fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, 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 In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...

of a sphere that has the same

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...

surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc ...

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 :

= 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 There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithme ...

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

of a drop having the same

ratio as the entire spray. :

D_s = \frac

f_i

is the

scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...

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.

References

{{DEFAULTSORT:Sauter Mean Diameter Fluid dynamics

Applications

See also

References