Drop size distribution in highly concentrated liquid liquid dispersions using a light back scattering method

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1 Journal of Chemical Technology and Biotechnology J Chem Technol Biotechnol :55 55 (5) DOI: 1.1/jctb.15 Drop size distribution in highly concentrated liquid liquid dispersions using a light back scattering method J Lovick, 1 AA Mouza, SV Paras, GJ Lye 3 and P Angeli 1 1 Department of Chemical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK Department of Chemical Engineering, Aristotle University of Thessaloniki, Univ Box 55, GR 51, Thessaloniki, Greece 3 Department of Biochemical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK Abstract: New data are presented on drop size distribution at high dispersed phase fractions of organicin-water mixtures, obtained with a light back scattering technique (3 Dimensional Optical Reflectance Measurement technique, 3D ORM). The 3D ORM technique, which provides fast, in-situ and on-line drop distribution measurements even at high concentrations of the dispersed phase, is validated using an endoscope attached to a high-speed video recorder. The two techniques compared favourably when used in a dispersion of oil (density (ρ) = kg m 3,viscosity(µ) = 5.5 mpa s, interfacial tension (σ i ) =.7 mn m 1 ) in water for a range of 5 1% dispersed phase fractions. Data obtained with the ORM instrument for dispersed phase fractions up to % and impeller speeds rpm showed a decrease in the maximum and the Sauter mean drop diameters with increasing impeller speed. Phase fractions did not seem to significantly affect drop size. Both techniques showed that drop size distributions could be fitted by the log-normal distribution. 5 Society of Chemical Industry Keywords: liquid liquid dispersions; drop size; stirred vessels 1 INTRODUCTION The mixing of immiscible liquids is commonly encountered in process industries, with many applications such as extraction, multiphase (bio)reactions and suspension polymerisation. In these processes drop diameter distribution is an important parameter as it defines the available interfacial area for mass transfer. Drop size will also affect phase separation after the completion of the multiphase process. Drop diameter distribution depends on the rate of drop break-up and coalescence. In turbulent systems the theory developed by Hinze 1 is being used to predict the maximum drop size, d max, that can resist break-up. In stirred tanks d max can be related to the tank Weber number, We T, as follows: We T = ρ cn D i 3 σ i (1) where ρ c is the continuous phase density, N is the impeller speed, D i is the impeller diameter and σ i is the interfacial tension. To account for the effect of increasing dispersed phase volume fraction (which can cause coalescence but also decrease turbulence intensity) correlations in the form of eqn () have been suggested for d max : d max /D i = c 1 (1 + c φ)we T. () where φ is the volume fraction of the dispersed phase and c 1 and c are constants. The maximum drop diameter is important since it is generally considered proportional to the Sauter mean diameter, d 3,,3 although this has been questioned.,5 The Sauter diameter, commonly used in processes depending on interfacial area,,3, is defined as the ratio of the third to the second moment of the drop size distribution: d 3 = k 3 n i d i i=1 k n i d i i=1 (3) where d i is the drop diameter in bin i and n i is the number of drops with diameter in bin i. Based on the proportionality to d max, correlations have been proposed for d 3 that take the form of Correspondence to: P Angeli, Department of Chemical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK p.angeli@ucl.ac.uk Contract/grant sponsor: Royal Society Contract/grant sponsor: EPSRC (Received 11 June ; revised version received 7 October ; accepted 1 October ) Published online March 5 5 Society of Chemical Industry. J Chem Technol Biotechnol 575/5/$3. 55

2 J Lovick et al. eqn (), which were verified experimentally. This aforementioned equation predicts an increase in drop size with increasing dispersed phase volume fraction, a phenomenon that was observed in investigations where dispersed phase fraction increased up to about %. 7 At higher fractions (usually above 5%), however, a further increase in the dispersed phase concentration results in decreasing drop size.,9 This behaviour was attributed to a change in the drop breakage mechanism from turbulent eddy at low concentrations to boundary layer at high concentrations. Similarly, in a dispersion, a minimum drop size exists, d min, which is the minimum drop diameter that can resist coalescence. 1 Compared with d max, fewer correlations have been proposed for predicting d min, while the Kolmogoroff length scale of turbulence has also been used as an estimate of the minimum drop size.,11 Shinnar 1 argued that in coalescing systems d 3 would be proportional to d min. Experimental data on average drop size mainly exist for low dispersed phase concentrations, where a variety of measuring techniques can be used. Few studies looked at high concentrations but only Brown and Pitt,13 and Pacek et al 1 obtained drop sizes in unstable dispersions; in all other cases surfactantstabilised emulsions were used.,9 Information on drop size distribution is even more limited while existing studies often propose different statistical correlations to describe the range of drop sizes in stirred vessels. Normal distributions have been suggested by Chen and Middleman 15 and Brown and Pitt for standard configuration stirred tanks. Brown and Pitt also reported a bi-modal distribution that can be modelled as a sum of two normal ones. Zhou and Kresta, 1 for a range of impeller types, found that the distribution shape changed with increasing impeller speed from a single peak at small drop sizes, to a double peak at small and large sizes and finally to a single peak at intermediate sizes. They concluded that a single distribution could not describe their experimental data satisfactorily. In aqueous organic systems close to phase inversion Pacek et al 1 found that the type of distribution would depend on the continuous phase, being uni-modal in the aqueous continuous systems and bi-modal in the organic continuous ones. In contrast Pacek et al 5 using a turbine impeller, observed a bi-modal distribution in aqueous continuous systems at low agitation speeds, which changed to a uni-modal one as the impeller speed increased. Interestingly, normal or log-normal functions that fitted the experimental data well when these were plotted in terms of cumulative volume, could not represent satisfactorily the same data when they were plotted in terms of drop number frequency. The Swarz Bezemer function also failed to predict the cumulative volume drop distribution. Some less known distributions that have been used for liquid liquid systems are the Erlang, the Weibull and the Gamma. 1 Gal-Or and Hoelscher 17 proposed a Gamma-type function that relates drop size distribution directly to the rotational speed of the impeller and the dispersed phase fraction. Gallego- Linzon and Perez de Ortis 1 applied a modified Rosin Rammler function to fit their data in emulsion liquid membrane systems using flat blade turbines with different diameters. The limited available data on average drop size and distribution, especially in unstable dispersions and at high dispersed phase volume fractions, are partly due to the difficulty in performing such measurements. Sample withdrawal was one of the first techniques to be used. The withdrawn drops can be measured continuously within the sampling tube by a microscope 9,19 or a Coulter counter, which records changes in electrical resistance caused by drops passing through. Alternatively, drops can be frozen using a surfactant and measured offline with a microscope and a photometer. 1 The problems associated with the withdrawal technique are coalescence of sampled drops inside the withdrawal tube or during the measurement and biased sampling of certain drop sizes. At high dispersed phase fractions further problems can arise from droplets overlapping in the sample tube, which can be overcome by sample dilution, 19 or by ensuring that the diameter of the sample tube is smaller than the smallest drop diameter. 1 Absorption of light transmitted through a dispersion has been used to obtain average interfacial area in stirred vessels.,3 Weinstein and Treybal 7 extended the technique by incorporating the light transmitter and detector into a probe that could be put at different locations within a dispersion; this enabled local average drop sizes to be measured. Photography/video recording provide additional information on the actual shape of the drops. If used outside the vessel, these methods are non-intrusive but allow measurements away from the walls only in dilute dispersions. Pacek et al 1 studied the area close to the wall using an internal light source and reported results for mixtures with dispersed phase fractions up to 7%. The recent use of endoscopes has allowed recording at different locations within the container, overcoming the problem of dense dispersions (up to 3% 1 ) but in an intrusive way. The introduction of lasers resulted in a number of drop-size measuring techniques, where the amount of light scattered by the drops is related to their size. In diffraction, light scattered at low forward angles is detected while in back scattering light reflected back is collected by a detector mounted in the same guide as the light source. 5 7 In the former technique light has to pass through the dispersion which limits it to low dispersed phase fractions, while in the latter there is no such limitation. Simmons et al suggested that light diffraction was only suitable for dispersed phase fractions less than 3%, while back scattering could only be used at fractions greater than 5%. Comparisons of the two techniques at low volume fractions gave inconclusive results, which may suggest that considerable error can incur when the techniques 5 J Chem Technol Biotechnol :55 55 (5)

3 Drop size distribution in liquid liquid dispersions are used outside their range of applicability. 5, A Phase Doppler Particle Analyser (PDPA), where the phase difference between light scattered is measured from two collection angles, has also been used but requires very dilute dispersions. In this work a light back scattering technique was applied in unstable kerosene water dispersions to obtain drop size distributions. The light back scattering probe can be used on-line and be placed at any location within the dispersion thus allowing fast measurements at high dispersed phase fractions even in unstable systems. Results from the technique were evaluated against data from high-speed video recording which was combined with an endoscope. The technique was subsequently used to study drop sizes in oil-in-water dispersions at volume fractions up to %. EXPERIMENTAL APPARATUS The set-up for measuring drop sizes consisted of a standard configuration baffled cylindrical tank (id 13 mm) equipped with a six-bladed Rushton turbine (5 mm diameter) with its centre located 5 mm from the bottom of the vessel (Fig 1). The six blades had dimensions of 15 mm 15 mm, while the disc had a diameter of 5 mm. The impeller was constructed of 1 mm thick stainless steel. The test fluids used were tap water and kerosene (EXXSOL D1 with density ρ = kg m 3, viscosity µ = 5.5 mpa s, interfacial tension σ i =.7mNm 1 ), with the kerosene forming the dispersed phase. No surfactant was added to 17 mm 5 mm ORM 13 mm 5 mm Figure 1. Schematic diagram of the experimental set-up. Endoscope 1 1 min min min Figure. Evolution of number frequency drop size distribution with time for 35 rpm impeller speed and % oil fraction. Data obtained by ORM instrument. the mixture. At high dispersed phase fractions phase continuity was monitored with a conductivity probe. Fluids were mixed for 15 min before any measurements were taken; initial measurements over a period of 1 h had shown that after 15 min the drop size distribution as well as d 3 remained constant. The change in size distribution with time is illustrated in Fig for % oil and 35 rpm impeller speed. A 3 Dimensional Optical Reflectance Measurement (3D ORM) technique, based on light back scattering, was used for drop size distribution measurements. The results were evaluated against a method based on in-situ video recording. Both techniques are described in detail below. Data were collected at 5 mm from the bottom of the vessel at the height of the impeller (Fig 1). The dispersed phase volume fraction varied from 1% to %; in this range water was the continuous phase at all impeller speeds used as confirmed by the use of the conductivity probe. Impeller speeds ranged from 35 rpm to 55 rpm. The minimum impeller speed was chosen so that there was complete mixing of the two phases at all volume fractions used, while the maximum speed was the one that gave no air entrainment..1 Optical Reflectance Measurement (ORM) technique The Optical Reflectance Measurement (3D ORM) particle size analyser (by Messtechnik Schwartz GmbH ) can provide in-situ and on-line drop size distribution measurements. The technique uses a laser beam (with 75 nm wavelength) with a focal point. µm in diameter at a maximum distance 1 mm from the instrument front. By having a focal point close to the probe, the laser beam does not have to travel far through the liquid mixture and can therefore be used to measure chord lengths in high concentration dispersions. This focal point is rotated at a known velocity within the sample and tracks a 3D volume with.5 mm diameter. When the rotating beam intercepts a drop, light is scattered back from the chord length J Chem Technol Biotechnol :55 55 (5) 57

4 J Lovick et al. in the beam path which through the optical system of the instrument is transmitted to a detector where it is transformed to an electrical signal. From the signal duration and the known velocity of the rotating beam the chord length that was intercepted can be determined. A chord length distribution is therefore built up over a period of time. If the drops are assumed to be spherical, then their chord length distribution can be found analytically. It is however, the inverse problem that needs to be solved, ie to derive from a (measured) chord length distribution the (unknown) drop diameter distribution. The solution of the inverse problem is achieved numerically with the software DISPAS.5e. Since the probe can be used in-situ, the problems associated with sample withdrawal are also avoided. Also a very large number of drops, of the order of thousands, is sampled with the probe, much larger than in the commonly used photographic or sampling techniques. This large number ensures that the maximum drop size, which is taken equal to the maximum chord length measured, has been captured. The drawback of this technique is the size of the probe (3 mm) in relation to the vessel. In this work, however, the probe was placed in parallel to the flow stream that leaves the impeller, ensuring that the measured drops did not interfere with the instrument and their size was least affected by its presence. Light back scattering techniques have previously been used in aqueous organic dispersions formed in stirred tanks where they were found to respond swiftly to any changes in process conditions which affect drop size. In all these investigations, however, the techniques were implemented in either low dispersed phase fractions 5,7 or in surfactant-stabilised emulsions. 9 Validation experiments were carried out initially with standard diameter latex and polystyrene monosized spheres ranging from. µm to 3 µm (±.1 µm) (from Polymer Laboratories, UK and Dynal Particles AS, Norway). These materials were chosen as they have optical properties close to those of oil. Particle concentrations up to 1% were used and the comparisons between the nominal particle diameters and those obtained by the 3D ORM instrument can be seen in Table 1.. High-speed video recording technique Theresultsfromthe3DORMprobewerecompared with those from in-situ video recording obtained with an endoscope (Schoelly) (od = mm) attached to a high-speed camera (Redlake MotionScope PCI ). The endoscope was inserted into the dispersion at Table 1. Comparison between the nominal sizes of the calibration particles and their average diameters obtained by the ORM instrument Nominal particle size (µm) Measured average particle size (µm) % difference Figure 3. A characteristic image obtained by the high-speed video recording technique for 1% oil fraction at 5 rpm impeller speed. the side of the vessel wall and at the same height as the 3D ORM instrument (Fig 1) (with a 9 viewing direction). The imaging system used is capable of recording up to 1 full frames per second, but in the present experiments pictures were taken with proper lighting at a speed of 5 fps, considered to be a suitable recording rate, and at a shutter rate of 1/1 s. It must be noted that the endoscope used has a very narrow depth of field and its focusing distance is approximately mm from the front lens. The length calibration, needed to ensure the accurate measurement of the drops, was carried out before each run by measuring a microscale placed at the focusing plane. Subsequent image analysis provided the sizes of the dispersed drops. Approximately drops were measured in each experimental run, which is considered to be adequate for statistical calculations. 1 The images collected with this technique (see Fig 3) proved the validity of the assumption used in the measurements with the 3D ORM instrument that drops are spherical. The repeatability of the method was good and Sauter mean diameters measured in repeated experiments were found to be less than 1 µm different. 3 RESULTS AND DISCUSSION 3.1 Comparison of the two techniques Due to the problems associated with video recording, only volume fractions up to 1% were used as volume fractions greater than this resulted in individual drops not being clear in the photographs. Conversely since ORM is not reliable for dispersed phase fractions below 5%, measurements to validate the ORM technique against the video recording one were restricted to dispersed phase volume fractions in the range 5% to 1%. Drop size distributions from both techniques are shown in Figs a and b, for number frequency and 5 J Chem Technol Biotechnol :55 55 (5)

5 Drop size distribution in liquid liquid dispersions 1 ORM endoscope 1 ORM log-normal dist. (a) (a) Cumulative number ORM endoscope 1 endoscope log-normal dist. (b) Figure. Drop size distribution for 5 rpm impeller speed and 1% oil fraction. (a) distribution; (b) cumulative number distribution. cumulative number distribution respectively. It can be seen that the two techniques are in reasonable agreement. Measurements at the other conditions also showed good agreement between the two techniques. Small differences are probably due to the small number of sampled drops that can be collected with the video recording technique compared with those sampled by the ORM (in the order of thousands). Both techniques also gave drop number distributions that could be fitted by the log-normal function, as can be seen from Figs 5a and b respectively. The log-normal distribution is described by the following equation: ( ln d ξ y(d) = 1 δ e.5 δ π ) () where d is the drop size and δ and ξ are parameters of the log-normal distribution, with δ affecting the distribution height and ξ affecting the distribution width. The above results suggest that the 3D ORM instrument, which provides fast, on-line drop measurements, can be used reliably to study unstable liquid liquid dispersions. Further studies with the ORM for different impeller speeds and dispersed phase concentrations are detailed below. The standard deviation in the Sauter mean diameter was in (b) Figure 5. Experimental data and log-normal distribution curve for 5 rpm and 1% oil fraction. (a) ORM instrument; (b) high-speed video recording technique. d 3, mm % % 3% % 5% % Impeller speed, rpm Figure. Sauter mean drop diameter vs impeller speed for different oil fractions. Data obtained by ORM instrument. all experiments less than about µm and on average about.5 µm. 3. Results at higher dispersed phase concentrations with the ORM technique The Sauter mean diameters, obtained from 3D ORM, at all experimental conditions used, are summarised in Fig. It can be seen that there is an overall trend for d 3 to decrease with increasing impeller speed. However, J Chem Technol Biotechnol :55 55 (5) 59

6 J Lovick et al rpm 5 rpm 55 rpm d max, mm (a) (b) (c) rpm 5 rpm 55 rpm rpm 5 rpm 55 rpm Figure 7. Drop size distribution at different impeller speeds for dispersed phase oil fractions: (a) %, (b) % and (c) %. Data obtained by ORM instrument. in some volume fractions an increase with the impeller speed can be seen. Interestingly, when the actual drop size distributions are used, in all cases increasing the impeller speed resulted in a shift in the distribution to smaller drop sizes (see Fig 7 for different dispersed phase volume fractions). This indicates that average drop diameters may not always be able to represent distributions satisfactorily. The maximum diameters were also found to decrease with impeller speed (see Fig ), while the ratio of d max to d 3 varied between 3.5 and.5 in all cases. There is little overall trend in d 3 values with increasing oil fraction at a constant impeller speed (Fig 9). However, local phenomena do seem to exist. After an initial decrease, Sauter mean diameters increase again up to % oil fraction. A peak at high dispersed phase volume fraction has been reported by 1 1% % 3% % 5% % Impeller speed, rpm Figure. d max vs impeller speed for different oil fractions. Data obtained by ORM instrument. d 3, mm rpm 5 rpm 55 rpm 5 Dispersed phase fraction, % Figure 9. Sauter mean drop diameter vs dispersed phase fraction for various impeller speeds. Data obtained by ORM instrument. previous investigators.,9 As the oil fraction increases further there is no clear trend between the impeller speeds. The increase in the impeller speed will increase drop breakage and lead to smaller drops. The effect on coalescence is less clear as the drop collision frequency will increase but the coalescence efficiency which depends on the contact time of colliding drops will decrease. As can be seen, the overall effect in the current system is a slight decrease in the drop size. On the other hand an increase in the volume fraction would be expected to result in an increase in the drop size. A large amount of dispersed phase, however, can change the properties of the continuous phase turbulence. 3 Currently there is little work available on the interactions between continuous and dispersed phase in liquid liquid systems but in the current mixture they seem to result in small changes in drop size with volume fraction. All drop distributions were found to be uni-modal and were represented satisfactorily by the log-normal correlation. It was found that as the impeller speed increased, parameter ξ, the log-normal distribution width, decreased from.7 to., indicating narrower distributions. There was no trend for parameter δ, 55 J Chem Technol Biotechnol :55 55 (5)

7 Drop size distribution in liquid liquid dispersions the distribution height, which ranged between.5 and 5.5. Correlations of the form of eqn () did not predict satisfactorily either the Sauter mean or the maximum diameters. Interestingly, d 3 and d max were found to be proportional to We..1 T, and to We T respectively, rather than to We. T suggested by eqn (). As was pointed out in the literature, however, experimental data against which these correlations were validated are mainly available for low volume fraction or surfactant-stabilised systems. Furthermore, the above dependence on We T has been questioned by a number of investigators. Pacek et al 5 and Cull et al, 7 found experimentally larger power than (.) at dispersed phase fractions up to %. Baldyga et al 31 had shown that in dilute systems powers smaller than (.) should be expected because of the phenomenon of turbulence intermittency. Desnoyer et al 3 also found higher values for the power in the We T for dispersed phase concentrations up to %, as well as a dependency of this value from the dispersed phase fraction. The value tended to that of the classical Hinze theory at very low phase fractions. According to the authors a different mechanism of drop turbulent eddy interaction compared with that of the Hinze theory may be needed for dense dispersions. Brauner 33 has also argued that while in dilute turbulent systems the drop size is determined by a static force balance on each drop in dense dispersions the turbulent kinetic energy flux should exceed the rate of surface energy generation required for the break up of drops. It is possible that the turbulent energy may not be sufficient to create the small drops attained in dilute dispersions. In addition, very few experimental data exist in the literature on drop size of unstable liquid liquid dispersions at high dispersed phase fractions to compare with the current work. Brown and Pitt investigated drop size distributions of oil (with viscosity 1. mpa s) in water, in a standard configuration vessel equipped with a disc turbine. Dispersed phase fraction varied from 5% to % and impeller speed ranged from 5 to rpm. In agreement with the findings of the current work, the authors also reported that volume fraction and impeller speed had little effect on d 3. Average drop sizes ranged between 1 and µm which are slightly different from the current ones, as would be expected given the differences in fluids properties and vessel sizes. Weinstein and Treybal 7 carried out experiments using three vessel sizes and eight combinations of organic liquids and water, agitated with a six-flat-bladed turbine up to 59% dispersed phase fractions. Experimental data (shown in the paper for dispersed phase fractions up to 3%) revealed that average drop diameters increase with increasing dispersed phase fraction and decreasing impeller speeds. Sauter mean diameters (between and 55 µm) were larger than the ones observed in the current work, probably because unbaffled vessels were used that have lower power consumption for the same impeller speed. No distribution data were reported. The authors suggested a predictive model similar to that by Hinze 1 that accounts for drops close to the turbulence dissipation range. In the current work average drop sizes were larger than the eddy dissipation range (between µm and3µm) and the model failed to predict the experimental data. CONCLUDING REMARKS A light back scattering technique (3D ORM technique) was used to obtain on-line drop size distributions in unstable kerosene-in-water dispersions for dispersed phase fractions from 1% to %. Drop size data from this technique compared favourably with those obtained with a high-speed video recording method that implemented an endoscope. Using the ORM technique, drop diameter distributions were found to become narrower and shift to smaller sizes with increasing impeller speed, a trend that was not always obvious from the average drop sizes. No significant effect of the dispersed phase volume fraction was found. Log-normal distributions represented satisfactorily the number frequency of the measured drops. Standard literature correlations of the form of eqn () were unable to predict average drop sizes. ACKNOWLEDGMENTS Dr Angeli, Dr Lye and Dr Paras would like to thank the Royal Society for the award of the Partnership Grant that made this collaboration between UCL and the Aristotle University of Thessaloniki possible. J Lovick would also like to thank EPSRC for providing financial support for his studentship. 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