WO2010055280A1

WO2010055280A1 - Determining the particle size distribution of a suspension

Info

Publication number: WO2010055280A1
Application number: PCT/GB2009/002599
Authority: WO
Inventors: Mingzhong Li
Original assignee: De Montfort University
Priority date: 2008-11-11
Filing date: 2009-11-02
Publication date: 2010-05-20
Also published as: GB2460305B; GB0820557D0; GB2460305A

Abstract

A method for determining the particle size distribution of particles within a suspension (12) comprises (i) directing light at a plurality of different wavelengths towards the suspension through a transparent light refractive medium (16), such as a prism, located adjacent to the suspension (12); (ii) measuring the critical angle θ_c, at which total internal reflection occurs at an interface (20) between the suspension (12) and the transparent light refractive medium (16), for each wavelength of directed light; (iii) calculating the refractive index of the suspension (12) for each wavelength of directed light using the measured critical angles θ_c; and (iv) determining the particle size probability distribution based on the calculated refractive indices. Also described is an apparatus (10) for determining the particle size distribution of particles within a suspension (12).

Description

Determining the particle size distribution of a suspension

TECHNICAL FIELD The present invention relates generally to determining the particle size distribution of a suspension. More particularly, embodiments of the present invention relate to a method and apparatus for determining the particle size distribution of particles within a suspension.

BACKGROUND ART

It is desirable in many industries to be able to perform in-process monitoring of manufacturing processes so that those processes can be controlled and optimised, in real-time, by adjusting the process parameters. With such in-process monitoring and control, both improved product consistency and reduced waste by minimising product rejection can be achieved.

The pharmaceutical, fine and speciality chemicals, nuclear fuel and food industries (to name but a few), which are all concerned with the manufacture of high value-added material in comparatively small quantities, are examples of industries in which in- process monitoring of manufacturing processes is highly desirable. For example, there is often a need to be able to determine the properties, such as particle size and concentration, of a suspension during particle formation processes such as crystallisation, precipitation grinding and emulsion polymerisation because these properties are an essential feature of many material specifications and can have a significant effect on the properties of intermediates.

There are a number of techniques which can be used to measure the size of particles within a suspension. Laser diffraction and spectral extinction are two known techniques, but these both require dilution of the process suspension when measuring from typical manufacturing streams because of the high concentration of the process suspension. Dilution to facilitate measurement can result in changes in both the size and form of the particles, especially during production processes such as crystallisation, and the results can, thus, be inaccurate. Furthermore, the need to dilute the process suspension to perform the necessary measurements means that these techniques are not suited to in-process particle size measurement.

In spectral extinction, the degree of light scattering and absorption by a suspension is measured and depends on the particle size, shape and composition and on the wavelength of the light. Particle size distribution can be determined from measurements of extinction at a range of wavelengths. However, for concentrated suspensions, the interpretation of light extinction measurements is more difficult because of multiple scattering and inter-particle interaction effects, and work in this field has established that spectral extinction measurements can be used to measure particle size distribution at particle concentrations below only about 3% by volume. At higher concentrations, extinction is essentially total so the technique cannot be employed.

Ultrasound attenuation is another feasible technique for determining the particle size distribution for spheres of known physical properties over a large range of particle sizes in high concentration suspensions. However, it has been shown that using ultrasound attenuation is not straightforward in many applications because information is required about seven physical properties of the continuous medium and about a further seven properties of the dispersed phase.

Optical chord measurement techniques have also been used in high concentration suspensions but, to be successful, these require a lengthy measurement period to obtain sufficient samples in order that the particle size distribution may be inferred accurately. Thus, this technique does not readily lend itself to in-process particle size measurement.

It would, therefore, be desirable to overcome the difficulties associated with the known techniques for determining the size of particles in turbid suspensions, and in particular to provide a method and apparatus which can be used to determine the particle size distribution within a suspension and, ideally, which can be used to perform in-process determination of particle size distribution to thereby enable control and optimisation of manufacturing processes in real-time.

SUMMARY OF THE INVENTION According to a first aspect of the present invention, there is provided a method for determining the particle size distribution of particles within a suspension, the method comprising:

(i) directing light at a plurality of different wavelengths towards the suspension through a transparent light refractive medium located adjacent to the suspension;

(ii) measuring the critical angle, at which total internal reflection occurs at an interface between the suspension and the transparent light refractive medium, for each wavelength of directed light;

(iii) calculating the refractive index of the suspension for each wavelength of directed light using the measured critical angles;

(iv) determining the particle size probability distribution based on the calculated refractive indices.

According to a second aspect of the present invention, there is provided apparatus for determining the particle size distribution of particles within a suspension, the apparatus comprising: a light source arrangement operable to direct light at a plurality of different wavelengths towards a suspension through a transparent light refractive medium locatable, in use, adjacent to the suspension; a detector for measuring the critical angle, at which total internal reflection occurs at an interface between the suspension and the transparent light refractive medium, for each wavelength of light directed by the light source arrangement; a processor operable to: calculate the refractive index of the suspension for each wavelength of directed light using the measured critical angles; and determine the particle size probability distribution based on the calculated refractive indices. - A -

Optional, but sometimes preferred, features of the invention are defined in the dependent claims.

DRAWINGS

Figure 1 is a schematic view of apparatus for determining the particle size distribution of particles within a suspension;

Figure 2 is a diagrammatic illustration of a technique for calculating the refractive index of the suspension based on a measured critical angle; Figure 3 is an intensity profile for a single wavelength of incident light; and

Figure 4 is a diagrammatic illustration of an example particle size probability distribution determined in accordance with embodiments of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS QF THE INVENTION Embodiments of the present invention will now be described by way of example only, and with reference to the accompanying drawings.

As described above, it can be desirable in many circumstances to be able to determine the size distribution of particles within a suspension, and embodiments of the invention thus provide a method and apparatus for determining the particle size distribution of particles within a suspension.

Figure 1 shows generally an apparatus 10 for determining the particle size distribution of particles within a suspension 12. The suspension 12 may be a static suspension but is more typically a flowing suspension that is produced by an appropriate manufacturing process. Examples of such manufacturing processes include, but are not limited to, crystallisation, precipitation grinding and emulsion polymerisation. For the avoidance of doubt, only a portion of the entire suspension is shown in Figure 1.

hi general terms, the apparatus 10 comprises a light source arrangement 14, a transparent light refractive medium 16 and a detector 18. The transparent light refractive medium 16 is located in use adjacent to the suspension 12 so that an interface 20 or boundary is defined between the suspension 12 and the transparent light refractive medium 16. In typical embodiments, the transparent light refractive medium 16 is a prism of any suitable shape and desirably has a high refractive index.

The light source arrangement 14 is operable to direct light towards the suspension 12 through the transparent light refractive medium 16 and the detector 18 is operable to measure the angle at which total internal reflection of the light directed into the transparent light refractive medium 16 occurs at the interface 20, this angle being referred to throughout this specification as the critical angle θ_c.

The concept of total internal reflection and the critical angle is well known to those skilled in the art but it is useful to provide a brief outline of the concept in the context of the present invention with reference to Figure 2, in which the suspension 12 and transparent light refractive medium 16 are shown diagrammatically along with a beam of light having a predetermined wavelength which is generated by the light source arrangement 14 shown in Figure 1.

As shown, the beam of light enters the transparent light refractive medium 16 at an angle θ to the normal AA. At angles to the normal that are less than the critical angle θ_c, the beam of light essentially splits at the interface 20 between the transparent light refractive medium 16 and the suspension 12, with a proportion of the light being refracted into the suspension 12 and a proportion of the light being reflected through the transparent light refractive medium 16. This is illustrated in Figure 2 by the dashed lines.

As the angle to the normal increases, the amount of light refracted into the suspension 12 decreases and the amount of light reflected at the interface 20 increases, until the point at which the beam of light is totally internally reflected at the interface 20, with there being no refraction of light into the suspension 12. This is illustrated in Figure 2 by the solid lines. The critical angle θ_c at which total internal reflection occurs at the interface 20 between the suspension 12 and the transparent light refractive medium 16 can be determined using the following formula:

θ_c [Equation 1]

where n₂ is the effective refractive index of the suspension 12 and H₁ is the refractive index of the transparent light refractive medium 16. The refractive index W₁ of the transparent light refractive medium 16 is known and, providing that the critical angle θ_c can be determined, the effective refractive index n₂ of the suspension 12 can itself be determined by rewriting the above equation as follows:-

H₂ = H₁ sin#_c [Equation 2]

The effective refractive index of a suspension 12 varies according to the size of the particles in the suspension 12 and, accordingly, it is possible to determine the size of the particles in the suspension 12 using the method and apparatus 10 according to embodiments of the present invention by measuring the critical angle θ_c at which total internal reflection occurs at the interface 20.

In order to enable the measurement of the critical angle θ_c, light is directed by the light source arrangement 14 towards the suspension 12, through the transparent light refractive medium 16, and the intensity of the light reflected at the interface 20 is detected by the detector 18, which typically comprises a linear charge-coupled device (CCD) array.

In some arrangements, the light source arrangement 14, which may for example comprise a laser diode or a light emitting diode (LED), may produce a single beam of light which is directed towards the suspension 12 and the apparatus 10 may include a motor (not shown), such as a stepper motor, to move the light source arrangement 14 to vary the angle of incidence θ of the beam of light relative to the normal AA. In other arrangements, the apparatus 10 may include a beam spreader (not shown), such as a diverging lens, which may form part of the light source arrangement 14. In such arrangements, light may be directed towards the suspension 12 simultaneously, at a plurality of angles of incidence θ relative to the normal AA.

Irrespective of which of the above arrangements is employed, the intensity of the reflected light is detected by the detector 18 as a function of the angle of incidence, and an intensity profile is generated. Figure 3 shows an example of an intensity profile for a single wavelength of light directed towards the suspension 12 by the light source arrangement 14.

The intensity profile includes three curves. The curve denoted by the dotted line illustrates the intensity I (or reflectance) of the reflected light detected by the detector 18 as a function of the angle of incidence θ of the light directed towards a turbid suspension 12 by the light source arrangement 14. It can be seen that because the suspension is turbid, the critical angle at which total internal reflection occurs is much less clearly identifiable than for a transparent liquid, denoted by the solid line in Figure 3. However, the variation of the intensity I of the reflected light with the angle of incidence θ remains a source of useful information and if the intensity profile for the turbid suspension is numerically differentiated, as denoted in Figure 3 by the dashed line, the critical angle θ_c can be identified from the peak value of the numerically differentiated intensity profile.

When the critical angle θ_c of the suspension 12 is measured in the manner described above, equation 2 can be used to determine the effective refractive index n₂ of the suspension 12 using the measured critical angle θ_c and the known refractive index H₁ of the transparent light refractive medium 16,

Although light directed towards the suspension 12 through the transparent light refractive medium 16 at the critical angle θ_c is totally internally reflected, an evanescent wave propagates along the interface 20 between the suspension 12 and the transparent light refractive medium 16. The optical properties of the suspension 12 in the short depth of the evanescent wave affect the critical angle θ_c, and hence the effective refractive index of the suspension. Since the refractive index is affected by the particle size, the particle size of the suspension 12 can, thus, be determined based on the refractive index of the suspension calculated in the manner outlined above. The method can, therefore, be applied to turbid suspensions and, indeed, has been used to determine the particle size for suspensions having particle sizes in the range lOOnm to lOμm at concentrations up to 50% by volume.

If a single wavelength of light is directed towards the suspension 12 through the transparent light refractive medium 16 in the manner described above, the technique outlined above can be used to determine the average or mean size of the particles within the suspension 12. This may not, however, be sufficient when the aim is to use the determined particle size to control and optimise the parameters of a manufacturing process in real-time to obtain a desired particle size or particle size distribution. A key aspect of this invention is, therefore, that light is directed towards the suspension 12 through the transparent light refractive medium 16 at a plurality of different wavelengths.

The critical angle θ_c, and hence the effective refractive index n₂ of the suspension 12, vary as a function of the wavelength of the light directed towards the suspension 12 by the light source arrangement 14. Accordingly, by directing light towards the suspension at a range of angles of incidence θ at a plurality of different wavelengths so that an intensity profile can be generated for each wavelength of directed light and so that the associated critical angle θ_c can be calculated for each wavelength of directed light based on the generated intensity profiles using the technique described above, it is possible to calculate an effective refractive index n₂ of the suspension for each wavelength of directed light.

It is then possible, based on these calculated effective refractive indices n₂ , to determine the particle size probability distribution of the particles within the suspension 12, as opposed to an average or mean particle size. This enables much greater control of the parameters of a manufacturing process in real-time to ensure that a desired particle size distribution within the suspension 12 is obtained.

The apparatus 10 also includes a processor 22 which is operable, using the critical angles θ_c measured for each of the plurality of wavelengths of light directed towards the suspension 12 by the light source arrangement 14, to calculate the effective refractive index n₂ of the suspension 12 for each wavelength of directed light. The processor 22 is also operable to determine the particle size probability distribution of the particles within the suspension 12 based on the calculated refractive indices n₂. hi some embodiments, the processor 22 may also be operable to determine the volume fraction of the particles within the suspension (i.e. the suspension concentration) based on the calculated effective refractive indices n₂. For example, it has been shown that the relationship between the effective refractive index n₂ of a suspension and the volume fraction of particles within the suspension is linear for concentrations up to approximately 50% by volume.

hi some embodiments, the measured effective refractive index n₂ corresponds to the real component of the refractive index of the suspension 12, which is determined for each wavelength of directed light in accordance with equation 2.

For a polydisperse suspension 12 containing generally spherical and optically non- absorbent isotropic particles, the following equation may then be employed to determine the particle size probability distribution function f(D) for the suspension 12:

dDj j [Equation 3]

where m_\ is the real component of the refractive index of the continuous phase; V₂ is the volume fraction of the particles; X₁ is the wavelength of directed light; /J₂(I,) is the calculated refractive index for a given wavelength X₁ of directed light; D is the particle diameter; m is the relative refractive index between the particle and the continuous phase; and P_ext is the refractive analogue of the scattering coefficient Q_ext.

The above equation can be solved by appropriate inversion schemes to determine the particle size probability distribution function f(D) based on the calculated effective refractive indices of the suspension 12 at a plurality of different wavelengths. Mathematical inversion schemes using intelligent optimisation techniques, such as neural networks and evolutionary programming, and/or the non-negative least squares method, can be used to determine the particle size probability distribution function f(D). Such inversion schemes can also be used to determine the volume fraction v∑ of the particles within the suspension 12 based on the calculated effective refractive indices of the suspension 12 at the plurality of different wavelengths.

For suspensions containing non-spherical and/or anisotropic and/or optically absorbent particles, which are typical of organic crystals, equation 3 would, of course, need to be suitably modified.

The number of different wavelengths of light that are employed in the method according to the invention will need to be selected to enable a satisfactory determination of the particle size probability distribution /(©λ Clearly, increasing the number of measurements of the critical angle θ_c at different wavelengths, and hence of the effective refractive index n₂ of the suspension 12, will increase the accuracy of the determined particle size probability distribution f(D). However, increasing the number of measurements will increase the time required for measurement and, more significantly, will increase the complexity of the inversion calculation needed to determine the particle size probability distribution f(D). Purely by way of example, in some circumstances it is believed that that the use of five or six different wavelengths of light and measurement of the critical angle θ_c at those five or six different wavelengths may be sufficient. As indicated above, a key aspect of the present invention is that light at a plurality of different wavelengths is directed towards the suspension 12 through the transparent light refractive medium 16. Different embodiments of the apparatus 10 may be employed to provide light at varying wavelengths, and the following are possible examples.

In one embodiment of the apparatus 10, a plurality of fixed wavelength light sources, such as laser diodes or light emitting diodes (LEDs), could be used to sequentially direct light at a plurality of different wavelengths towards the suspension 12 through the transparent light refractive medium 16. In this embodiment, the detector 18 would be used to sequentially measure the intensity of the reflected light for each wavelength of directed light, thus enabling the critical angle θ_c to be determined for each wavelength of directed light and hence, enabling the effective refractive index n₂ of the suspension 12 to be determined sequentially for each wavelength of directed light.

In another embodiment of the apparatus 10, a plurality of such fixed wavelength light sources, each producing light at a different wavelength, could be used to simultaneously direct light at a plurality of different wavelengths towards the suspension 12 through the transparent light refractive medium 16. The detector 18, which in this embodiment would preferably be in the form of a two-dimensional charge-coupled device (CCD) array, could then be used to simultaneously measure the intensity of the reflected light corresponding to each wavelength of light directed by the plurality of fixed wavelength light sources. This would enable the critical angles θ_c for each wavelength of directed light to be measured simultaneously, thus enabling the effective refractive index n₂ of the suspension 12 to be determined simultaneously for each wavelength of directed light.

In a further embodiment, a single variable wavelength light source could be used to direct light at a plurality of different wavelengths towards the suspension 12 through the transparent light refractive medium 16. For example, a white light source with an associated grating could be used to direct light simultaneously at a plurality of different wavelengths and, preferably also simultaneously across a range of angles of incidence, towards the suspension 12 through the transparent light refractive medium 16. In this embodiment, the detector 18 would again preferably be in the form of a two-dimensional charge-coupled device (CCD) array which would simultaneously measure the intensity of the reflected light corresponding to each wavelength of light directed towards the suspension 12 by the variable wavelength light source. This would enable the critical angles θ_c for each* wavelength of directed light to be measured simultaneously, thus enabling the effective refractive indices n₂ of the suspension 12 to be determined simultaneously for each wavelength of directed light.

hi typical embodiments, both the light source arrangement 14, comprising its one or more light sources, and the transparent light refractive medium 16 would be embodied in the form of a refractometer and the processor 22 would be provided by a microcomputer or the like. Other arrangements are, however, possible and entirely within the scope of the present invention.

Although embodiments of the invention have been described in the preceding paragraphs with reference to various examples, it should be understood that various modifications may be made to those examples without departing from the scope of the present invention, as claimed.

Claims

1. A method for determining the particle size distribution of particles within a suspension, the method comprising:

(ii) measuring the critical angle, at which total internal reflection occurs at an interface between the suspension and the transparent light refractive medium, for each wavelength of directed light; (iii) calculating the refractive index of the suspension for each wavelength of directed light using the measured critical angles;

2. A method according to claim 1 , wherein the method further comprises:

(v) determining the volume fraction of the particles within the suspension based on the calculated refractive indices.

3. A method according to claim 1 or claim 2, wherein step (i) comprises directing a beam of light at each wavelength towards the suspension through the transparent light refractive medium and varying the angle of incidence each directed beam of light.

4. A method according to claim 1 or claim 2, wherein step (i) comprises directing light at each wavelength towards the suspension through the transparent light refractive medium simultaneously across a range of angles of incidence.

5. A method according to claim 4, wherein step (i) comprises spreading a single beam of light using a beam spreader to direct light towards the suspension simultaneously across a range of angles of incidence.

6. A method according to any preceding claim, wherein step (i) comprises sequentially directing light towards the suspension through the transparent light refractive medium at a plurality of different wavelengths.

7. A method according to any of claims 1 to 5, wherein step (i) comprises simultaneously directing light towards the suspension through the transparent light refractive medium at a plurality of different wavelengths.

8. A method according to any preceding claim, wherein step (ii) comprises detecting the intensity of light reflected from the interface between the suspension and the transparent light refractive medium as a function of the angle of incidence of the directed light to generate an intensity profile for each wavelength of directed light.

9. A method according to claim 8, wherein step (ii) comprises detecting the intensity of the reflected light using a detector array.

10. A method according to claim 9, wherein step (ii) comprises detecting the intensity of the reflected light using a linear charge-coupled device (CCD) array.

11. A method according to any of claims 8 to 10, wherein step (ii) further comprises numerically differentiating the generated intensity profile for each wavelength of directed light to identify the critical angle.

12. A method according to claim 11, wherein the method comprises identifying the peak value of the numerically differentiated intensity profile for each wavelength of directed light to identify the critical angle.

13. A method according to any preceding claim, wherein step (iii) is performed using the following equation: H₂ = H₁ sin#_c where n₂ is the refractive index of the suspension for a given wavelength of directed light; n_λ is the known refractive index of the transparent light refractive medium for the given wavelength of directed light; and θ_c is the critical angle for the given wavelength of directed light measured during step (ii).

14. A method according to claim 13, wherein step (iv) is performed using the following equation:

where ni_\ is the real component of the refractive index of the continuous phase; V₂ is the volume fraction of the particles; X₁ is the wavelength of directed light; n₂(X_t) is the calculated refractive index for a given wavelength X₁ of directed light; D is the particle diameter; f(D) is a particle size probability distribution function; m is the relative refractive index between the particle and the continuous phase; and P_ext is the refractive analogue of the scattering coefficient Q_eχ_t.

15. A method according to any preceding claim, wherein the steps of the method are performed continuously and repeatedly in real-time and the method further comprises varying, in real-time, the operating parameters of a manufacturing process in response to the particle size probability distribution determined in step (iv).

16. Apparatus for determining the particle size distribution of particles within a suspension, the apparatus comprising: a light source arrangement operable to direct light at a plurality of different wavelengths towards a suspension through a transparent light refractive medium locatable, in use, adjacent to the suspension; a detector for measuring the critical angle, at which total internal reflection occurs at an interface between the suspension and the transparent light refractive medium, for each wavelength of light directed by the light source arrangement; a processor operable to: calculate the refractive index of the suspension for each wavelength of directed light using the measured critical angles; and determine the particle size probability distribution based on the calculated refractive indices.

17. Apparatus according to claim 16, wherein the processor is also operable to determine the volume fraction of the particles within the suspension based on the calculated refractive indices.

18. Apparatus according to claim 16 or claim 17, wherein the transparent light refractive medium is a prism.

19. Apparatus according to any of claims 16 to 18, wherein the light source arrangement includes a plurality of fixed wavelength light sources which are operable either sequentially or simultaneously to direct light at different wavelengths towards the suspension through the transparent light refractive medium.

20. Apparatus according to any of claims 16 to 18, wherein the light source arrangement includes a variable wavelength light source which is operable to sequentially or simultaneously direct light at different wavelengths towards the suspension through the transparent light refractive medium.

21. Apparatus according to any of claims 16 to 20, wherein the light source arrangement is operable to direct a beam of light towards the suspension through the transparent light refractive medium and the apparatus further includes a motor operable to move the light source arrangement to vary the angle of incidence of the directed beam of light.

22. Apparatus according to any of claims 16 to 20, wherein the light source arrangement includes a beam spreader operable to spread a single beam of light to direct light towards the suspension through the transparent light refractive medium simultaneously at a plurality of angles of incidence.

23. Apparatus according to any of claims 16 to 22, wherein the detector comprises a linear charge-coupled device (CCD) array.

24. Apparatus according to any of claims 16 to 23, wherein the detector is operable to detect the intensity of light reflected from the interface between the suspension and the light refractive medium as a function of the angle of incidence of the directed light and the processor is operable to generate an intensity profile for each wavelength of directed light.

25. Apparatus according to claim 24, wherein the processor is operable to numerically differentiate the generated intensity profile for each wavelength of directed light and to identify the peak value of the numerically differentiated intensity profile to identify the critical angle for each wavelength of directed light.

26. A method for determining the particle size distribution of particles within a suspension substantially as hereinbefore described with reference to the accompanying drawings.

27. Apparatus for determining the particle size distribution of particles within a suspension substantially as hereinbefore described with reference to the accompanying drawings.