Expression of particle size distribution

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  • Professor Seki retired from Hokkaido University in March, 2024.
    

• Particle size distribution

  ➤Frequency distribution curve

  ➤Cumulative distribution curve

  
  

• Representative particle size and definition

  Stokes diameter
  

  Particle diameter calculated from Stokes formula

  Specific surface area diameter
  

  Particle diameter based on specific surface area

  Mode diameter
  

  Particle diameter with the largest frequency distribution

  Median diameter
  

  Particle diameter at which the residual (pass-through) ratio is 0.5

  
  

  
  

• Frequency distribution curve
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    アオコ　Blue-green algae

    酵母　Yeast

    珪藻土　Diatomaceous earth

• Cumulative distribution curve
  • Residual rate curve (R-curve) and passage rate curve (P-curve)
    

    
    

    フルイに「残留」する分画　Fraction "remaining" in the sieve

    フルイを「通過」する分画　Fraction "passing" through the sieve

  • Residual curves: R-curve
    

    
    

    Percentage of the total amount of particles larger than a certain particle size

    
    

    Passage curve: P-curve
    

    
    

    Percentage of the total amount of particles smaller than a certain particle size

    
    

    P = 1 - R

• Particle size distribution
  • ➤Frequency distribution curve

    ↓Integration　↑ Differentiation
    

    ➤Cumulative distribution curve

  • Frequency Distribution Curve
    

    
    

  • Residual rate distribution: R curve
    

    
    

  • Passage rate distribution: P curve (P = 1 - R)
    

    
    

• Rosin-Rammler Equation
  • ➤Empirical equation for the residual curve
    

    
    

    De ：Particle size with a residual of 0.37 (D/De = 1)

    n ：The larger this value, the more uniform the particle size.