Sauter mean diameter

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'':

:$d_s = \sqrt$

and volume diameter, ''d''_''v'':

:$d_v = \left(\frac\right)^,$

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_ = \frac.

If the actual surface area, ''A''_''p'' and volume, ''V''_''p'' of the particle are known the equation simplifies further:

:$\frac = \frac = \frac = \frac$

:$d_ = 6\frac.$

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.

:$D_s = \frac$
::$f_i$ 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
Fluid dynamics