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Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions
Colloids and Surfaces A: Physiochemical and Engineering Aspects 153 Ž1999. 495]502
Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions F. Albaa , G.M. Crawley b, J. Fatkinb,U , D.M.J. Higgsb, P.G. Kippax b b
a Felix Alba Consultants Inc., Murray, UT, USA Mal¨ ern Instruments Ltd., Spring Lane South, Mal¨ ern, Worcestershire, UK
Abstract The particle size distribution of particles in liquid-based suspensions and emulsions is an important parameter in a wide variety of industrial applications. Many particle-sizing methods require the transmission of light through a sample of the system, and therefore these particulate systems must be severely diluted. Many systems are unstable on dilution and therefore have to be measured at high volume concentration. Sound waves interact with both the suspending medium and the dispersed phase and are able to propagate through concentrated systems. The development of new ultrasonic transducer technology together with advances in digital signal processing has opened the way for a powerful new analysis termed acoustic attenuation spectroscopy. The technique consists of propagating ultrasonic waves of a range of frequencies through the particulate system and accurately measuring the attenuation at each frequency. This attenuation spectrum can be converted to a particle size distribution and a measure of the concentration of the dispersed phase. It offers the particle technologist the means to monitor and control particle formation and reduction processes. Q 1999 Elsevier Science B.V. All rights reserved. Keywords: Particle size analysis; Concentrated systems; Acoustic spectroscopy
1. Introduction The particle size distribution of suspensions and emulsions is an important parameter in a wide variety of industrial applications. The techniques to measure particle size have been developed in response to specific needs and the technology available at the time. Laser diffraction is currently the most widely used technique for U
Corresponding author.
measurement of particle size in suspensions, emulsions, dry powders, and aerosols in the range between one tenth of a micron and a few millimetres. It is successful because of its wide applicability and the reproducibility, speed, and simplicity of the measurement procedure. However, since the principle requires transmission of light and assumes single particle scattering, the technique is limited to making measurements on dilute samples. Sound waves interact with particles in a similar manner to light but have the advantage that they
0927-7757r99r$ - see front matter Q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 Ž 9 8 . 0 0 4 7 3 - 7
496
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
can travel through concentrated suspensions and emulsions. Particle size analysers using soundbased measurement principles have been available for a number of years, however, these techniques operate over limited size ranges and work best with dense, rigid particles. A technique for particle size analysis using acoustic attenuation spectroscopy has been developed specifically to overcome these limitations. It utilises state of the art ultrasonic transducer technology, digital signal processing and is based upon classical acoustical principles allowing the particle technologist to study high concentration particle systems. These advances have been incorporated in an instrument known as the Ultrasizer and it has been used in a number of applications where accurate particle size measurement was previously impossible, for example in the on-line monitoring of lubricant emulsions or the direct measurement of a foodstuff such as mayonnaise. The instrument measures particles in the size range from 0.01 mm to 1000 mm Ždepending on the application. and simultaneously calculates the dispersed phase concentration. Robust construction enables the technique to be used in on-line applications in particulate process control. Particle size analysis using acoustic attenuation spectroscopy consists of Ža. predicting the attenuation spectra for any particle size distribution and concentration; Žb. measuring the attenuation spectra for the sample; and Žc. inverting the measured attenuation spectrum to a particle size distribution and dispersed phase concentration. 2. Theory of acoustic attenuation spectroscopy Acoustic attenuation spectroscopy for the particle size measurement of suspensions and emulsions consists of transmitting ultrasound of different frequencies, typically from 1 MHz up to 160 MHz through a sample with the attenuation being accurately measured. Such a broad frequency range is obtained by using two pairs of broad band ultrasonic transducers that produce waves with minimal deviation from the plane wave regime. The measured attenuation of the sound wave
as a function of frequency is called the acoustic attenuation spectrum and constitutes a signature for the particular suspension or emulsion in the sense that there is a one-to-one correspondence between the particle size distributionrparticle concentration pair and the associated spectrum. To derive the particle size distribution and particle concentration from the spectral data, the spectrum associated with any conceivable particle size distribution and particle concentration has to be capable of being accurately predicted. The actual spectral data produced by the specific suspensionremulsion being tested has then to be measured with very high accuracy and, finally, a stable, high resolution, mathematical inversion procedure is used to extract the size information from the measured spectral data. 3. Attenuation mechanisms When a sound wave passes through a particulate system, changes occur to the wave, as well as to the two phases of the medium. A particle presents a discontinuity to sound propagation and the wave scatters with a redistribution of the acoustic energy throughout the volume before being detected at the receiver Žscattering and diffraction losses.. In addition, absorption phenomena occur when particles move relative to the suspending medium and the mechanical energy degrades to heat Žviscous losses.; and temperature differences develop between phases with mechanical energy going again into heat Žthermal losses.. Epstein and Carhart w1x and Allegra and Hawley w2x have shown that any of these attenuation phenomena can be accurately characterised, through fundamental equations based on the laws of conservation of mass, energy, and momentum, the thermodynamic equations of state, and stress-strain relations for isotropic elastic solids or viscous fluids. That is, by formulating the wave equations which describe the interaction between sound waves and particulates. In this manner, the attenuation spectrum associated with any particle size distribution and particle concentration can be predicted for any suspension or emulsion as
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
Fig. 1. Variation of attenuation with particle size at different frequencies.
long as a set of mechanical, thermodynamic, and transport properties is known for both the dispersed and continuous phases. 4. Attenuation spectra The relationship between spectral data and the particle size distribution can be understood by considering the curves shown in Fig. 1 which are valid for the case of rigid high density particles suspended in water. Each curve depicts the attenuation at a fixed frequency as a function of the size of a monosize
497
population with a fixed known concentration. The cyclic nature of the functional dependence of the attenuation with particle size illustrates that if we measured the attenuation at a single frequency with perfect accuracy and resolution, there would be four potential monosize distributions Žtwo in the region of viscous attenuation, one in the Rayleigh scattering region, and a fourth in the diffraction zone. which could have produced that measured attenuation. On further analysis, as the frequency increases, the curves maintain a similar shape but shift towards smaller sizes, i.e. the different attenuation phenomena seem to depend on the ratio between the particle size and the wavelength. Therefore, if the attenuation of the sound wave were to be measured at two properly selected different frequencies then the number of monosize distributions which could have produced the measured attenuation is theoretically reduced to just one by simply comparing the four candidates coming out from each of the two curves associated with the transmitted frequencies and searching for a coincidence. In the absence of either measurement or modelling errors, two frequencies would suffice to
Fig. 2. Ultrasizer schematic.
498
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
Fig. 3. Acoustic attenuation spectrum } glass beads.
identify the correct size from the four possible sizes for each frequency. However, in the real world of noisy measurements, more than two frequencies are needed to differentiate the size of a monosize population. The actual size determined by observing how only one of the four candidate sizes for each frequency cluster around the same value for all frequencies while the other potential sizes seem to be totally dispersed. In the general case of a polysize distribution, there will be an infinite number of particle size distributions that could produce the single measured attenuation. However, the principle remains the same although, advanced mathematical inversion routines are needed to derive the particle size distribution. In practice, the wider the frequency range over which the spectral measurements are taken, the more independent pieces of information there are to uniquely deconvolve the size distribution, and the more stable, accurate,
and capable of a higher resolution, the performance of the instrument will be. 5. Attenuation measurement Alba following work with Du Pont and Alcoa, developed an instrument, Ultraspec, using the principles of acoustic spectroscopy for the measurement of the particle size of suspensions and emulsions. The full details of the instrument are outlined in US Patent No. 5,121,629 w3x the rights to which have been acquired by Malvern Instruments and which led to the development of the Malvern Ultrasizer. A schematic of the instrument is shown in Fig. 2. In order to make measurements of particle size distribution and concentration for a particular system, it is first necessary to calculate the model matrix for the particle-dispersant system. This is done automatically by the software following en-
Fig. 4. Particle size distribution of glass bead sample.
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
try of the appropriate physical constants. It is then necessary to place the sample under test into the instrument and to define the measurement conditions, which includes setting the frequency range for analysis and transducer spacing. Again this procedure is fully automated. Finally the acoustic attenuation spectrum is measured, and the particle size distribution is calculated. The whole measurement procedure can be completed in a matter of minutes once the instrument has been set up. The acoustic attenuation spectra for a sample of glass beads and the resulting particle size distribution and concentration as measured by the Ultrasizer are shown in Figs. 3 and 4. The result output can be displayed as shown or as a cumulative undersize curve. Various distribution statistics can be displayed as well as time series of a single parameter such as the mean of the distribution or the concentration. 6. Applications 6.1. Comparison with laser diffraction It is important to understand how acoustic spectroscopy compares with existing particle measurement technologies. Since laser diffraction is so widely used for determining final product quality, a number of samples have been measured using both techniques and good agreement between techniques has been obtained. Fig. 5 shows a comparison for a sample of glass beads with a mean size of 52 microns measured on a Malvern Mastersizer and Ultrasizer. The samples were dispersed in water in both cases but
Fig. 5. Glass beads Mastersizer vs. Ultrasizer.
499
Fig. 6. Comparison of mean diameter at various concentrations.
on the Mastersizer the measurement was made at a volume concentration of 0.1% whilst the Ultrasizer measurements were carried out at a volume concentration of 4%. 6.2. High concentration measurements A series of measurements on a glass bead sample was carried out at a number of concentrations. Fig. 6 shows that at concentrations varying from 2]12% by volume the size distribution measured by Ultrasizer did not vary. A number of measurements have also been made on polystyrene latexes. Fig. 7 shows the measurement of a 240 nm latex measured at a volume concentration of 10%. A significant amount of work has been conducted on inorganic pigments. Fig. 8 shows the particle size measurement conducted at-line for a milling process over a period of time. 6.3. Emulsions The measurement of particle size at high concentration is also important for emulsions whose properties can change on dilution. The measurement of low contrast density systems such as these can present difficulties for instruments based on sound just as transparent particles can cause difficulties for light scattering instruments. However the collection of spectral data over a broad frequency range, and its subsequent analysis using models based on theories due to Epstein and Carhart w1x, Allegra and Hawley w2x, Foldy w4x, Waterman w5x and others, plus theoretical extensions conducted by Alba enable good measurements to be achieved. The microemulsion illus-
500
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
Fig. 7. 240 nm polystyrene latex at 10% vrv.
trated in Fig. 9 is an emulsion produced by blending oil and water for 2 min in an industrial mixer. This produces a very stable colloidal emulsion,
which displays minimal creaming, aggregation or coalescence even after standing for several months.
Fig. 8. At line milling of a submicron inorganic pigment.
Fig. 9. Microemulsion measured at different temperatures.
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
501
7. Conclusions
Fig. 10. Meta-stable lubricant emulsion Ž¤ª 60 mm..
Fig. 9 depicts Ultrasizer results at 258C and 358C. The instrument delivered the same distribution in both cases. It is worth noting, however, that the basic spectra associated with these two measurements were significantly different over the whole frequency range. It is the change in physical properties with temperature, which establishes different spectra for the same distribution, the mathematical model built-in to the Ultrasizer taking into account that physical reality. A meta-stable lubricant emulsion consisting of 5% oil Ždensity 0.78 g cmy3 . was prepared in an industrial blender and measured on the Ultrasizer. Figs. 10 and 11 show the bimodal nature of an emulsion as captured using an image analysis system and the resulting measurement on Ultrasizer.
Acoustic techniques for the measurement of particle size at high concentrations have been available for a number of years. These techniques have in general used approximations to simplify the measurement apparatus. These approximations have limited the range of situations to which the techniques could be applied. The application of acoustic spectroscopy as laid out in this paper is based upon the accurate measurement of the sample’s attenuation spectrum over a wide frequency range. The analysis of these data is then carried out using models, which comprehensively describe the interaction of ultrasonic waves with particulate systems. These features have enabled the development of an instrument which can measure the particle size distribution and dispersed phase concentration of samples of low contrast density, such as emulsions as well as high density contrast systems such as suspensions of rigid particles. This can be achieved both over a wide size range from 0.01 mm to 1000 mm and concentration range from 0.5% V to 50% V, dependent upon the application. Acoustic spectroscopy as embodied in the Malvern Ultrasizer provides the means to characterise colloids, emulsions and suspensions at their normal concentrations, enabling new research into high concentration particulate systems to be car-
Fig. 11. Meta-stable lubricant emulsion measured on the Ultrasizer.
502
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
ried out. The robust sensor technology used provides the basis for the development of instrumentation for the on-line monitoring and ultimately the control systems of particulate production processes. References w1x P.S. Epstein, R.R. Carhart, J. Acoust. Soc. Am. 25 Ž1953. 533.
w2x J.R. Allegra, S.A. Hawley, J. Acoust. Soc. Am. S1 Ž1972. 1545]1564. w3x F. Alba, Method and Apparatus for Determining Particle Size Distribution and Concentration in a Suspension Using Ultrasonics, US Patent No. 5,121,629, 1992. w4x L.L. Foldy, Phys. Rev. 67 Ž1945. 107]119. w5x P.C. Waterman, R. Truell, J. Math. Phys. 2 Ž1961. 512]537.
Acoustic spectroscopy as a technique for the particle sizing of high concentration colloids, emulsions and suspensions F. Albaa , G.M. Crawley b, J. Fatkinb,U , D.M.J. Higgsb, P.G. Kippax b b
a Felix Alba Consultants Inc., Murray, UT, USA Mal¨ ern Instruments Ltd., Spring Lane South, Mal¨ ern, Worcestershire, UK
Abstract The particle size distribution of particles in liquid-based suspensions and emulsions is an important parameter in a wide variety of industrial applications. Many particle-sizing methods require the transmission of light through a sample of the system, and therefore these particulate systems must be severely diluted. Many systems are unstable on dilution and therefore have to be measured at high volume concentration. Sound waves interact with both the suspending medium and the dispersed phase and are able to propagate through concentrated systems. The development of new ultrasonic transducer technology together with advances in digital signal processing has opened the way for a powerful new analysis termed acoustic attenuation spectroscopy. The technique consists of propagating ultrasonic waves of a range of frequencies through the particulate system and accurately measuring the attenuation at each frequency. This attenuation spectrum can be converted to a particle size distribution and a measure of the concentration of the dispersed phase. It offers the particle technologist the means to monitor and control particle formation and reduction processes. Q 1999 Elsevier Science B.V. All rights reserved. Keywords: Particle size analysis; Concentrated systems; Acoustic spectroscopy
1. Introduction The particle size distribution of suspensions and emulsions is an important parameter in a wide variety of industrial applications. The techniques to measure particle size have been developed in response to specific needs and the technology available at the time. Laser diffraction is currently the most widely used technique for U
Corresponding author.
measurement of particle size in suspensions, emulsions, dry powders, and aerosols in the range between one tenth of a micron and a few millimetres. It is successful because of its wide applicability and the reproducibility, speed, and simplicity of the measurement procedure. However, since the principle requires transmission of light and assumes single particle scattering, the technique is limited to making measurements on dilute samples. Sound waves interact with particles in a similar manner to light but have the advantage that they
0927-7757r99r$ - see front matter Q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 Ž 9 8 . 0 0 4 7 3 - 7
496
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
can travel through concentrated suspensions and emulsions. Particle size analysers using soundbased measurement principles have been available for a number of years, however, these techniques operate over limited size ranges and work best with dense, rigid particles. A technique for particle size analysis using acoustic attenuation spectroscopy has been developed specifically to overcome these limitations. It utilises state of the art ultrasonic transducer technology, digital signal processing and is based upon classical acoustical principles allowing the particle technologist to study high concentration particle systems. These advances have been incorporated in an instrument known as the Ultrasizer and it has been used in a number of applications where accurate particle size measurement was previously impossible, for example in the on-line monitoring of lubricant emulsions or the direct measurement of a foodstuff such as mayonnaise. The instrument measures particles in the size range from 0.01 mm to 1000 mm Ždepending on the application. and simultaneously calculates the dispersed phase concentration. Robust construction enables the technique to be used in on-line applications in particulate process control. Particle size analysis using acoustic attenuation spectroscopy consists of Ža. predicting the attenuation spectra for any particle size distribution and concentration; Žb. measuring the attenuation spectra for the sample; and Žc. inverting the measured attenuation spectrum to a particle size distribution and dispersed phase concentration. 2. Theory of acoustic attenuation spectroscopy Acoustic attenuation spectroscopy for the particle size measurement of suspensions and emulsions consists of transmitting ultrasound of different frequencies, typically from 1 MHz up to 160 MHz through a sample with the attenuation being accurately measured. Such a broad frequency range is obtained by using two pairs of broad band ultrasonic transducers that produce waves with minimal deviation from the plane wave regime. The measured attenuation of the sound wave
as a function of frequency is called the acoustic attenuation spectrum and constitutes a signature for the particular suspension or emulsion in the sense that there is a one-to-one correspondence between the particle size distributionrparticle concentration pair and the associated spectrum. To derive the particle size distribution and particle concentration from the spectral data, the spectrum associated with any conceivable particle size distribution and particle concentration has to be capable of being accurately predicted. The actual spectral data produced by the specific suspensionremulsion being tested has then to be measured with very high accuracy and, finally, a stable, high resolution, mathematical inversion procedure is used to extract the size information from the measured spectral data. 3. Attenuation mechanisms When a sound wave passes through a particulate system, changes occur to the wave, as well as to the two phases of the medium. A particle presents a discontinuity to sound propagation and the wave scatters with a redistribution of the acoustic energy throughout the volume before being detected at the receiver Žscattering and diffraction losses.. In addition, absorption phenomena occur when particles move relative to the suspending medium and the mechanical energy degrades to heat Žviscous losses.; and temperature differences develop between phases with mechanical energy going again into heat Žthermal losses.. Epstein and Carhart w1x and Allegra and Hawley w2x have shown that any of these attenuation phenomena can be accurately characterised, through fundamental equations based on the laws of conservation of mass, energy, and momentum, the thermodynamic equations of state, and stress-strain relations for isotropic elastic solids or viscous fluids. That is, by formulating the wave equations which describe the interaction between sound waves and particulates. In this manner, the attenuation spectrum associated with any particle size distribution and particle concentration can be predicted for any suspension or emulsion as
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
Fig. 1. Variation of attenuation with particle size at different frequencies.
long as a set of mechanical, thermodynamic, and transport properties is known for both the dispersed and continuous phases. 4. Attenuation spectra The relationship between spectral data and the particle size distribution can be understood by considering the curves shown in Fig. 1 which are valid for the case of rigid high density particles suspended in water. Each curve depicts the attenuation at a fixed frequency as a function of the size of a monosize
497
population with a fixed known concentration. The cyclic nature of the functional dependence of the attenuation with particle size illustrates that if we measured the attenuation at a single frequency with perfect accuracy and resolution, there would be four potential monosize distributions Žtwo in the region of viscous attenuation, one in the Rayleigh scattering region, and a fourth in the diffraction zone. which could have produced that measured attenuation. On further analysis, as the frequency increases, the curves maintain a similar shape but shift towards smaller sizes, i.e. the different attenuation phenomena seem to depend on the ratio between the particle size and the wavelength. Therefore, if the attenuation of the sound wave were to be measured at two properly selected different frequencies then the number of monosize distributions which could have produced the measured attenuation is theoretically reduced to just one by simply comparing the four candidates coming out from each of the two curves associated with the transmitted frequencies and searching for a coincidence. In the absence of either measurement or modelling errors, two frequencies would suffice to
Fig. 2. Ultrasizer schematic.
498
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
Fig. 3. Acoustic attenuation spectrum } glass beads.
identify the correct size from the four possible sizes for each frequency. However, in the real world of noisy measurements, more than two frequencies are needed to differentiate the size of a monosize population. The actual size determined by observing how only one of the four candidate sizes for each frequency cluster around the same value for all frequencies while the other potential sizes seem to be totally dispersed. In the general case of a polysize distribution, there will be an infinite number of particle size distributions that could produce the single measured attenuation. However, the principle remains the same although, advanced mathematical inversion routines are needed to derive the particle size distribution. In practice, the wider the frequency range over which the spectral measurements are taken, the more independent pieces of information there are to uniquely deconvolve the size distribution, and the more stable, accurate,
and capable of a higher resolution, the performance of the instrument will be. 5. Attenuation measurement Alba following work with Du Pont and Alcoa, developed an instrument, Ultraspec, using the principles of acoustic spectroscopy for the measurement of the particle size of suspensions and emulsions. The full details of the instrument are outlined in US Patent No. 5,121,629 w3x the rights to which have been acquired by Malvern Instruments and which led to the development of the Malvern Ultrasizer. A schematic of the instrument is shown in Fig. 2. In order to make measurements of particle size distribution and concentration for a particular system, it is first necessary to calculate the model matrix for the particle-dispersant system. This is done automatically by the software following en-
Fig. 4. Particle size distribution of glass bead sample.
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
try of the appropriate physical constants. It is then necessary to place the sample under test into the instrument and to define the measurement conditions, which includes setting the frequency range for analysis and transducer spacing. Again this procedure is fully automated. Finally the acoustic attenuation spectrum is measured, and the particle size distribution is calculated. The whole measurement procedure can be completed in a matter of minutes once the instrument has been set up. The acoustic attenuation spectra for a sample of glass beads and the resulting particle size distribution and concentration as measured by the Ultrasizer are shown in Figs. 3 and 4. The result output can be displayed as shown or as a cumulative undersize curve. Various distribution statistics can be displayed as well as time series of a single parameter such as the mean of the distribution or the concentration. 6. Applications 6.1. Comparison with laser diffraction It is important to understand how acoustic spectroscopy compares with existing particle measurement technologies. Since laser diffraction is so widely used for determining final product quality, a number of samples have been measured using both techniques and good agreement between techniques has been obtained. Fig. 5 shows a comparison for a sample of glass beads with a mean size of 52 microns measured on a Malvern Mastersizer and Ultrasizer. The samples were dispersed in water in both cases but
Fig. 5. Glass beads Mastersizer vs. Ultrasizer.
499
Fig. 6. Comparison of mean diameter at various concentrations.
on the Mastersizer the measurement was made at a volume concentration of 0.1% whilst the Ultrasizer measurements were carried out at a volume concentration of 4%. 6.2. High concentration measurements A series of measurements on a glass bead sample was carried out at a number of concentrations. Fig. 6 shows that at concentrations varying from 2]12% by volume the size distribution measured by Ultrasizer did not vary. A number of measurements have also been made on polystyrene latexes. Fig. 7 shows the measurement of a 240 nm latex measured at a volume concentration of 10%. A significant amount of work has been conducted on inorganic pigments. Fig. 8 shows the particle size measurement conducted at-line for a milling process over a period of time. 6.3. Emulsions The measurement of particle size at high concentration is also important for emulsions whose properties can change on dilution. The measurement of low contrast density systems such as these can present difficulties for instruments based on sound just as transparent particles can cause difficulties for light scattering instruments. However the collection of spectral data over a broad frequency range, and its subsequent analysis using models based on theories due to Epstein and Carhart w1x, Allegra and Hawley w2x, Foldy w4x, Waterman w5x and others, plus theoretical extensions conducted by Alba enable good measurements to be achieved. The microemulsion illus-
500
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
Fig. 7. 240 nm polystyrene latex at 10% vrv.
trated in Fig. 9 is an emulsion produced by blending oil and water for 2 min in an industrial mixer. This produces a very stable colloidal emulsion,
which displays minimal creaming, aggregation or coalescence even after standing for several months.
Fig. 8. At line milling of a submicron inorganic pigment.
Fig. 9. Microemulsion measured at different temperatures.
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
501
7. Conclusions
Fig. 10. Meta-stable lubricant emulsion Ž¤ª 60 mm..
Fig. 9 depicts Ultrasizer results at 258C and 358C. The instrument delivered the same distribution in both cases. It is worth noting, however, that the basic spectra associated with these two measurements were significantly different over the whole frequency range. It is the change in physical properties with temperature, which establishes different spectra for the same distribution, the mathematical model built-in to the Ultrasizer taking into account that physical reality. A meta-stable lubricant emulsion consisting of 5% oil Ždensity 0.78 g cmy3 . was prepared in an industrial blender and measured on the Ultrasizer. Figs. 10 and 11 show the bimodal nature of an emulsion as captured using an image analysis system and the resulting measurement on Ultrasizer.
Acoustic techniques for the measurement of particle size at high concentrations have been available for a number of years. These techniques have in general used approximations to simplify the measurement apparatus. These approximations have limited the range of situations to which the techniques could be applied. The application of acoustic spectroscopy as laid out in this paper is based upon the accurate measurement of the sample’s attenuation spectrum over a wide frequency range. The analysis of these data is then carried out using models, which comprehensively describe the interaction of ultrasonic waves with particulate systems. These features have enabled the development of an instrument which can measure the particle size distribution and dispersed phase concentration of samples of low contrast density, such as emulsions as well as high density contrast systems such as suspensions of rigid particles. This can be achieved both over a wide size range from 0.01 mm to 1000 mm and concentration range from 0.5% V to 50% V, dependent upon the application. Acoustic spectroscopy as embodied in the Malvern Ultrasizer provides the means to characterise colloids, emulsions and suspensions at their normal concentrations, enabling new research into high concentration particulate systems to be car-
Fig. 11. Meta-stable lubricant emulsion measured on the Ultrasizer.
502
F. Alba et al. r Colloids Surfaces A: Physiochem. Eng. Aspects 153 (1999) 495]502
ried out. The robust sensor technology used provides the basis for the development of instrumentation for the on-line monitoring and ultimately the control systems of particulate production processes. References w1x P.S. Epstein, R.R. Carhart, J. Acoust. Soc. Am. 25 Ž1953. 533.
w2x J.R. Allegra, S.A. Hawley, J. Acoust. Soc. Am. S1 Ž1972. 1545]1564. w3x F. Alba, Method and Apparatus for Determining Particle Size Distribution and Concentration in a Suspension Using Ultrasonics, US Patent No. 5,121,629, 1992. w4x L.L. Foldy, Phys. Rev. 67 Ž1945. 107]119. w5x P.C. Waterman, R. Truell, J. Math. Phys. 2 Ž1961. 512]537.