Numerical simulation and experimental study of emulsification in a narrow-gap homogenizer
Introduction
The design of new procedures for the fabrication of nano-structured materials is one of the hot topics in the current materials science with a great potential for applications in various modern chemical production technologies (Xia et al., 1999, Velev and Kaler, 2000, Kralchevsky and Nagayama, 2001, Kralchevsky and Denkov, 2001, Caruso, 2004). The fabrication of nano-composites can be based on the production of emulsions, whose finely dispersed droplet phase provides sufficient surface area for adsorption of the nano particles (Velev et al., 1996, Dinsmore et al., 2002).
It is the subject of the present study to investigate the main effects relevant in the emulsification process using a high-pressure, continuous stream homogenizer. The emulsion is stabilized by adding surface active emulsifiers at a sufficiently high concentration to the primary suspension. In such a surfactant-rich regime the rate of recoalescence of the newly formed drops during emulsification is low, and the final drop size distribution is determined primarily by the hydrodynamic conditions in the underlying flow. The fine droplets highly dispersed in the final emulsion could serve then as templates for the fabrication of the nano-composites.
There exist various techniques of emulsification. A common feature of these procedures is that they involve an interplay between capillary and hydrodynamic forces, which determine the final outcome of the emulsification process. In all techniques the drop breakage is promoted by a strong deformation of the primary droplets in the coarse premixture of the immiscible continuous and dispersed phases fed into the homogenizer.
Depending on the governing flow regime, three types of forces can be identified which may dominate the process of droplet fragmentation: the viscous shear forces, the form drag forces, and the inertial forces. Their relevance can be decided by the magnitude of drop-size based Weber number and Reynolds number . The Weber number relates the inertial and the surface tension forces, while the Reynolds number relates the inertial to the viscous forces, involving the density of the continuous carrier phase , the drop size , and some reference velocity . At low Weber numbers, where the inertial forces are negligibly small, the droplet deformation and breakup is dominated by the viscous shear forces and the form drag forces. The shear forces prevail in the Stokes flow regime with very low Reynolds numbers of the order of unity. The form drag forces become dominant at higher, but still subcritical, Reynolds numbers, where the flow separation significantly affects the pressure acting on the drop surface. The drop breakage caused by these two mechanisms is typically realized in laminar pipe flow configurations and colloid mills (Walstra, 1983, Stone, 1994). At high Weber numbers typically found in strongly turbulent flows the deformation and breakup of the droplets is mainly due to dynamic pressure forces associated with the turbulent fluctuations of the velocity of the carrier phase. This kind of breakup mechanism, which is basically driven by inertial forces, is frequently utilized in emulsifiers with stirring or shaking devices to enhance the turbulent motion.
The present work investigates the case of droplet fragmentation in the turbulent flow regime. The considered Reynolds numbers based on the bulk flow conditions of the carrier phase in the most active emulsification zone are of the order of . The values of the drop-size based Weber and Reynolds numbers and , described above, are of the order of or higher. Rather than using a stirring device, the facility considered here enhances locally the turbulence by forcing the emulsion through a cylindrical pipe containing a strong contraction, which reduces the pipe's cross-sectional area to a narrow annular gap. This device, termed a “narrow-gap homogenizer” in the following, is to some extent similar to high-pressure valve homogenizers, where the emulsion is pumped through a homogenizing valve (Phipps, 1975). However, unlike in the narrow-gap homogenizer considered here, the height of the gap of the valve homogenizers is determined by the aperture between the valve and its seat. Thus, the resulting gap height varies with the lift of the valve adjusting to the flow rate through the device, and it is typically much smaller than the gap height in the present narrow-gap homogenizer. The major advantage of the narrow-gap homogenizer used in the current study is its fixed, well-defined geometry, which allows one to perform precise numerical simulations of the fluid flow inside the homogenizer chamber.
Using a narrow-gap homogenizer with a one- and a two-gaps design, emulsification experiments were carried out to study the influence of the number of gaps, as well as the effects of hydrodynamic parameters, such as flow rate, viscosity of the dispersed phase, and interfacial tension, on the drop size distribution. Aside from the experimental investigation of the drop size distributions produced, the present study also aims at demonstrating how numerical simulations of the emulsifying flow can help to obtain accurate predictions of the maximum stable drop size from theoretical models. Particularly, the dissipation rate of turbulent kinetic energy, which represents an essential input parameter to the models, is often estimated based on very crude assumptions. The present work instead utilizes the results of the numerical simulation of the flow field inside the emulsifying device to provide more adequate model input values for the average dissipation rate. This approach based on numerical flow simulations finally leads to drop size predictions, which are in a very good overall agreement with the corresponding experimental data.
The present work is organized as follows: the available theoretical expressions for the maximum drop size during emulsification in turbulent flow are briefly discussed in Section 2. The experimental setup and the measuring techniques are described in Section 3. In Section 4, the experimental results are shown. The corresponding numerical simulations and their results are presented in Section 5. The model predictions for the maximum stable droplet diameter are compared against the corresponding experimental data in Section 6. The conclusions follow in Section 7.
Section snippets
Emulsification theory in turbulent flows
The mathematical description of the droplet breakup mechanism in turbulent emulsifying flow dates back to the fundamental work by Kolmogorov (1949) and Hinze (1955). This classical concept, also known as the Kolmogorov–Hinze theory, is based on several assumptions. First, non-coalescing conditions are assumed, which is the case if the concentration of the dispersed phase is very low, or, if the coalescence is impeded by the addition of surfactants. Second, the maximum stable size of the drops
Materials
Three emulsifiers were used in different series of experiments, which ensured different interfacial tensions of the oil-water interface: the nonionic surfactant polyoxyethylene-20 hexadecyl ether (Brij 58, product of Sigma), the anionic surfactant sodium dodecyl sulfate (SDS, product of Acros), and the protein emulsifier sodium caseinate (Na caseinate; ingredient name Alanate 180; product of NXMP). All emulsifiers were used as delivered from the supplier, and their concentrations in the aqueous
Experimental results
All experiments were performed at a high surfactant concentration and a low oil volume fraction of to suppress dynamic drop-drop interactions and drop coalescence during emulsification. Two processing elements, with one gap and with two gaps, were used in parallel series of experiments. Most of the experiments were carried out at the flow rate , and several series of experiments were performed at the lower flow rate to study the effect of the Reynolds
Computational domain and boundary conditions
The considered narrow-gap homogenizer consists basically of an axisymmetric channel, which contains a processing element with either one or two consecutive gaps. The computational domain is shown in Fig. 4 including the alternatively used processing elements. The total axial extension of the domain is , the diameter at the inlet is . In both the one- and the two-gaps cases, the processing element is located at the same axial position in the channel, and the radial height, as well
Comparison of model predictions for the drop size with experimental data
As outlined in Section 3, the turbulent energy dissipation rate represents a key input quantity to the models proposed for the maximum stable drop size in turbulent emulsifying flows. The present work attempts to provide a most reliable value for from the numerical flow simulations of the narrow-gap homogenizer at hand. Since in all models considered here the maximum stable droplet diameter is basically proportional to the inverse of , it is conceivable to assume the region with the
Conclusions
The present study investigates the emulsifying flow through a narrow-gap homogenizer with varying geometry, flow rate, and material properties. The experiments which were carried out using processing elements with one gap and with two gaps, yielded the following main results.
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For otherwise constant conditions, the homogenizer with two annular gaps produces finer droplets with mean diameters being about 15% smaller as compared to the one-gap design. However, due to the additional friction losses
Notation
cross-sectional area, specific heat capacity, constants drop diameter in histogram interval , m maximum stable drop diameter, m root mean square diameter, m volumetric maximum drop diameter, m number based mean drop diameter, m Sauter-mean drop diameter, m pipe diameter, m hydraulic diameter, m inlet diameter, m outer gap diameter, m friction factor gap height, m total length, m number of drops in histogram interval i static pressure,
Acknowledgements
The authors gratefully acknowledge the financial support from the CONEX Program funded by the Austrian Federal Ministry for Education, Science and Culture. The useful discussions with Professor Ivan B. Ivanov and the help in the preparation of the homogenizer by Dr. V. Valchev (both at Sofia University) are also gratefully acknowledged.
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