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In fluid dynamics, Sauter mean diameter (SMD, d₃₂ or D[3, 2]) is an average 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.

SMD is typically defined in terms of the surface diameter, d_s:

${\displaystyle d_s=\sqrt{\frac{A_p}{\pi }}}$

and volume diameter, d_v:

${\displaystyle d_v={\left(\frac{6V_p}{\pi }\right)}^{1/3},}$

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

${\displaystyle SD=D[3,2]=d_{32}=\frac{d_v^3}{d_s^2}.}$

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

${\displaystyle \frac{V_p}{A_p}=\frac{\frac{4}{3}\pi (d_v/2{)}^3}{4\pi (d_s/2{)}^2}=\frac{(d_v/2{)}^3}{3(d_s/2{)}^2}=\frac{d_{32}}{6}}$

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${\displaystyle d_{32}=6\frac{V_p}{A_p}.}$

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.

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Applications[edit]

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

${\displaystyle D_s=\frac{1}{\sum _i\frac{f_i}{d_i}}}$

${\displaystyle f_i}$ is the scalar variable for the dispersed phase

${\displaystyle d_i}$ 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[edit]

References[edit]

1. ^Sauter J. 'Die Grössenbestimmung der in Gemischnebeln von Verbrennungskraftmaschinen vorhandenen Brennstoffteilchen' VDI-Forschungsheft Nr. 279 (1926) und Nr. 312 (1928) ISSN0042-174X
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.

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Doo lets you turn your reminders into cards that help you focus and teach you better habits. Work small to achieve big.

Features
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Beautiful illustrations that add personality and warmth
Custom repeat schedules
Custom snooze options
Custom date options, including early and optional alerts per reminder
Schedule view
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