optical methods for in-situ particle sizing michel cournil, department of chemical engineering...

Optical methods for in-situ particle sizing

Michel COURNIL, Department of Chemical Engineering

(Centre SPIN), Ecole des Mines de Saint-Etienne (France)

[email protected] www.emse.fr

TU Wien 18. January 2002

A sample of granular solid = a huge number of grains of different shape and size

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)

Introduction

Particle size distribution

Assumption : one size parameter – " mean " diameter D – of a crystal is characteristic of all its properties

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), visualizationIn situ : a few of the previous methods

Size range :

Introduction

Particle size distribution

0.001 0.01 1010.1 100001000100 D in m

SievingSettling

Microscopy

Laser beam scattering

Light scattering

- problem of sampling (off-line and on-line characterisations) :general problem of sample withdrawal (isokinetic character)hydrodynamic perturbationscrystal or aggregate fragility

- interest of in-situ characterizationsprocess controlbetter mastering of the product qualityunderstanding of the processes

- problem of sampling (off-line and on-line characterisations) :general problem of sample withdrawal (isokinetic character)hydrodynamic perturbationscrystal or aggregate fragility

- interest of in-situ characterizationsprocess controlbetter mastering of the product qualityunderstanding 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 particle size distribution determinations from optical measurements spectral turbidimetry ( pseudo-absorbance) for dilute suspensions analysis of backscattered light for concentrated suspensions

A difficult experimental problem

Introduction

How to monitor (continuously) a crystallization process ?How to monitor (continuously) a crystallization process ?

In situ optical methods for particle size determinations

Light scattering fundamentals

Scattering angle and and mean scattering angle Scattering angle and and mean scattering angle

i

Incident rayIncident ray

Scattered rayScattered ray

small particle dp < isotropic scatteringsmall particle dp < isotropic scattering large particle dp > anisotropic scatteringlarge particle dp > anisotropic scattering

0

2 sincos4

disca

0

2 sin4

diCsca

Anisotropy factor Scattering cross sectionAnisotropy factor Scattering cross section

scaC

ip 2

Phase functionPhase function

ALGORITHM

1 0

L

I

I L

ln

I0IL

LEXPERIMENTALS

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

0,50

240 290 340 390 440 490 540 590 640 690 740

0,0

0,5

1,0

1,5

2,0

2,5

3,0

I0

IL

Intensity Turbidity

(nm)

I0

IL

[nm]

Intensity Turbidity

I0 IL

DTHEORY

0,00E+0

5,00E+7

1,00E+8

1,50E+8

2,00E+8

2,50E+8f (D)

D

Crystal population density function f (D)

D

DDfQsca d)(m)DD,,(4

2

0


Spectral turbidimetry measurement principle

slurry

laser diode

holder

optical fiber bundle A bundle B

photodiode

bundle A + Breceiving fiber

emitting fiber


Backscattering measurement principle

Suspension of monodisperse non-absorbing spherical particles Suspension of monodisperse non-absorbing spherical particles

INCdxdI

sca: Light intensity at abscissa x: Light intensity at abscissa x

: Particle number per unit volume [#/cm3]: Particle number per unit volume [#/cm3]

: Scattering area [cm2]: Scattering area [cm2]

IN

scaC

Scattering coefficient :Scattering coefficient :

géom

sca

C

CQ : area of particle cross-section: area of particle cross-sectiongéomC

for a spherical particlefor a spherical particle4

2DCgéom


Fundamentals of spectral turbidimetry (1)

Case of a monodisperse suspension of non-absorbing spherical particles : Case of a monodisperse suspension of non-absorbing spherical particles :

24QND

dDDDQf

0

24

Case of a polydisperse suspension of non-absorbing spherical particles : Case of a polydisperse suspension of non-absorbing spherical particles :





index refractive medium dispersingindex refractive particlem

Determination of scattering coefficient Q : Mie theory Determination of scattering coefficient Q : Mie theory

Q : function of wavelength , particle diameter D, and mQ : function of wavelength , particle diameter D, and m

0

0,51

1,52

2,53

3,5

0 5 10 15 20

Dm 12

scaQ

Example : methane hydrate crystals in water

Example : methane hydrate crystals in water

1 : Rayleigh1 : Rayleigh

2 : Rayleigh-Debye (Gans)2 : Rayleigh-Debye (Gans)

2-3 : Anomalous diffraction2-3 : Anomalous diffraction

3 : Fraunhoffer scattering3 : Fraunhoffer scattering

4 : Total reflection4 : Total reflection

1-4 : Optical resonance1-4 : Optical resonance

Elsewhere : : MIE (no approximation)

Elsewhere : : MIE (no approximation)

Different possible approximationsDifferent possible approximations

MIEMIE

mm

00 11

11

22

44

33

D

1-41-4

2-32-3

dDDDfmDQ

0

2,,4

“Direct” calculation for a polydisperse suspension“Direct” calculation for a polydisperse suspension

t

MMT

,...,,

11 tNDfDfDf ,...,2,1f

fAMT withwith NDDDMDA ,...,1;,...,1mD,,Q 2

No particular difficulty in the “direct” problemNo particular difficulty in the “direct” problem


Particle size distribution calculation from turbidity spectra (1)

Suspension water/polystyrene latex particles

mean diameter Dp=0.778 m ; nearly monodisperse

“Direct” calculation for a polydisperse suspension : example“Direct” calculation for a polydisperse suspension : example



Experimental data : nm750350

“Turbidity vector” definition :

Discretization of the turbidity spectrum (M values)t

MMT

,...,,

11

Data to obtain : population density function

Restriction to size range

Df

Discretization of the diameter range (N values)

max,min DD

“Population density vector” definition

tNDfDfDf ,...,2,1f

The "inverse" problem The "inverse" problem



An ill- conditioned problem : Matrix A nearly singularAn ill- conditioned problem : Matrix A nearly singular

The "inverse" problem : derivation of f from experimental TM The "inverse" problem : derivation of f from experimental TM



TM = A.fTM = A.f

Constrained least-square method: Min( ||TM - Af||2 + q(f))

(Twomey, 1977; Eliçabe and Garcia Rubio, 1989)

Constrained least-square method: Min( ||TM - Af||2 + q(f))

(Twomey, 1977; Eliçabe and Garcia Rubio, 1989)

A solution…..A solution…..

1st method : simple inversion:1st method : simple inversion:

Mtt TAAA

1f̂

MTA 1f̂

Catastrophic !Catastrophic !

Small variation in TM large variation in f Small variation in TM large variation in f

2nd method : least square2nd method : least square

Crystallization of methane hydrate in pressurized reactor [30-100 bars]Methane + water Methane hydrate (gas) (liquid) (solid)

Crystallization of methane hydrate in pressurized reactor [30-100 bars]Methane + water Methane hydrate (gas) (liquid) (solid)


Examples of application of turbidimetry

Crystallization of titanium oxide in a two-jet reactorTitanium chloride + water Titanium dioxide + HCl (gas) (gas) (solid)

Crystallization of titanium oxide in a two-jet reactorTitanium chloride + water Titanium dioxide + HCl (gas) (gas) (solid)

• Isothermal (1°C)

• Isobaric [30-100 bars] gas consumption

•Turbidity sensor

Pt10

0

Pref1

Pref2

Pref

C.D.P.

W EST 6100

2105

SET AT ALM2130 1

2

AL1AL2AL3 65 b

SET

MAXMIN

form ation dissociation

PRESSION TEM PERATURE

réacteur (P)

référence (Pref)

RégulationPID

AL1AL2AL3 65 b

SET

MAXMIN

AL1AL2AL3 2 °C

SET

MAXMIN

W EST 6100

2105

SET AT ALM2130 1

2

Sortie

Sortie

M éthane

Azote

Sortie

Spectrophotomètre

Analyseur Source

Injecteurliquidehautepression

Cryostat

P

EXPERIMENTAL SET-UP :

Semi-batch pressurizedand stirred reactor


Example of application of turbidimetry : crystallization of

methane hydrate

Turbidity sensor

Turbidity sensor

Parallel light beam

Parallel light beam

Scattering eventsScattering events

Particle number per unit volume

Influence of stirring rate

0dD)D(fD

Np1D

0dD)D(fNp Particle mean

diameter

6.0E+07

P = 45 bar ; t # 250 sf(D) [cm-4]

-1.0E+07

0.0E+00

1.0E+07

2.0E+07

3.0E+07

4.0E+07

5.0E+07

0 20 40 60 80 100 120

200 rpm

300 rpm

400 rpm

D [µm]

Stirring rate

0.0E+0

2.0E+5

4.0E+5

6.0E+5

8.0E+5

1.0E+6

1.2E+6

1.4E+6

0 200 400 600 800 1000 1200 1400

200 tr/min

300 tr/min

400 tr/min

500 tr/min

45 bar ; 0% PVP K30Np [cm-3]

t-tL [s]6

7

8

9

10

11

12

13

14

15

0 200 400 600 800 1000 1200 1400

200 tr/min

300 tr/min

400 tr/min

500 tr/min

45 bar ; 0% PVP K30D [µm]

t-tL [s]

Population density function

Calculated granular data

Crystallization of methane hydrate

Crystallization of methane hydrate


Example of application of turbidimetry : reaction between

two jets

Effect of the jet velocity on the particle mean diameterEffect of the jet velocity on the particle mean diameter


Example of application of turbidimetry : reaction between two jets

Method easy to operate and relatively cheapMethod easy to operate and relatively cheap

Possibility of in situ measurements even in difficult conditionsPossibility of in situ measurements even in difficult conditions

Reliable method however only in a restricted size range (0.1 m – 5 m for most crystals)

Reliable method however only in a restricted size range (0.1 m – 5 m for most crystals)


Conclusions on spectral turbidimetry

Main drawback : limitation to highly dilute suspensions : concentration less than 10-4 in volume in most cases

Main drawback : limitation to highly dilute suspensions : concentration less than 10-4 in volume in most cases


Analysis of backscattered light

I

If d mb

p0

, ,

w i th : I b : b a c k s c a t t e r e d in t e n s i t yI 0 : i n c id e n t i n t e n s i t yd p : p a r t i c l e d i a m e te r : s o l i d s v o lu m e f r a c t i o nm : r e f r a c t i v e i n d i c e s r a t i o ( s o l id / l i q u id )L : r e a c to r w a l l - s e n s o r d i s t a n c e


Analysis of backscattered lightExample : variation of backscattered intensity vs

volume fraction in solid

1,0E-4

1,0E-3

1,0E-2

1,0E-1

1,0E-7 1,0E-6 1,0E-3 1,0E-2 1,0E-1 1,0E+0

I b/I

0

TiO2 (0,35 µm)

Glass beads (56,9 µm)

Al2O3 (0,21 µm)

Al2O3 (1,79 µm)

1,0E-5 1,0E-4

z

d

0,0E+0

5,0E-3

1,0E-2

1,5E-2

2,0E-2

2,5E-2

3,0E-2

3,5E-2

1,0E-4 1,0E-3 1,0E-2 1,0E-1 1,0E+0

l *-1 (µm-1)

I b/I 0

SiO2 0,5 µmSiO2 1,0 µmSiO2 1,5 µmTiO2Al2O3 1µmAl2O3 3µmlatex 0,46µmbilles de verreglass beads


Analysis of backscattered lightDimensionless diagramme

Relevant parameter : transport mean free pathRelevant parameter : transport mean free path ~*

N sca 11

1. single backscattering approximation2. Monte Carlo simulation3. radiative transfer theory : diffusion approximation

1. single backscattering approximation2. Monte Carlo simulation3. radiative transfer theory : diffusion approximation

I b/I

02 22 31


Analysis of backscattered lightModels (1)


Analysis of backscattered lightModels (2)

Single backscatteringSingle backscattering

z

d

I

IN f N Rb

b s0

( , , )

Radiative transfer theoryRadiative transfer theory

s I r s I r s N

Np s s I r s dsca

sca ( , ) ( , ) ( , ' ) ( , ) ', , ,

4 4

I

If N Rb

sca0

25 ( , , , )Approximation of diffusionApproximation of diffusion

1.0E-5

1.0E-4

1.0E-3

1.0E-2

1.0E-1

1.0E-6 1.0E-5 1.0E-4 1.0E-3 1.0E-2 1.0E-1 1.0E+0

mesure

simulation deMonte Carlo

approximation dediffusion

Presi 3µm


Analysis of backscattered lightModels (3) : agreement theory-measurements

1.0E-5

1.0E-4

1.0E-3

1.0E-2

1.0E-1

1.0E-6 1.0E-5 1.0E-4 1.0E-3 1.0E-2 1.0E-1 1.0E+0

mesure

simulations deMonte Carlo

approximation dediffusion

Presi 1µm

0,0E+0

1,0E-2

2,0E-2

3,0E-2

4,0E-2

1,0E-4 1,0E-2 1,0E+0

l *-1 (µm-1)

I b/I

0

mesures

~

measurements


Analysis of backscattered lightApplication to particle sizing (1)

By using the universal curve as calibration curve :

Measured backscattered intensity transport mean free path mean diameter

By using the universal curve as calibration curve :

Measured backscattered intensity transport mean free path mean diameter

0,01

0,1

1

10

100

1000

1,0E-5 1,0E-4 1,0E-3 1,0E-2 1,0E-1 1,0E+0

dp

(µm)

m = 1,087 (silica in water)

m = 1,367 (alumina in water)

Measurement range : moderate and high

concentrations in solid

Measurement range : moderate and high

concentrations in solid


Analysis of backscattered lightApplication to particle sizing (2)

Comparison between the measurement size ranges of turbidimetry and backscattering for 2 different values of the

solid phase refractive index

Comparison between the measurement size ranges of turbidimetry and backscattering for 2 different values of the

solid phase refractive index

0.015

0.017

0.019

0.021

0.023

0.025

-50 0 50 100 150 200 250

t (s)

I b/I 0

5,00E-033,13E-04


Example of application of turbidimetry : monitoring of titanium dioxide aggregation in water

0.0E+0

5.0E-3

1.0E-2

1.5E-2

2.0E-2

2.5E-2

3.0E-2

3.5E-2

1.0E-4 1.0E-3 1.0E-2 1.0E-1

l *-1 (µm-1)

I b/I

0~

Two different behaviours according to the volume fraction in solidTwo different behaviours according to the volume fraction in solid

0.01

0.015

0.02

0.025

-100 100 300 500 700 900 1100 1300

t (s)

I b/I 0

= 175 tr/min

= 343 rpm

= 1084 rpm= 610 rpm

= 1500 rpm


Example of application of turbidimetry : monitoring of titanium dioxide aggregation in water

Influence of stirring rateInfluence of stirring rate

Method easy to operate and relatively cheapMethod easy to operate and relatively cheap

Possibility of in situ measurementsPossibility of in situ measurements

Possibility of characterization of contrated suspensionsPossibility of characterization of contrated suspensions

In situ optical methods for particle size determinationsConclusions on the use of light backscattering for particle sizing

For the moment only information on mean diameterFor the moment only information on mean diameter

optical methods for in-situ particle sizing michel cournil, department of chemical engineering...

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