60 = 8.0 g + 42.0 g = 50.0 g
M80 = 50.0 g + 78.0 g = 128.0 g
M120 = 128.0 g + 52.0 g = 180.0 g
Mpan = 180.0 g + 20.0 g = 200.0 g
Report the cumulative percentage passing (Pi) if required:
Pi = 100 − Ci P40 = 96 %, P60 = 75 %, P80 = 36 %, P120 = 10 %, Ppan = 0 %
Final Answer: The sieve analysis yields the following cumulative percentage retained: 4 % on 0.425 mm, 25 % on 0.250 mm, 64 % on 0.180 mm, 90 % on 0.125 mm, and 100 % at pan size. All values are dimensionless percentages based on the 200 g total sample.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
