Size Analysis

  • Sphericity \(\Phi_s\) \[\Phi_s = \frac{\text{surface area of a sphere having the same volume as the particle}}{\text{surface area of the particle}} = \frac{6V_p}{D_pS_p}\] where

    \(D_p\) = equivalent diameter or nominal diameter of particle
    \(S_p\) = surface area of one particle
    \(V_p\) = volume of one particle

    Equivalent diameter is defined as the diameter of sphere of equal volume as the particle.

    \(\Phi_s = 1\) corresponds to a sphere. Sphericities of all other particles must be less than one, because for a given volume a sphere has the minimum possible surface area.

  • Microscopic analysis: (1–100\(\mu\)m). This analysis permits measurement of the projected area of the particle and also enables an assessment to be made of its two dimensional shape. The optical microscope may be used to measure particle sizes down to 5\(\mu\)m. The electron microscope may be used for size analysis below 5\(\mu\)m.

  • Sedimentation/elutriation methods: (\(> 1\mu\)m). These methods depend on the fact that the terminal falling velocity of a particle in a fluid increases with size.

  • Permeability methods: (\(> 1\mu\)m). These methods depend on the fact that at low flow rates the flow through a packed bed is directly proportional to the pressure difference, the proportionality constant being proportional to the square of the specific surface area of the powder.

  • Sieving

    • Dry sieving using woven wire sieves is a simple, cheap method of size analysis suitable for particle sizes greater than 45 \(\mu\)m.

    • The mesh number of a sieve is normally defined as the number of apertures per square inch. Thus, higher the mesh number smaller is the aperture. 400 mesh Taylor standard sieve has a aperture of 37 \(\mu\)m; and that of 200 mesh is 74 \(\mu\)m.

    • The efficiency of screening is defined as the ratio of the weight of material which passes the screen to that which is capable of passing.

    • The effectiveness of a screen (often called the screen efficiency) is a measure of the success of a screen in closely separating materials 1 (oversize) and 2 (undersize). If the screen functioned properly, all of material 1 would be in the overflow and all of material 2 would be in the underflow.

    • Material balance: \[\begin{aligned} F &= D + B \\ Fx_{1F} &= Dx_{1D} + Bx_{1B} \end{aligned}\] where \(F=\) feed; \(D=\) overflow; and, \(B=\) underflow.

    • Effectiveness:

      • Based on oversize: \[E_1 = \frac{Dx_{1D}}{Fx_{1F}}\]

      • Based on undersize: \[E_2 = \frac{Bx_{2B}}{Fx_{2F}} = \frac{B(1-x_{1B})}{F(1-x_{1F})}\]

      • Overall: \[E = E_1\cdot E_2\]

screen effectiveness   sieve analysis   sphericity