Mean Particle Size

• Mean Particle Size affects dissolution, stability, flow, and bioavailability of pharmaceutical products.
• Mean Particle Size indicates the average dimension of particles in a sample for uniform analysis.
• Because particle populations contain a range of sizes, different types of mean particle sizes are used:

1. Arithmetic Mean Diameter(D₁)

$D_1 = \frac{\sum_i n_i D_i}{\sum_i n_i}$

• Where:
  • $D_i = \text{size of particles in each group}$
  • $n_i = \text{number of particles in that group}$

2. Surface Area Mean Diameter (Sauter Mean, D₃,₂)

$\[D_{3,2} = \frac{\sum_{i} n_i D_i^3}{\sum_{i} n_i D_i^2}\]$

• Emphasizes surface area, relevant for dissolution and reaction rates.

3. Volume Mean Diameter (D₄,₃)

$D_{4,3} = \frac{\sum n_i D_i^{4}}{\sum n_i D_i^{3}}$

• Sensitive to larger particles, often used in laser diffraction.
• Each type of mean gives different insight depending on whether surface, number, or volume is the focus.

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