Sauter mean diameter

The Sauter diameter (SD, also denoted D[3,2] or d_{32}) for a given particle is defined as:

${\displaystyle SD={\frac {d_{v}^{3}}{d_{s}^{2}}}}$ 

where d_s is the so-called surface diameter and d_v is the volume diameter, defined as:

${\displaystyle d_{s}={\sqrt {\frac {A_{p}}{\pi }}}}$ 

${\displaystyle d_{v}=\left({\frac {6V_{p}}{\pi }}\right)^{1/3},}$ 

The quantities A_p and V_p are the ordinary surface area and volume of the particle, respectively.

The equation may be simplified further as:

${\displaystyle SD=6{\frac {V_{p}}{A_{p}}}.}$ 

This is usually taken as the mean of several measurements, to obtain the Sauter mean diameter (SMD):

${\displaystyle SMD=\sum _{i}^{n}SD_{i}/n}$ 

This provides intrinsic data that help determine the particle size for fluid problems.

The SMD can be defined as the diameter of a drop having the same volume/surface area ratio as the entire spray.

SMD is especially important in calculations where the active surface area is important. Such areas include catalysis and applications in fuel combustion.

• Sphericity