Sauter diameter

The Sauter mean diameter (SMD) is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. Originally developed by German scientist, J. Sauter in the late 1920s. The SMD is common measure in fluid dynamics as a way estimating the average particle size. Several methods have been devised to obtain a good estimate of the SMD. The SMD is typically defined in terms of the surface diameter, d_s:

:$d\_s\; =\; sqrt\{frac\{A\_p\}\{pi$

and volume diameter, d_v:

:$d\_v\; =\; left(frac\{6\; V\_p\}\{pi\}\; ight)^\{frac\{1\}\{3$

where A_p and V_p are the surface area and volume of the particle, respectively. d_s and d_v are usually measured directly by other means without knowledge of A_p or V_p. The Sauter diameter for a given particle is:

:$SD\; =\; D\; [3,2]\; =\; d\_\{32\}\; =\; frac\{d\_v^3\}\{d\_s^2\}$

If the actual surface area, A_p and volume, V_p of the particle are known the equation simplifies further:

:$frac\{V\_p\}\{A\_p\}\; =\; frac\{frac\{4\}\{3\}pi\; (d\_\{32\}/2)^3\}\{4pi\; (d\_\{32\}/2)^2\}\; =frac\{(d\_\{32\}/2)^3\}\{3\; (d\_\{32\}/2)^2\}\; =\; frac\{d\_\{32\{6\}$

:$d\_\{32\}\; =\; 6frac\{V\_p\}\{A\_p\}$

This is usually taken as the mean of several measurements, to obtain the Sauter mean diameter, SMD: The provides intrinsic data that helps determine the particle size for fluid problems.

Applications

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

:$D\_\{s\}\; =\; frac\{1\}\{sum\_\{i\}\; frac\{f\_\{i\{d\_\{i\}$

::$f\_\{i\}$ is the scalar variable for the dispersed phase

::$d\_\{i\}$ is the discrete bubble size

Sauter Mean Diameter (SMD) is also referred to as D [3,2] . It is especially important in calculations where the active surface area is important. Such areas include catalysis and applications in fuel combustion.

See also

*Sphericity