Optical methods for in-situ particle sizing

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

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

3. Introduction Particle size distribution Light scattering Laser beam scattering Microscopy Settling Sieving 0.01 100 1000 10000 Dinmm 0.001 0.1 1 10 Overviewof the different methods of particle sizing They depend on the sizing operating mode : off-line, on lineor in situand on thesize domainof 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 :

4. 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 particlesize 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 Scattered ray Incident ray small particle dp < isotropic scattering large particle dp>anisotropic scattering Anisotropy factorScattering cross section Phase function

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

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

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

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 Different possible approximations Example : methane hydrate crystals in water 1 : Rayleigh 1 0 2 : Rayleigh-Debye (Gans) MIE 1 2 2-3 2-3 : Anomalous diffraction 3 3 : Fraunhoffer scattering m 4 : Total reflection 1-4 : Optical resonance 4 1-4 Elsewhere : : MIE (no approximation)

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

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

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

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

15. In situ optical methods for particle size determinations Examples of application of turbidimetry Crystallization of methane hydrate in pressurized reactor [30-100 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 [30-100 bars] gas consumption • Turbidity sensor

17. Parallel light beam Turbidity sensor Scattering events

18. 5.0E+07 200 rpm 4.0E+07 300 rpm 400 rpm 3.0E+07 2.0E+07 1.0E+07 0.0E+00 0 20 40 60 80 100 120 -1.0E+07 -4 f(D) [cm ] Crystallization of methane hydrate P = 45 bar ; t # 250 s 6.0E+07 Population density function Stirring rate 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. Effect of the jet velocity on the particle mean diameter In situ optical methods for particle size determinations Example of application of turbidimetry : reaction between two jets

21. 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 In situ optical methods for particle size determinations Conclusions on spectral turbidimetry

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) Measurement range :moderate and high concentrations in solid By using the universal curve as calibration curve : Measured backscattered intensity  transport mean free path mean diameter

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. 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 In situ optical methods for particle size determinations Conclusions on the use of light backscattering for particle sizing