In fluid dynamics, Sauter mean diameter (SMD, ''d''_{32} or ''D'', 2 is an average of particle size. It was originally developed by German scientist Josef Sauter in the late 1920s. 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.
SMD is typically defined in terms of the surface diameter, ''d''_{''s''}:
:$d\_s\; =\; \backslash sqrt$
and volume diameter, ''d''_{''v''}:
:$d\_v\; =\; \backslash left(\backslash frac\backslash right)^,$
where ''A''_{''p''} and ''V''_{''p''} are the surface area and volume of the particle, respectively. If ''d''_{''s''} and ''d''_{''v''} are measured directly by other means without knowledge of ''A''_{''p''} or ''V''_{''p''}, Sauter diameter for a given particle is
:$SD\; =\; D,2=\; d\_\; =\; \backslash frac.$
If the actual surface area, ''A''_{''p''} and volume, ''V''_{''p''} of the particle are known the equation simplifies further:
:$\backslash frac\; =\; \backslash frac\; =\; \backslash frac\; =\; \backslash frac$
:$d\_\; =\; 6\backslash frac.$
This is usually taken as the mean of several measurements, to obtain the Sauter __mean__ diameter, SMD:
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. :$D\_s\; =\; \backslash frac$ ::$f\_i$ is the scalar variable for the dispersed phase ::$d\_i$ is the discrete bubble size 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

{{DEFAULTSORT:Sauter Mean Diameter Category:Fluid dynamics

Applications

The SMD can be defined as the diameter of a drop having the same volume/surface area ratio as the entire spray. :$D\_s\; =\; \backslash frac$ ::$f\_i$ is the scalar variable for the dispersed phase ::$d\_i$ is the discrete bubble size 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

{{DEFAULTSORT:Sauter Mean Diameter Category:Fluid dynamics