Sauterdiameter

The Sauter diameter, or Sauter mean diameter, is a size descriptor used to characterize particle or droplet size distributions in aerosols, sprays, and suspensions. It is denoted as D32 or d32 and is defined as the diameter of a sphere that has the same volume-to-surface area ratio as the dispersed particles.

For a discrete distribution with particle diameters D_i and counts n_i, the Sauter diameter is calculated as D32 = sum_i (n_i D_i^3) / sum_i (n_i D_i^2). If the distribution is represented by mass or volume fractions w_i, the Sauter diameter is D32 = sum_i (w_i D_i^3) / sum_i (w_i D_i^2). This weighting makes the Sauter diameter more sensitive to larger particles than the arithmetic mean.

The Sauter diameter is related to the overall surface-area-to-volume characteristics of the dispersion. Since the volume-to-surface ratio of a sphere is proportional to D/6, the distribution’s total volume-to-surface ratio equals D32/6. Consequently, D32 is particularly relevant for processes where surface area controls rate phenomena, such as evaporation, heat transfer, or chemical reactions.

Measurement and use: D32 can be estimated from size distributions obtained by methods such as laser diffraction, optical particle counting, or mobility analysis, by applying the above weighting. It is widely used in spray drying, atomization, combustion modeling, aerosol science, pharmaceutical formulations, and filtration design.

Limitations: As a single-number descriptor, D32 cannot capture all aspects of a polydisperse or non-spherical distribution. Different distributions can yield the same D32, and interpretations may be limited for highly irregular particles.