1. Optical methods for in-situ particle sizing
Michel COURNIL, Department of Chemical Engineering
(Centre SPIN), Ecole des Mines de Saint-Etienne (France)
TU Wien 18. January 2002

2. Particle size distribution
Introduction
Particle size distribution
A sample of granular solid = a huge number of grains of different shape and size
Assumption : one size parameter – " mean " diameter D – of a crystal is characteristic of all its properties
The crystal population is described by function f(D) population density : f(D).dD is the crystal number per unit volume the diameter of which ranges between D and D + dD
Large variety in particle size distribution ; for monomodal distributions, simple laws with two parameters are used : mean diameter and standard deviation (dispersion)

3. Particle size distribution
Introduction
Particle size distribution
Overview of the different methods of particle sizing
They depend on the sizing operating mode : off-line, on line or in situ and on the size domain of the crystals
Off-line : sieving, settling, image analysis,…
On line : optical methods (light scattering), visualization
In situ : a few of the previous methods
Size range :
0.001
0.01 10 1
0.1
10000
1000
100
D in mm
Sieving
Settling
Microscopy
Laser beam scattering
Light scattering

4. How to monitor (continuously) a crystallization process ?
Introduction
How to monitor (continuously) a crystallization process ?
A difficult experimental problem
- problem of sampling (off-line and on-line characterisations) :
general problem of sample withdrawal (isokinetic character)
hydrodynamic perturbations
crystal or aggregate fragility
- interest of in-situ characterizations
process control
better mastering of the product quality
understanding of the processes
In situ particle size distribution determinations from optical measurements
spectral turbidimetry ( pseudo-absorbance) for dilute suspensions
analysis of backscattered light for concentrated suspensions

5. In situ optical methods for particle size determinations
Light scattering fundamentals
Scattering angle q and and mean scattering angle
Incident ray
Scattered ray
small particle dp <   isotropic scattering
large particle dp >  anisotropic scattering
Anisotropy factor Scattering cross section
Phase function

6. In situ optical methods for particle size determinations
Spectral turbidimetry measurement principle I0 IL L
EXPERIMENTALS 
[nm]
Intensity
Turbidity  I0 IL D
THEORY
Crystal population density function f (D) A L G O R I T H M

7. In situ optical methods for particle size determinations
Backscattering measurement principle
slurry
laser diode
holder
optical fiber bundle A
bundle B
photodiode
bundle A + B
receiving fiber
emitting fiber

8. In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (1)
Suspension of monodisperse non-absorbing spherical particles
: Light intensity at abscissa x
: Particle number per unit volume [#/cm3]
: Scattering area [cm2]
Scattering coefficient :
: area of particle cross-section
for a spherical particle

9. In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (2)
Case of a monodisperse suspension of non-absorbing spherical particles :
Case of a polydisperse suspension of non-absorbing spherical particles :

10. In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (3)
Determination of scattering coefficient Q : Mie theory
Q : function of wavelength l, particle diameter D, and m
1 : Rayleigh
2 : Rayleigh-Debye (Gans)
2-3 : Anomalous diffraction
3 : Fraunhoffer scattering
4 : Total reflection
1-4 : Optical resonance
Elsewhere : : MIE (no approximation)
Different possible approximations
MIE m 1 2 4 3
1-4
2-3
Example :
methane hydrate crystals in water

11. In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (1)
“Direct” calculation for a polydisperse suspension
with
No particular difficulty in the “direct” problem

12. In situ optical methods for particle size determinations
“Direct” calculation for a polydisperse suspension : example
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (2)
Suspension water/polystyrene latex particles
mean diameter Dp=0.778 mm ; nearly monodisperse

13. A B In situ optical methods for particle size determinations
The "inverse" problem
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (3)
Experimental data :
“Turbidity vector” definition :
Discretization of the turbidity spectrum (M values) A
Data to obtain : population density function
Restriction to size range
Discretization of the diameter range (N values)
“Population density vector” definition B

14. In situ optical methods for particle size determinations
The "inverse" problem : derivation of f from experimental TM
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (4)
TM = A.f
1st method : simple inversion:
Catastrophic !
Small variation in TM large variation in f
2nd method : least square
An ill- conditioned problem : Matrix A nearly singular
Constrained least-square method: Min( ||TM - Af||2 + g q(f))
(Twomey, 1977; Eliçabe and Garcia Rubio, 1989)
A solution…..

15. In situ optical methods for particle size determinations
Examples of application of turbidimetry
Crystallization of methane hydrate in pressurized reactor [ bars]
Methane + water  Methane hydrate
(gas) (liquid) (solid)
Crystallization of titanium oxide in a two-jet reactor
Titanium chloride + water  Titanium dioxide + HCl
(gas) (gas) (solid)

16. In situ optical methods for particle size determinations
Example of application of turbidimetry : crystallization of methane hydrate
EXPERIMENTAL SET-UP :
Semi-batch pressurized
and stirred reactor
Isothermal (1°C)
Isobaric [ bars]  gas consumption
Turbidity sensor

17. Parallel light beam
Turbidity sensor
Scattering events

18. Calculated granular data
Crystallization of methane hydrate
f(D) [cm -4 ]
P = 45 bar ; t # 250 s
6.0E+07
Population density function
Stirring rate
-1.0E+07
0.0E+00
1.0E+07
2.0E+07
3.0E+07
4.0E+07
5.0E+07 20 40 60 80
100
120
200 rpm
300 rpm
400 rpm
Calculated granular data
Influence of stirring rate
D [µm]
Particle number
per unit volume
Particle mean diameter

19. In situ optical methods for particle size determinations
Example of application of turbidimetry : reaction between two jets

20. In situ optical methods for particle size determinations
Example of application of turbidimetry : reaction between two jets
Effect of the jet velocity on the particle mean diameter

21. In situ optical methods for particle size determinations
Conclusions on spectral turbidimetry
Method easy to operate and relatively cheap
Possibility of in situ measurements even in difficult conditions
Reliable method however only in a restricted size range
(0.1 mm – 5 mm for most crystals)
Main drawback : limitation to highly dilute suspensions :
concentration less than 10-4 in volume in most cases

22. In situ optical methods for particle size determinations
Analysis of backscattered light

23. In situ optical methods for particle size determinations
Analysis of backscattered light
Example : variation of backscattered intensity vs volume fraction in solid

24. In situ optical methods for particle size determinations
Analysis of backscattered light
Dimensionless diagramme
Relevant parameter : transport mean free path

25. In situ optical methods for particle size determinations
Analysis of backscattered light
Models (1)
1. single backscattering approximation
2. Monte Carlo simulation
3. radiative transfer theory : diffusion approximation

26. In situ optical methods for particle size determinations
Analysis of backscattered light
Models (2)
Single backscattering
Radiative transfer theory
Approximation of diffusion

27. In situ optical methods for particle size determinations
Analysis of backscattered light
Models (3) : agreement theory-measurements

28. In situ optical methods for particle size determinations
Analysis of backscattered light
Application to particle sizing (1)
By using the universal curve as calibration curve :
Measured backscattered intensity  transport mean free path  mean diameter
Measurement range : moderate and high concentrations in solid

29. In situ optical methods for particle size determinations
Analysis of backscattered light
Application to particle sizing (2)
Comparison between the measurement size ranges of turbidimetry and backscattering for 2 different values of the solid phase refractive index

30. In situ optical methods for particle size determinations
Example of application of turbidimetry : monitoring of titanium dioxide aggregation in water
Two different behaviours according to the volume fraction in solid

31. In situ optical methods for particle size determinations
Example of application of turbidimetry : monitoring of titanium dioxide aggregation in water
Influence of stirring rate

32. In situ optical methods for particle size determinations
Conclusions on the use of light backscattering for particle sizing
Method easy to operate and relatively cheap
Possibility of in situ measurements
Possibility of characterization of contrated suspensions
For the moment only information on mean diameter