In fluid dynamics, Sauter mean diameter (SMD) is an average measure of particle size. It was originally developed by German scientist Josef Sauter in the late 1920s.^[1][2] It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. Several methods have been devised to obtain a good estimate of the SMD.

Definition

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):

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

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

Applications

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.