Experimental comparison of measurement techniques for drop size distributions in liquid/liquid dispersions
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DOI: 10.1007/s00348-010-0918-9
- Cite this article as:
- Maaß, S., Wollny, S., Voigt, A. et al. Exp Fluids (2011) 50: 259. doi:10.1007/s00348-010-0918-9
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Abstract
An online measurement technique for drop size distribution in stirred tank reactors is needed but has not yet been developed. Different approaches and different techniques have been published as the new standard during the last decade. Three of them (focus beam reflectance measurement, two-dimensional optical reflectance measurement techniques and a fiber optical FBR sensor) are tested, and their results are compared with trustful image analysis results from an in situ microscope. The measurement of drop sizes in liquid/liquid distribution is a major challenge for all tested measurement probes, and none provides exact results for the tested system of pure toluene/water compared to an endoscope. Not only the size analysis but also the change of the size over time gives unreasonable results. The influence of the power input on the drop size distribution was the only reasonable observation in this study. The FBR sensor was not applicable at all to the used system. While all three probes are based on laser back scattering, the general question of the usability of this principle for measuring evolving drop size distributions in liquid/liquid system is asked. The exterior smooth surface of droplets in such systems is leading to strong errors in the measurement of the size of the drops. That leads to widely divergent results. A different measurement principle should be used for online measurements of drop size distributions than laser back scattering.
Abbreviations
- CLD
Chord length distribution
- DSD
Drop size distribution
- FBR
Forward–backward ratio
- FBRM
Focus beam reflectance measurement
- fps
Frames per second
- ORM
Optical reflectance measurement
- PSD
Particle size distribution
List of symbols
- D
Stirrer diameter (m)
- d_{32}
Sauter mean diameter (m)
- d_{l,B}
Immersion depth of baffles (m)
- d_{P}
Particle diameter (m)
- d_{Max}
Maximum measurable particle diameter (m)
- H
Liquid level of the tank (m)
- h
Distance between stirrer and tank bottom (m)
- l_{C}
Chord length (m)
- N
Stirrer speed (rpm)
- n
Refractive index (−)
- P/V
Power input (W/m³)
- Po
Power number
- Q_{0}
Cumulative number distribution (−)
- q_{0}
Number density distribution (1/m)
- q_{3}
Volume density distribution (1/m)
- T
Tank diameter (m)
- t
Temperature (°C)
- t_{S}
Scanning time of one particle (s)
- v_{S}
Scanning velocity of the laser focal point (m/s)
- w_{B}
Width of baffles (m)
- w_{Tip}
Tip velocity of the stirrer (m/s)
- γ
Interfacial tension (mN/m)
- η
Dynamic viscosity (mPa s)
- ρ
Density (kg/m³)
- σ
Standard deviation (%)
- φ
Dispersed-phase fraction (−)
1 Introduction
Liquid–liquid dispersions in stirred vessels or mixers are often used technical applications in the chemical, pharmaceutical, mining, petroleum and food industry. For controlling and optimizing these systems, exact knowledge about the drop size distribution and its transient behavior under changes of energy input, temperature or composition is of major importance. Current mathematical descriptions of dispersion properties such as the drop size distribution (DSD) as a function of process and physical parameters in an inhomogeneous flow field are still inaccurate. With more accurate models, it would be much easier and cheaper to design and set up such reactors. The DSD describes the interfacial area, which is often the limiting factor for the mass transfer, a key parameter for industrial systems and scale-up. But scale-up on the base of theoretical assumptions is not possible without reliable and consequently validated models. In conclusion, sizing of particles in industrial processes is of great technical interest, and therefore, techniques have been developed, based on different physical principles.
The difficulty in the use of stirred vessels is that the turbulence in the vessel is not very well characterized since it is not only inhomogeneous throughout the vessel, but it is highly anisotropic consisting of high shear regions on the surface of the impeller. Today, many different techniques for sizing transient drop behavior in such vessels are available. Some work in situ but a lot of them analyze by withdrawing samples over time (Bae and Tavlarides 1989; Bürkholz and Polke 1984; Desnoyer et al. 2003; Hay et al. 1998; Hurlburt and Hanratty 2002), which are later diluted or stabilized, prior to their measurements. These sampling techniques neither guarantee that the drop sizes are frozen, nor that they are preserved during the sampling (Martinez-Bazan et al. 1999; Pacek et al. 1994). In the following work, we want to focus on inline measurement techniques for sizing drops in liquid/liquid dispersions.
Simmons et al. (2000) tested two optical laser-based drop size measurement techniques, an offline diffraction technique and an inline back scattering technique. They have been tested with glass beads of a known size. Both techniques were found to be suitable for the measurement of liquid–liquid dispersions in pipe flows, but they are limited to different concentration ranges. The diffraction technique is limited to dispersed-phase concentrations below 3% by volume, while the backscatter technique operated satisfactorily only at concentrations above 5%.
Based on this promising results, the use of laser back scattering probes for different applications like sizing cell cultures (McDonald et al. 2001), nucleation or crystallization processes (Barrett and Glennon 2002) increased. The technique of focused beam reflectance measurement (FBRM) became very well suited for in situ particle characterization. Heath et al. (2002) compared the FBRM to conventional particle sizing techniques (laser diffraction and electrical sensing zone) for a range of sieved aluminum or calcite suspensions. The mode average of the square-weighted chord length was found to be comparable to other sizing techniques. However, FBRM measurements are not easy to interpret, because the measured chord length distribution (CLD) is different from any type of particle size distribution (PSD) (Kail et al. 2009). Methods are discussed to transform the measured chord length distribution into a size (diameter) distribution (Li and Wilkinson 2005; Worlitschek et al. 2005; Yu et al. 2008).
For a spherical drop, chord lengths are generally shorter than the real drop diameter and so the chord length distribution is wider than the originally one. While the laser beam crosses each chord randomly, the number of times a given chord length is measured takes the form of a probability density function. Stochastically models have been developed and published for transformation of CLD’s into DSD’s under the assumption of perfect spherical particles. For a broader overview, see especially the work of Hu et al. (2006). Large errors were found between calculated DSD’s from CLD’s and measured DSD’s (Greaves et al. 2008; Tadayyon and Rohani 1998; Yu et al. 2008).
A large community of users successfully applies FBRM technology for monitoring, fault detection and quality control of dynamic solid–liquid or gas–liquid processes. Greaves et al. (2008) applied it to emulsions and ice and clathrate hydrate formation processes. The accuracy of the FBRM has been explored by a direct comparison with a visual method. Therefore, a particle video microscope (PVM) probe was used. It was found that while the FBRM can successfully identify system changes, certain inaccuracies exist in the chord length distributions. Particularly, the FBRM was found to undersize droplets in an emulsion and was unable to measure full agglomerate sizes. The onset of ice and hydrate nucleation and growth were successfully detected by the FBRM. Also, Boxall et al. (2010) analyzed water drop sizes in crude oil emulsions with a PVM and an FBRM probe for a variety of oils spanning over two orders of magnitude in viscosity and for varying shear rates. The droplet size was shown to be dramatically undersized by the FBRM probe, even taking into account that it measures chord lengths rather than actual sizes. An empirical fit was found to give reasonable agreement between the FBRM and PVM mean sizes measured for droplets with an average error less than 20%.
Cull et al. (2002) and Lovick et al. (2005) employed an 3D optical reflectance measurement (ORM) technique, similar in operation to the FBRM and the 2D optical reflectance measurement in a liquid–liquid biocatalytic reactor.
Direct photography of liquid–liquid dispersions remains a trustful technique for measuring drop size distributions. It has been compared to capillary techniques (Pacek and Nienow 1995), external sampling with stabilized emulsions (O’Rourke and MacLoughlin 2005) and became a standard for testing the reliability of other measurement devices (Andrès et al. 1996; Greaves et al. 2008; Hu et al. 2006). In the following work, the focus beam reflectance measurement, the two-dimensional optical reflectance measurement and fiber optical sensor will be used for the comparative experiments. These laser-based online techniques will be evaluated with image analysis results. However, the aim of this publication is to test promising measurement techniques for drop size distributions to find a tool that allows online particle sizing, a necessary base for drop size control.
2 Experimental apparatus and procedure
2.1 Measurement technique: laser systems
Laser methods can be subdivided into three main groups, based on their specific operating principle (Fraunhofer diffraction, spatial filtering and laser back scattering). Generally, all are very fast and so able to be used online. The most common method is laser back scattering, which is the basic principle for all presented probes in this study.
2.1.1 Dimensional optical reflectance measurement technique
With additional mathematical transformation algorithms, the chord length distribution can be transformed into a droplet size distribution. The 2D-ORM technique is especially suited for high-density emulsions as the droplet sizes are estimated by back reflection in close vicinity to the sensor window (Fricke et al. 2007). A very large number of drops, a magnitude of several thousands, are analyzed by the probe. This large number should ensure that the maximum drop size, which is equal to the maximum chord length measured, has been captured. A drawback of this technique is the size of the probe (diameter = 30.0 mm) in relation to laboratory scale geometry.
2.1.2 Fiber optical FBR sensor
2.1.3 Focus beam reflectance measurement
Another in situ laser-based measurement technique that uses light back scattering effects is the focused beam reflectance method (FBRM) (Ruf et al. 2000). The principle of the cylindrical FBRM probe is shown in Fig. 2b. The optic rotates at a high velocity and focuses the laser beam near to the sapphire window. Passing particles backscatter the laser beam so that the chord length of the particle is computed by multiplying the scanning time with the beam speed. Usually, thousands of chord lengths are measured each second. This allows determining a robust chord length distribution, which can be used to illustrate changes in particle dimension, particle population and particle shape in time.
All laser techniques used in this article determine characteristic chord length distributions (CLD). Therefore, the backscattered pulse from the laser probe is measured in the focus plane from one edge of the particle to an opposing edge. In the first approximation, the chord length of a scanned particle l_{C} can be accounted for by l_{C} = v_{S} × Δt_{S}. Here, Δt_{S} is the time of flight for a pulse. The proportionality constant in this equation is v_{S}, the velocity of the scanning focal point.
2.1.4 Measurement technique: endoscope technique
Another major type of measurement techniques sizing drops in situ are photo-based methods working with image recognition. This method gives accurate values for the drop sizes in the analyzed system which are reliable and accurate (Hu et al. 2006; Pacek et al. 1994). The endoscope results are used as the “standard” with which the other probes are compared.
2.2 Stirred tank
Listing of the data on used toluene/water system
γ (mN/m) at 20°C | Refractive index n (−) at 20°C | ρ_{toluene} (kg/m^{3}) at 20°C | η_{toluene} (mPa s) at 20°C |
---|---|---|---|
36 | 1.496 | 870 | 0.55 |
Dimensions and characteristics of the used stirred tank
T | H | d_{l, B} | w_{B} | h | D | Po |
---|---|---|---|---|---|---|
150 mm | T | 0.8 T | 0.08 T | 0.33 T | 0.33 T | 3.8 (−) |
2.3 Measurement procedure
The probes were introduced into the tank close to the stirrer at the same position to eliminate influence of the local position. As shown in Fig. 5, always one laser probe was tested together with the endoscope. Transient drop size distributions were measured for each parameter combination for about 1 h. The Sauter mean diameter (d_{32} = Σd_{i}^{3}/Σd_{i}^{2}) is calculated out of the measured distribution. The particle diameter d_{i} is replaced with the chord length l_{C} for the calculation of the Sauter mean diameter resulting from the focus beam reflectance measurement system.
The used standard is the endoscope system. It was checked and then tested for sensitivity to the number of counted particles to ensure reliable results. For verification, a glass spheres/water suspension with known particle size distribution was used. This distribution was determined earlier, using a microscope over a plane with well-known distance. The satisfying comparison results for a monodisperse and a bimodal distribution are published by Ritter and Kraume (2000).
3 Results and discussion
For many processes, not only the mean diameter but also the width and the shape of the particle distributions are of major importance for the product. Only three of the four measurement techniques, used in this study, provide information about the whole distribution. The two-dimensional optical reflectance measurement techniques, the focus beam reflectance measurement and the endoscope are used to investigate the drop size distribution of the introduced system.
3.1 Drop size distributions
Comparing the results, it is obvious that all techniques achieve different drop size distributions, while analyzing the same system. The trustful image analysis results show drop diameter between 30 and 600 μm. These values are ten times larger than the results occurring from the FBRM or even 15 times larger than the results from the 2D-ORM. Therefore, the particle diameter is logarithmic plotted. Yet this axial allocation does not provide clear results of the particle diameter distributions for different stirrer speeds. The increasing energy dissipation with the increasing stirrer speed shows only explicit smaller drops for the endoscope technique but not for the two laser probes.
The two laser probes show a clear difference in the number of counts and in the characterization of the counts over the energy dissipation. The data achieved with the FBRM show a clear increase in the particle counts with an increase in the energy dissipation. The constant volume of the organic phase is dispersed more with increasing energy dissipation, so the particle size is decreasing and therewith the number of particles is increasing with a proportionality of (P/V)^{0.34}. The absolute numbers for the FBRM are about a factor of ten smaller than the absolute numbers for the 2D-ORM. Both probes are counting the bypassing drops over 5 s. This time delta can be changed by the user for shorter or longer integrations. The two-dimensional optical reflectance measurement techniques does not capture the maximum drop diameter even with the higher number of drop counts. The development over an increasing power input is increasing as for the FBRM but with a much lower proportionality of (P/V)^{0.01}, which means the counts are almost constant. Therefore, only the FBRM gives interpretable data.
3.2 Sauter mean diameter
The results of the FBR sensor are again close to the values of the endoscope but they do not reflect the change of the power input. The values generated from the measuring signal stayed nearly constant. Many different set-ups were used to adapt the FBR sensor to the used system of toluene and water but all attempts were without success. Only a suspension with a particle size smaller than 10 μm could be analyzed satisfactorily. This solid/liquid system of calcium carbonate (calcilit 4: CaCO_{3}) and water was mentioned for calibration by the producer.
For all dependencies of the steady-state Sauter mean diameter over the power input, the proportionalities have been calculated. The results in Fig. 13 from endoscope are comparable with the results from Ritter (2002). The dependency he found for the system of toluene/water of the Sauter mean diameter on P/V was d_{32} ~ P/V^{−0.08} for φ = 0.125. The higher dispersed-phase fraction in this study leads to a slightly lower exponent of P/V which was generally also reported by Kraume et al. (2004). Higher values of φ are leading to higher coalescence rates and therewith to a lower dependency on the power input.
The 2D-ORM and the endoscope technique show nearly the same proportionally of the Sauter mean diameter over power input. So it should be possible to use the 2D-ORM probe in liquid/liquid dispersions to analyze and control the change of DSD for different power inputs.
Also the focus beam reflectance measurement shows physical meaning full behavior. For higher energy dissipation rates, the mean drop size is decreasing. The exponent of P/V with −0.11 is stronger than the exponent resulting from the image analysis. Such proportionalities and even higher values in a toluene/water system have been reported by Gäbler et al. (2006) at a pH 3. So it seems that the results from the FBRM do roughly reflect the influence of P/V on the steady-state Sauter mean diameter. It has already been presented in literature that the deviations of the FBRM to image analysis results are reproducible and can be correlated with a linear relation (Wollny et al. 2008).
In pure systems like used in this study, one drop scatters the laser light back to the probe as three separated beams. Therefore, the measured chord length is too small and the number of measured particles is too high. For ceramic spheres of comparable size with a rougher surface, both measurement techniques achieve higher values for the particle size (see also the reports of Greaves et al. (2008)). An alternative for solid particles is the increasing in the roughness of the drop surface. The deviation between the endoscope and the FBRM was decreasing for experiments with surfactants, which are changing the shape of the drops (but also the physical properties).
Summary of the parameters and results of the four different techniques for the decision process
Requirements | 2D-ORM | FBRM | FBR sensor | Endoscope |
---|---|---|---|---|
In situ | + | + | + | + |
Online | + | + | + | − |
Local analysis | + | + | + | + |
Probe diameter (mm) | 30 | 25 | 4 | 6–15 |
Measurement range (μm) | 1–1,000 | 1–1,000 | 1–300 | 5–5,000 |
Output quantity | DSD/CLD | CLD | Mean particle diameter | DSD |
Quantitative results for the water/toluene system | No transient analysis possible, right tendencies with wrong absolute values (two decades deviation) | No transient analysis possible, right tendencies with wrong absolute values (one decade deviation) | Not usable for the applied system | Usable as standard method for exact results |
4 Conclusion
Comparative experiments between a photo-based endoscope technique and three laser techniques (FBR sensor, 2D-ORM and FBRM) have been carried out to determine an exact online measurement technique for drop size distributions. The endoscope has been used as a standard, which against the other techniques compete.
It is clearly shown that the measurement of drop sizes in liquid/liquid distribution is a major challenge for all tested measurement probes and none provides exact results for the tested system of pure toluene/water. Differencing the free laser probes, the worst results were observed from the FBR sensor. It was not applicable at all to the used system. The influence of the power input on the drop sizes showed reasonable results for the FBRM and the 2D-ORM. The same proportionally range of the Sauter mean diameter over power input for the image analysis results and both probes, the focus beam reflectance measurement and the two-dimensional optical reflectance measurement techniques, was observed. So it is possible to use them in liquid/liquid dispersions to analyze and control the change of DSD for different stirrer speeds. Both probes gave unreasonable results over time for a constant stirrer speed and are thereby no online probes for such liquid/liquid dispersions. While all three probes are based on laser back scattering, the general question of the usability of this principle for measuring drop size distributions in liquid/liquid system is asked. The exterior smooth surface of droplets in such systems is leading to strong errors in the measurement of the size of the drops. That leads to widely divergent results. This effect of the kind of the surface is analyzed in detail by adding micro-particles to the system. The produced synthetic roughness of the drop surface is leading to much more reasonable results of the FBRM probe. Still the absolute values are divergent from the image analysis results. A different measurement principle has to be used for online measurements of drop size distributions than laser back scattering.
Acknowledgments
We gratefully acknowledge the financial support from the Bayer Technology Services GmbH and especially Dr. Joachim Ritter, who gave the basic ideas for this research.