Determination of particle size of powders by air elutriation methods

IS 4961: Scope - Key Formulas, Tables, and Specifications

1. Particle Diameter Correlation Factors (Clause 3.1, Table B-3)

• Use: Convert particle diameters between different measurement methods:
  • Sieve aperture
  • Projected diameter (area-based)
  • Stokes diameter (free-fall velocity-based)

2. True Free-Falling Diameter (Stokes Diameter) Table (Clause 1.1, Table A-1)

• Use: Adjust Stokes diameter for particle density to get true free-falling diameter in air.

3. Combined Sieving and Elutriation Results (Clauses 8.4.3 & 10.4.2)

IS 4961 - Key Definitions, Formulas & Tables

1. Definitions (Clause 2.0)

• Refer to IS 4124-1967 for glossary of powder-related terms.
• Key particle size types:
  • Sieve diameter: Nominal aperture size particle passes.
  • Projected diameter: Diameter of circle equal to particle's projected area.
  • Stokes diameter: Diameter of sphere with same free-fall velocity in fluid.

2. Stokes Diameter (Clause 1.1, Table A-1)

Use to convert sieve size to actual aerodynamic diameter.

3. Correlation Factors Between Particle Diameters (Clause 3.1, Table B-3)

4. Example of Combined Sieving & Elutriation (Clause 10.4.2, Table 8)

Basic Principle of Elutriation (IS 4961 - Clauses 3.1 & 8.2.3)

Elutriation separates particles by size using an upward gas flow in a vertical tube. The largest particle size elutriated corresponds to the velocity of the gas flow, calculated using Stoke's Law:

[ v = \frac{g d^2 (\rho_o - \rho)}{18 \eta} \times 10^{-8} ]

Where:

Table 1: Elutriation Periods (Clause 8.2.3.2)

Summary:

• Elutriation velocity is controlled to separate particles by size.
• Larger particles settle faster; smaller particles are carried upward.
• Use the table to select elutriation periods based on particle size and tube diameter.

flowchart

IS 4961: Preparation of Analysis Sample (Clause 4.1 Summary)

To prepare the analysis sample for testing:

1. Air-dry the sample thoroughly.
2. Break down large aggregates carefully to avoid contamination.
3. Sieve through a 75-micron IS sieve (IS:460-1962) and record the % weight retained.
4. Sub-divide the portion passing the sieve to get a representative analysis sample.
5. Determine particle density of the sample.
6. Dry the sample at 110°C (if permissible to avoid moisture).
7. Cool in a desiccator to prevent moisture absorption.
8. Disaggregate again if clumps form.
9. Weigh the powder container before adding the sample.
10. Transfer the prepared sample into the container for analysis.

Key Specifications:

Notes:

• Accurate weighing and representative sampling are critical for valid analysis.
• Follow the sequence strictly to maintain sample integrity.

flowchart TD
    A[Air-dry sample] --> B[Break down aggregates]
    B --> C[Sieve through 75-micron sieve]
    C --> D[Record % retained on sieve]
    D --> E[Sub-divide passing portion]
    E --> F[Determine particle density]
    F --> G[Dry at 110°C]
    G --> H[Cool in desiccator]
    H --> I[Disaggregate if needed]
    I --> J[Weigh powder container]
    J --> K[Transfer sample to container]

This ensures a standardized, reproducible analysis sample per IS 4961.

IS 4961: Apparatus Key Specifications & Tables

1. Apparatus Setup (Clause 8.2.1)

• Clean inner surfaces of elutriator tubes, cones, and sample container with grease-removing solvent (e.g., petroleum ether).
• Polish with soft cloth; do not lubricate screw threads.

2. Nozzle Sizes & Air Rates (Table 4, Clause 9.2.3)

3. Gonell Elutriator Dimensions

• Powder Container (Fig. 2):

  • Brass sheet 1.60 mm thick, polished, chromium plated.
  • 5 mm bore brass tube, airtight flat ground top face.

• Conical Adaptor (Fig. 3):

• Top Plate & Bell Jar (Fig. 4):

IS 4961: Elutriation Medium & Gas Supply - Key Points

1. Elutriation Medium (Clause 6.1, 6.1.1)

• Gas: Usually clean, dry air; other gases allowed if powders react with air.
• Pressure: Gauge pressure between 0.3 to 1.0 kg/cm².
• Drying: Remove water vapor using a drying train.
• Oil Removal: Filter oil mist through a 1-inch layer of superfine glass wool.

2. Air Supply & Flow Rate (Clause 9.1.1, 10.2.3)

• Air Supply: Compressed air dried via alumina dryer with indicating tube.
• Flow Measurement: Use capillary flowmeter or rotameter.
• Back-pressure: Measure at air nozzle; correct air rate accordingly.
• Elutriation Rate: Adjust air velocity to match the free-falling velocity (Vf) of the largest particles.

3. Key Formula (from Clause 3.2) for Free-Falling Velocity, Vf:

[ V_f = \sqrt{\frac{4gd(\rho_p - \rho_g)}{3C_d \rho_g}} ]

Where:

• (g) = acceleration due to gravity
• (d) = particle diameter
• (\rho_p) = particle density
• (\rho_g) = gas density
• (C_d) = drag coefficient (depends on Reynolds number)

4. Elutriator Tube Diameters (Clause 9.1.1a):

5. Process Flow (Simplified)

flowchart LR
    A[Compressed Air Supply] --> B[Drying Train (Alumina Dryer)]
    B --> C[Flow Meter (Rotameter/Capillary)]

IS 4961: Air Elutriation Methods - Key Formulas & Specifications

1. Elutriation Principle (Clause 3.1)

The largest particle size elutriated by gas velocity (v) is given by Stoke's Law:

[ v = \frac{g d^2 (\rho_p - \rho_g)}{18 \mu} \times 10^{-8} ]

Where:

2. Apparatus (Clause 9.1.1a)

• Four vertical elutriation tubes with diameter ratios: 1 : 2 : 4 : 8.
• Tubes used one at a time; connected at base to a U-tube with sample.
• Sample dispersed by air jet; particles carried upward and collected on thimble filters.
• Separate filters for size fractions if needed.

3. Air Supply Requirements (Clauses 6.1.1 & 9.1.1b)

• Clean, dry air at 0.3 to 1.0 kg/cm² gauge pressure.
• Water vapor removed by drying train; oil mist filtered through superfine glass wool.
• Air dried in alumina dryer with indicator.
• Flow metered by capillary flowmeter or rotameter.
• Back-pressure at nozzle measured and corrected.

4. Limitations

• Not suitable for particle fractionation 0 to 5 microns.
• Sample volume: 5 to 15 ml.

flowchart TD
    A[Compressed Air Supply] --> B[Drying Train]
    B --> C[Alumina Dryer]
    C --> D[Flow Meter (Capillary/Rotam

IS 4961: Procedure for Readily Dispersed Particles

Key Formulas & Tables

1. True Free-Falling Diameter (Stokes Diameter)

Used to correct particle size based on density for settling velocity in air.

(Refer to Clause 1.1 Table A-1 for full data)

2. Combined Results of Sieving and Elutriation

(Clause 9.4.2, Table 6)

Procedure Summary

• Step 1: Determine particle size distribution by sieving.
• Step 2: Use elutriation to separate finer particles by settling velocity.
• Step 3: Convert sieve sizes to true free-falling diameters using Stokes diameter table.
• Step 4: Combine results to get cumulative undersize percentages.

Important Notes

• Stokes diameter accounts for particle density and shape affecting settling.
• Cumulative weight undersize (%) is read off sizing curves combining sieve and elut

IS 4961: Procedure for Poorly Dispersed Particles (Clause 9.4.2 & related)

Key Points:

• Particle size distribution must be measured with particles freely dispersed to avoid aggregates.
• Use combined sieving and elutriation methods for size analysis.
• Powders in wet processes → use liquid sedimentation.
• Powders dispersed in air → use air elutriation.
• Pre-treatment: extraction with dehydrated liquid (e.g., alcohol) followed by highly volatile liquid (e.g., ether) helps dispersion.
• Mechanical dispersion: gentle rolling or brushing helps break aggregates without fracturing particles.

Combined Results Table (Typical Cumulative Weight % Undersize)

Notes:

• Read cumulative weight undersize from sizing curves.
• Ensure test conditions simulate actual use (Clause 0.3).
• Use gas/solid distributor systems in elutriators for better dispersion.
• Avoid fracturing particles during dispersion.

flowchart LR
    A[Powder Sample] --> B{Is powder wet or dry?}
    B -->|Wet| C[Liquid Sedimentation]
    B -->|Dry, air dispersed| D[Air Elutriation]
    D --> E[Pre-treatment: Alcohol → Ether]
    E --> F[Mechanical Dispersion]
    F --> G[Sieving + Elutriation]
    C --> G
    G --> H[Particle Size Distribution]

This procedure ensures accurate particle size distribution by proper dispersion and combined sieving-elutriation analysis per IS 4961.

Miniature Elutriator Method (IS 4961 - Clause 10)

• Purpose: Size powders difficult to disperse, particle size 10–75 microns, sample weight 0.1–0.5 g (typically 0.2 ml volume).
• Apparatus: Single small tube with a high-speed air jet (~30 m/s) for dispersing powder. Use fine jet for smaller particles, coarser for larger.

Key Specifications:

• Sample size: 0.1 to 0.5 g
• Particle size range: 10 to 75 microns
• Air jet velocity: ~30 m/s

Important Table Extract (Stokes Diameter vs Weight Reduction):

Notes

IS 4961: Calculation and Plotting of Results

Key Instructions (Clauses 8.3.1, 9.3.1, 10.3.1)

• Plotting: Use micron sizes (particle size) on the x-axis (abscissae).
• Use percentages undersize on the y-axis (ordinates).
• Draw a smooth sizing curve through the cumulative percentage points.
• From this curve, select cumulative percentages for the required series.

Important Table: Correlation Factors (Clause 3.1, Table B-3)

Usage Notes:

• Use these factors to convert particle diameters between different measurement methods if direct data is unavailable.
• This ensures consistency when plotting or comparing sizing curves.

Summary Diagram

graph LR
A[Particle Size Data] --> B[Convert Diameters (if needed)]
B --> C[Plot Micron Size (x-axis)]
D[Percent Undersize] --> C[Plot Percent Undersize (y-axis)]
C --> E[Draw Smooth Sizing Curve]
E --> F[Select Cumulative Percentages]

This method ensures accurate representation of particle size distribution per IS 4961.

IS 4961 — Reporting of Results: Key Formulas & Tables

1. Combined Results Reporting (Clauses 8.4.3, 9.4.2, 10.4.2)

• Results from different size determination methods (sieving, elutriation, Stokes law) are combined to give a unified particle size distribution.
• Tables 3, 6, and 8 present cumulative weight percentages undersize for various particle sizes.

2. Example: Table 3 — Combined Sieving & Elutriation Results

*Note: Stokes law sizing values are read off the sizing curve.

3. Key Formula: Stokes Law for Particle Size

[ d = \sqrt{\frac{18 \mu V}{g (\rho_p - \rho_f)}} ]

Where:

• (d) = particle diameter (m)
• (\mu) = dynamic viscosity of fluid (Pa·s)
• (V) = settling velocity (m/s)
• (g) = acceleration due to gravity (9.81 m/s²)
• (\rho_p), (\rho_f) = densities of particle and fluid (kg/m³)

Summary

• Report cumulative percentage undersize at standard sieve sizes.
• Use combined data from sieving, elutriation, and Stokes law for fine particles.
• Present results in tabular form as shown for clarity and consistency.

IS 4961: Free-Falling Diameters of Particles

Key Points from Clause A-1.1 & A-1.2

• Stokes' Law Limitation: Valid only for Reynolds number (Re) ≤ 0.2. For Re > 0.2, Stokes diameter underestimates particle size.
• True free-falling diameter must be used for accurate particle size, especially when correlating elutriation with sieve analysis.
• Values are tabulated for air at 27°C and 760 mm Hg.

Table: True Free-Falling Diameter (μm) vs Stokes Diameter (μm) for Various Particle Densities (g/cm³)

Formula Context (Stokes Law):

[ d_s = \sqrt{\frac{18 \mu v}{g (\rho_p - \rho_f)}} ]

• (d_s): Stokes diameter
• (\mu): Dynamic viscosity

IS 4961 - Correlation of Results from Different Methods (Clause 9.4.3, Appendix B)

Key Correlation Factors (Table B-3.1)

• Sieve diameter: Nominal aperture size particle passes through.
• Projected diameter: Diameter of a circle equal to particle's projected area.
• Stokes diameter: Diameter of sphere with same settling velocity in fluid.

Usage Notes (Clause 3.2)

• Apply factors cautiously if particles have extreme shapes (e.g., acicular, cleavage planes).
• Prefer to establish specific correlation factors by:
  • Overlapping size classes measured by both methods.
  • Testing similar samples by both methods.

Practical Applications (Clause 2.5)

• Converting size distributions (number ↔ weight) assuming volume ∝ (measured diameter)³.
• Estimating size-dependent powder properties.
• Combining size distributions from different measurement methods.

flowchart LR
    A[Sieve Diameter] -->|×1.40| B[Projected Diameter]
    A -->|×0.94| C[Stokes Diameter]
    B -->|×0.71| A
    B -->|×0.67| C
    C -->|×1.07| A
    C -->|×1.50| B

Summary: Use these correlation factors to convert particle size data between sieve, projected, and Stokes methods, ensuring careful validation for irregular particle shapes.