Sauter mean diameter

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):

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

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.

See also

• Sphericity

References

1. Sauter, Josef (1926). Die Grössenbestimmung der in Gemischnebeln von Verbrennungskraftmaschinen vorhandenen Brennstoffteilchen [The determination of the size of the fuel particles present in the mixture mist of internal combustion engines] (in German). VDI publishing house. ISSN 0042-174X. OCLC 1070480151.
2. Wang, D.; Fan, L.-S. (2013). "Particle characterization and behavior relevant to fluidized bed combustion and gasification systems". In Scala, Fabrizio (ed.). Fluidized Bed Technologies for Near-Zero Emission Combustion and Gasification. Elsevier. pp. 42–76 [p. 45]. doi:10.1533/9780857098801.1.42. ISBN 9780857095411.