Liquid sedimentation methods for determination of particle size of powders

Scope of IS 5282: Particle Size and Dispersion of Powders

Key Specifications:

• Particle Size Limits (Clause 1.00):
  Particle size limits depend on material density (g/cc). For viscosity = 0.01 poise, fluid density = 1.00 g/cc, Reynolds number = 0.2 (upper limit).

• Conversion Factors between Particle Diameter Types (Clause 3.1):

• Liquid and Dispersing Agents for Materials (Clause 5.2, Appendix B):
  Examples:
  • Alumina: Water, water with calgon (0.1%), dilute HCl (pH 3)
  • Aluminium powder (sp.gr. 2.5): Isopropanol, chloroform
  • Calcium carbonate: Water, xylene

Summary:

• Particle size limits vary with density and fluid properties.
• Use conversion factors for comparing sieve, projected, and Stokes diameters.
• Select appropriate dispersing agents per material type for accurate testing.

flowchart LR
    A[Material Density] --> B[Particle Size Limits]
    B --> C[Upper & Lower Limits]
    A --> D[Select Dispersing Agent]
    E[Particle Diameter Types] --> F[Conversion Factors]
    F --> G[Sieve, Projected, Stokes]

This encapsulates the scope related to particle size, measurement

IS 5282: Terms and Definitions - Key Specifications

1. Reference Standard

   • Terms and definitions as per IS 4124-1967 apply.

2. Particle Size Limits (Clause 1.00 & 5.2)
   Particle size limits depend on material density (g/cc), fluid viscosity (0.01 poise), fluid density (1.00 g/cc), and Reynolds number (0.2).

3. Liquid & Dispersing Agents (Appendix B)
   Common agents for powders:

4. Calculation Notes (Clause 7.9)
   • Follow procedure in Clause 6.5 for result calculations.

Key Formula for Particle Size Limits

Using Reynolds number (Re = 0.2), fluid viscosity (η), and densities (ρ):

[ d \propto \sqrt{\frac{18 \eta v}{(\rho_s - \rho_f) g}} ]

Where:

• (d) = particle diameter
• (\eta) = fluid viscosity
• (\rho_s), (\rho_f) = densities of solid and fluid
• (g) = acceleration due to gravity
• (v) = settling velocity (related to Re)

flowchart TD
    A[Material Density] --> B[Particle Size Limits]
    B --> C[Upper Limit]
    B --> D[

IS 5282 covers Liquid Sedimentation Methods for particle size determination but does not classify these methods explicitly nor provide detailed formulas or tables for classification.

Key points from IS 5282 context:

• It discusses liquid sedimentation methods broadly.
• Mentions an additional liquid column method with sedimentation accumulation, but this is not covered in the standard.
• No specific clause on classification or detailed formulas.

General Engineering Insight on Liquid Sedimentation Methods:

Liquid sedimentation methods classify based on particle settling behavior under gravity or centrifugation, commonly:

• Stokes' Law governs settling velocity ( v ):

  [ v = \frac{d^2 (\rho_p - \rho_f) g}{18 \mu} ]

  where:

  • ( d ) = particle diameter,
  • ( \rho_p ), ( \rho_f ) = densities of particle and fluid,
  • ( g ) = acceleration due to gravity,
  • ( \mu ) = fluid viscosity.

• Classification often includes:

  • Gravity sedimentation
  • Centrifugal sedimentation
  • Liquid column sedimentation (less common)

Summary Table of Methods

If you need formulas or procedure details for a specific sedimentation method, please specify!

Suspension and Dispersion (IS 5282 Key Points)

1. Suspension Preparation (Clause 4.1)

• Prepare suspensions with ~2% volume powder in suitable media.
• Good dispersions settle slowly, with no sharp interface between clear and turbid layers.
• Sediment in good dispersion: rigid, minimum volume.
• Flocculated suspension: large, mobile sediment, visible wall deposits on tilting.

2. Selection of Suspending Medium (Clause 4.1, Appendix B)

• Reynolds number (Re) ≤ 0.2 to limit error within 5%.
• Use dispersing agents to avoid flocculation (trial and error).
• Examples of media & agents:

(See Appendix B for full list)

3. Reynolds Number Formula (Clause 3.3.1)

[ Re = \frac{u d_p}{\nu} \times 10^{-1} \quad \text{where} \quad u = \frac{h}{t} ]

• (u): settling velocity (height/time)
• (d_p): particle diameter
• (\nu): kinematic viscosity of fluid

Re ≤ 0.2 ensures laminar flow and accurate sedimentation.

flowchart LR
    A[Powder Sample] --> B[Prepare Suspension (~2% vol)]
    B --> C[Add Dispersing Agent]
    C --> D[Stir Thoroughly]
    D --> E[Observe Settling Behavior]
    E -->|Good Dispersion| F[Rigid Sediment, Slow Settling]
    E -->|Flocculated| G[Mobile Sediment, Wall Deposit]

Summary:

• Use suitable liquid + dispersing agent (Appendix B).
• Ensure

IS 5282: Preparation of Sample - Key Points

1. Sample Concentration

• Use ≤ 1% by volume concentration of powder in suspension (Clauses 7.5, 8.4).

2. Sample Weight and Volume

• Weigh sample accurately to 0.0001 g.
• Prepare 300 ml suspension volume in chosen sedimentation liquid (Clause 8.4).

3. Sedimentation Liquid Selection (Appendix B)

Choose liquid based on material type for dispersion and sedimentation:

(Refer full Appendix B for detailed list)

4. Procedure Summary

• Select sedimentation liquid per material.
• Accurately weigh sample.
• Mix to prepare 300 ml suspension.
• Ensure concentration ≤1% by volume.

Diagram: Sample Preparation Flow

flowchart TD
    A[Select Material] --> B[Choose Sedimentation Liquid (Appendix B)]
    B --> C[Weigh Sample (0.0001 g accuracy)]
    C --> D[Prepare 300 ml Suspension]
    D --> E[Adjust Concentration ≤ 1% by volume]
    E --> F[Ready for Analysis]

This ensures uniform dispersion and accurate particle size analysis per IS 5282.

IS 5282: Apparatus and Calibration Key Points

Apparatus (Clauses 6.2, 6.2.3, 7.2)

• Sedimentation Vessel (Figs. 1 & 2): Main apparatus for sedimentation test.
• Ancillary Apparatus:
  • Transparent constant temperature bath (≥15 L), immersing sedimentation vessel up to graduation mark.
  • Balance with sensitivity ≤ 0.1 mg.
  • Drying oven with controlled temperature to evaporate suspending liquid without altering material.
  • Wide-mouthed weighing bottle (≥ 20 ml capacity).

Calibration of Pipette (Clause 6.3.1)

1. Clean and dry the sedimentation vessel and pipette.
2. Fill sedimentation vessel with water (~20 cm level).
3. Draw water into pipette bulb to graduation mark using rubber tube.
4. Drain water into pre-weighed weighing bottle by opening tap.
5. Blow remaining water from bulb and discharge tube into bottle.
6. Calculate volume ( V ) of pipette from weight of water collected:

[ V = \frac{W}{\rho} ]

Where:

• ( W ) = weight of water (g)
• ( \rho ) = density of water at test temperature (g/ml)

Summary Table: Ancillary Apparatus

flowchart LR
  A[Start: Clean apparatus] --> B[Fill sedimentation vessel with water]
  B --> C[Draw water into pipette bulb to graduation]
  C --> D[Drain water into weighing bottle]
  D --> E[Blow remaining water into bottle]
  E --> F[Weigh bottle to find water weight]
  F --> G[Calculate pipette volume: V = W/ρ]

This ensures precise volume calibration critical for sedimentation tests as per IS 5282.

IS 5282: Incremental Sedimentation Method - Key Points

Procedure Summary (Clause 7.7)

• Clean sedimentation vessel; close outlet with pinch cock.
• Pour suspension into vessel; rinse beaker with sedimentation liquid to transfer all particles.
• Fill up to 18 cm mark with sedimentation liquid.
• Optional: Use pressure pump to bubble air for 3 minutes agitation.
• Stop air; start stopwatch.
• Withdraw samples at predetermined depths using pipette.
• Determine particle size distribution based on sedimentation velocity.

Key Formula (Clause 1.946)

Corrected weight of particles (Wre):

[ W_{re} = W_r \times \rho_l \times \frac{h_0}{h_0 - h_x} ]

Where:

• (W_r) = observed weight of particles
• (\rho_l) = density of liquid
• (h_0) = initial suspension height (e.g., 18 cm)
• (h_x) = sampling depth from free surface

Example:
[ W_{re} = 0.0037 \times \frac{18}{(18 - 7.13)} = 0.0065 \text{ g} ]

Notes

• Incremental method measures concentration at a specific depth.
• Particle size corresponds to settling velocity at sampling time.
• Clay content and particle size distribution can be correlated with observed weights.

Summary Table: Parameters for Sampling

flowchart TD
    A[Prepare sedimentation vessel] --> B[Pour suspension + rinse beaker]
    B --> C[Fill to 18 cm mark]
    C --> D{Agitate by air bubbling?}
    D -- Yes --> E[Bubble air for 3 min]
    D -- No --> F[Start stopwatch immediately]
    E --> F

Centrifugal Sedimentation Method (IS 5282)

Principle (Clause 8.1)

• Used for particles < 2 microns; gravity sedimentation is slow and affected by convection/diffusion.
• Centrifugal acceleration increases settling velocity.
• Modified Stokes' equation under centrifugal force:

[ d_e = \frac{18 \eta \ln(R_2/R_1)}{(\rho_p - \rho) \omega^2 t} ]

Where:

• (d_e) = equivalent particle diameter (microns)
• (\eta) = viscosity of fluid
• (\rho_p, \rho) = densities of particle and fluid
• (\omega) = angular velocity (rad/s)
• (R_1, R_2) = radial distances from axis of rotation
• (t) = centrifugation time

Procedure

• Centrifuge suspension for time (t) at angular velocity (\omega).
• Separate sediment and suspension; dry and weigh both.
• Plot % sedimented vs. particle size.
• Draw tangents on curve to get size distribution.

Sedimentation Vessel (Clause 7.2.1)

• Diameter: ~4.8 cm
• Length: ~28 cm with graduated scale 0–18 cm (zero at sampling level)
• Outlet at bottom for draining/air vent
• Ground glass stopper with air vent at top

flowchart TD
    A[Prepare Suspension] --> B[Centrifuge at ω for time t]
    B --> C[Separate Sediment & Suspension]
    C --> D[Dry & Weigh Both Fractions]
    D --> E[Plot % Sedimented vs Particle Size]
    E --> F[Draw Tangents for Size Distribution]

This method provides rapid, accurate sizing of fine particles using centrifugal acceleration and sedimentation principles.

IS 5282: Comparison with Other Particle Size Methods

Key Points from Clause 9.1 & Appendix F

• No single method covers full size range (1,000 to 1 micron).
  Combine methods like sieving, sedimentation, elutriation, microscope for full distribution.

• Correlation factors convert particle diameters between methods (Appendix F, Table F-3):

• Interpretation:
  A particle just passing a 75 µm sieve corresponds to:
  • 106 µm projected diameter (microscope)
  • 70.5 µm Stokes diameter (sedimentation)

Important Formula (Sedimentation Weight Correction)

[ W_{rc} = W_r \rho_l (h_o - h_x) ]

• (W_r) = observed weight
• (\rho_l) = liquid density
• (h_o) = initial column height (18 cm)
• (h_x) = depth at which particles settle

Tangential Intercept Method (Sedimentation Curve)

• Plot % sedimented material vs. (1/d^2) (where (d) = particle diameter)
• Tangents to curve intercept vertical axis → % undersize for corresponding diameter

Summary

• Use combined methods for wide size ranges.
• Convert sizes using correlation factors from Table F-3.
• Apply sedimentation corrections and tangential intercept for accurate size distribution.

flowchart LR
    A[Sample with wide size range] --> B[Sieving (large particles)]
    A --> C[Sedimentation (medium particles)]
    A --> D[Microscope (small particles)]
    B --> E[Convert sizes using correlation factors]
    C --> E
    D --> E
    E --> F[Combined particle size distribution]

IS 5282: Upper and Lower Particle Size Limits for Different Densities

Key Points from Clause 1.00 & Appendix A (Clause 3.3.1)

• Viscosity (η) = 0.01 poise
• Fluid density (ρ_f) = 1.00 g/cc
• Reynolds Number (Re) upper limit = 0.2 (to limit error ≤ 5%)
• Free-fall velocity ( v = \frac{h}{t} )

Reynolds Number Formula:

[ Re = \frac{u d \rho_f}{\eta} \times 10^{-1} ]

• ( u ) = velocity of particle
• ( d ) = particle diameter (microns)
• ( \rho_f ) = fluid density
• ( \eta ) = fluid viscosity

Particle Size Limits Table (Diameter in microns)

• Lower limit scales with density similarly to upper limit.
• For density 2 g/cc, lower limit = 3.0 microns.

Notes:

• Lower limit: particle size unaffected by convection or diffusion.
• Upper limit: size at which Re ≤ 0.2.
• Particle size measurement may require multiple methods (Clause 9.1).

Summary Diagram: Particle Size Limits vs Density

graph LR
A[Density 2 g/cc] -->|Upper Limit 72 μm| UL2
A -->|Lower Limit 3 μm| LL2
B[Density 4 g/cc] -->|Upper Limit 50 μm| UL4
B -->|Lower Limit 2.1 μm| LL4
C[Density 8 g/cc] -->|Upper Limit 37 μm| UL8
C -->|Lower Limit 1.6 μm| LL8

For detailed dispersion media and liquid agents, refer to Clause 5.2 Appendix B.

IS 5282: Tests for Dispersion - Key Points & Formulas

1. Quantitative Test for Dispersion (Clause 5.1)

• Principle: Reducing powder concentration by half should not significantly increase the proportion of undersize particles.
• Initial concentration limit: ≤ 2% by volume.

2. Test Methods (Appendix C, Clause 4.1)

At least two tests must be done to confirm dispersion efficiency:

• a) Rheological Behaviour:

  • Prepare ~2% volume suspension.
  • Good dispersion → slower settling, no sharp interface, rigid sediment.
  • Flocculated suspension → rapid settling, large sediment volume, sediment moves on tilting.

• b) Microscopical Examination:

  • Visual check for agglomerates or uniform particle distribution.

• c) Qualitative Sedimentation:

  • Observation of settling behavior and sediment appearance.

• d) Quantitative Sedimentation:

  • Measure sediment volume or height over time for dispersion quality.

3. Particle Size Distribution Test (Appendix D, Clause 7.12)

• Liquid: Water (450 ml)
• Dispersing agent: Sodium tartrate (0.1%)
• Powder weight: 0.9 g
• Pipette volume: 10 ml

4. Dispersing Agents (Clause 1.0)

• Sodium hexametaphosphate: 0.5 - 1.0 g/L
• Sodium pyrophosphate: 0.005 mol/L
• Water + alcohol (1:1)
• Methyl alcohol + HCl (N/100)

Summary Table: Dispersion Test Criteria

IS 5282: Worked Example & Key Data on Particle Size Distribution

1. Particle Size Distribution (Clause 8.3 & Appendix E)

• Use combined methods (sieving, sedimentation, elutriation, microscope) to cover full size range (1000 µm to 1 µm).
• Determine smallest particle size by pipette or sedimentation methods.
• Example in Appendix E illustrates stepwise calculation of weight fractions and particle sizes.

2. Correlation Between Methods (Clause 9.1 & Appendix F)

• Different methods yield different particle diameters.
• Use correlation factors (Appendix F) to convert sizes between methods for consistency.

3. Particle Size Limits for Different Densities (Appendix A & Table)

• Calculations assume fluid viscosity = 0.01 poise, density = 1 g/cc, Reynolds number = 0.2.

4. Key Formula for Corrected Weight (Clause 1.946)

[ W_{re} = W_r \times \rho_l \times \frac{(h_0 - h_x)}{(h_0 - h_l)} ]

Where:

• (W_r) = observed weight
• (\rho_l) = density of liquid
• (h_0, h_x, h_l) = depths in sedimentation column

Summary Diagram: Particle Size Determination Methods & Range

flowchart LR
    A[Sample] --> B[Sieving (>50 µm)]
    A --> C[Sedimentation (1-50 µm)]
    A --> D[Microscope (<10 µm)]
    B --> E[Size Distribution]
    C --> E
    D --> E
    E --> F[Combined Particle Size Distribution]

Use these guidelines and tables for accurate particle size distribution analysis per IS 5282

IS 5282: Correlation Factors for Different Particle Size Methods

Key Correlation Factors (Clause 3.1, Table F-3)

• These factors convert particle diameters between:
  • Sieve diameter: Nominal aperture size.
  • Projected diameter: Diameter of circle equal to particle's projected area.
  • Stokes diameter: Diameter of sphere with same settling velocity.

Important Notes (Clause 3.2)

• Use factors cautiously if particles have extreme shapes (e.g., acicular or with cleavage planes).
• Prefer to establish specific correlation factors for your powder by:
  • Overlapping size classes measured by both methods.
  • Testing a similar sample by both methods.

Practical Example

• Particles passing a 75 μm sieve correspond approximately to:
  • 106 μm projected diameter
  • 70.5 μm Stokes diameter

Summary Diagram

graph LR
A[Sieve Diameter] -- x1.40 --> B[Projected Diameter]
A -- x0.94 --> C[Stokes Diameter]
B -- x0.71 --> A
B -- x0.67 --> C
C -- x1.07 --> A
C -- x1.50 --> B

Use these correlation factors to convert particle sizes between methods when direct measurement is unavailable or to combine size distributions from different techniques.