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

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)

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

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

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

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

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

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

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 :

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

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

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

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

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…..

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)

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

Parallel light beam Turbidity sensor Scattering events

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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