Chemistry Reference
In-Depth Information
Wood (1964) showed that the velocity of sound
c
in
homogeneous
liquids and gases is independent of frequency and is given by the Wood
equation:
B
ρ
1
κρ
=
=
c
(3.7)
A simple approach to calculate the velocity of sound in a dispersion is
the Urick equation (Urick, 1947) in which
κ
and
ρ
in the Wood Equation
3.7 are replaced by the following:
κ
=
φ
i
κ
i
,ρ
=
φ
i
ρ
i
(3.8)
where
i
is the
i
th component of the mixture. This is called a homo-
geneous description because the properties of each phase contribute
independently to the properties of the system (Povey and Mason, 1998,
Chapter 3). By adding a second transducer opposite to the one for the
velocimetry, this simple relation of concentration and sound velocity
can be used to determine approximately the composition, for example
solid concentration, in the pipe (Birkhofer
et al.
, 2008; Wiklund and
Stading, 2008).
In order to consider scattering effects, Pinfield and Povey (1997) pro-
posed a modified Wood equation. The Urick equation and its extensions
were reviewed by McClements and Povey (1987).
3.4.4
Scattering
The scattering of ultrasound in dispersions depends on the size ratio of
the wavelength and the particle diameter. Thus, the scattering charac-
teristics can also be used for particle size analysis (Epstein and Carhart,
1953; Allegra and Hawley, 1972; Harker and Temple, 1988; Riebel and
L offler, 1989; Holmes
et al.
, 1993, 1994; Pinfield and Povey, 1997;
Storti
et al.
, 2000; Dukhin and Goetz, 2002). Regarding velocity profile
measurements, study of Atkinson and Kytomaa (1993) is of interest, as
it describes the development of the ultrasonic pressure field, attenuation
and sound velocity in suspensions of different concentrations (up to the
maximum packing density) and relates it to velocimetry.
3.4.5
Backscattering
The backscattering or the echogenicity of suspensions is investigated
mostly in the medical field. For the velocimetry, this property is quite
crucial as it decides if and with which penetration depth a measurement
