Abstract
The object of this study is to develop a particle measurement system on the basis of the Statistical Extinction Method, which provides an inline monitoring of different particle processes. The Statistical Extinction Method determines from the mean value and root mean square deviation of a transmission signal through a particle collective, a mean particle size and a particle concentration. For the determination of particle size distribution, an advanced Statistical Extinction Method is developed and verified. This method requires the measurement of transmission signals of several light beams of different beam cross sections through a particle collective.
The validity of the Statistical Extinction Method is examined according to the derivation of its fundamental equations. The requirements on the metrological implementation of the method, as a result, are analyzed and evaluated. Since the method is influenced by some effects that are interacting with each other and difficult to examine, a simulation model for the extinction of light beams by particles is developed. With the simulation calculations, the effects can be examined separately and the quantitative correlation between the transmission signal and the effects influencing the signals can be discussed. Furthermore, the influence of the hardware-related measurement uncertainty on the Statistical Extinction Method is investigated by the simulation calculations. For a process-related applicability of the SE-Method, a number of optical sensor principles and concepts are formulated and developed on the basis of the derived requirements. These are verified with regard to their measurement capability. The validation of the method for different particle processes is carried out with suspensions, emulsions (Schwarz et al., Chemie Ingenieur Technik 86:1544, 2014), and spray processes at specifically designed test benches and sensor assemblies.
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Abbreviations
- A meas :
-
Measurement cross section [m2]
- c N :
-
Number concentration of particles [1/m3]
- c V :
-
Volume concentration of particles [1]
- C :
-
Coefficient matrix [m2]
- C ext :
-
Extinction cross section [m2]
- C ext,rel :
-
Relative extinction cross section [1]
- E :
-
Extinction [1]
- f :
-
Random error [1]
- I :
-
Light intensity [W/m2]
- k ext :
-
Extinction coefficient [1]
- L mv :
-
Length of the measurement volume [m]
- m :
-
Refractive index ratio [1]
- N P :
-
Number of particles [1]
- p :
-
Pressure [Pa]
- P :
-
Light output [W]
- q 0(x):
-
Number density distribution [1/m]
- Q 0(x):
-
Number cumulative distribution [1]
- R :
-
Resultant vector [m2]
- S :
-
Solution vector [1]
- T :
-
Transmission of a light beam [1]
- V meas :
-
Measurement volume [m3]
- x :
-
Particle size [m]
- x 1.2 :
-
Sauter mean diameter [m]
- x L :
-
Diameter of the pinhole [m]
- α :
-
Aperture angle [rad]
- λ :
-
Wave length of the light beam [m]
- μ :
-
Expected value [1]
- σ(x):
-
Root mean square deviation of the particle size [m]
- σ(T):
-
Root mean square deviation of the transmission signal [1]
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Dannigkeit, F., Schwarz, N., Ripperger, S. (2016). Statistical Extinction Method for the Inline Monitoring of Particle Processes. In: Fritsching, U. (eds) Process-Spray. Springer, Cham. https://doi.org/10.1007/978-3-319-32370-1_12
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DOI: https://doi.org/10.1007/978-3-319-32370-1_12
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