Experimental and numerical investigation on mixing of dilute oil in water dispersions in a stirred tank
Introduction
Liquid–liquid dispersion is a challenging process because of the inherent complexity existing among the droplets’ interactions (Patel et al., 2015). The successful design and scale-up for a liquid–liquid mixing tank depends on a deep understanding of the liquids’ hydrodynamic characteristics and droplet size distributions (DSD). In fact, knowledge of the DSD is key to creating a stable dispersion system and is of great importance for achieving efficient liquid–liquid mixing performance.
A better understanding of the mixing hydrodynamics of a liquid–liquid dispersion can be achieved with the electrical resistance tomography (ERT) system (Kim et al., 2006). ERT is broadly utilized in many chemical processes, such as in solid–liquid tanks (Hosseini et al., 2010; Tahvildarian et al., 2011), aerated reactors (Gumery et al., 2011; Hamood-ur-Rehman et al., 2012, 2013; Babaei et al., 2015a, 2015b; Hashemi et al., 2016; Malik and Pakzad, 2018), and mixing of non-Newtonian fluids (Pakzad et al., 2008a, 2008b; Patel et al., 2014a, 2014b). Holden et al. (1998) applied ERT to investigate the unsteady dynamic macromixing of miscible liquids with two types of impellers in a plant-scale reactor. Kim et al. (2006) used ERT to measure mixing time and dispersion velocity of the dispersed phase in the mixing of two immiscible liquids. However, an in-depth literature review shows a gap in the application of ERT in the mixing of two immiscible liquid–liquid dispersions.
On the other hand, DSD in stirred tanks has received much attention in past decades (Lovick et al., 2005; Singh et al., 2009; Khalil et al., 2010). One of the most common and simple techniques for DSD measurement is the sample withdrawal technique. The size of withdrawn droplets is measured by a microscope (Godfrey and Grilc, 1977; Kumar et al., 1991) or a photometer (Verhoff et al., 1977). The drawbacks of this technique include biased sampling of certain droplet sizes and its limitation to the dilute dispersion system (Godfrey and Grilc, 1977). Solsvik and Jakobsen (2015) used a high-speed imaging technique to assess the breakage mechanism in a liquid–liquid dispersion system. The disadvantage of this technique is that the sample image may not be a good representation of all available droplet sizes in the dispersion system. Jin et al. (2018) used an advanced image processing technique to capture the DSD and velocity at Rod Bundle Heat Transfer (RBHT) test facility. They concluded that the droplet size generally follows a modified log-normal distribution which does not significantly deviate from the normal distribution. Topuz and Wilkinson (2017) performed an experimental study on dispersion of immiscible liquids in single stage mixer-settler unit using six-flat blade impeller. The fiber optic probe and photography technique were applied for droplet size measurements, and they correlated the Sauter mean diameter with the impeller speed. The recent development of lasers, i.e. laser diffraction or laser backscattering methods, introduce new particle size measurements that overcome the above-mentioned limitations (Lovick et al., 2005). Lovick et al. (2005) used an optical reflectance measurement (ORM) particle size analyser and an endoscope to obtain on-line DSDs for a kerosene in water dispersion system with volume fraction ranges of 10–60%. They concluded that the effect of the dispersed phase volume fraction on droplet size is insignificant in highly concentrated dispersions. Liu et al. (2017) investigated the effect of a non-ionic surfactant (Tween 80) concentration on DSD of an oil in water dispersion in a stirred tank, experimentally and numerically. They concluded that an increase in surfactant concentration decreased the mean droplet size and stabilized the emulsion. Zhou and Kresta (1998) used phase Doppler particle analyser (PDPA) to measure the size, velocity, and concentration of droplets. They found that the shape of the particle size distribution changed from a unimodal to bimodal distribution by increasing impeller speeds. Pacek et al. (1999) additionally found that the unimodal distribution of an aqueous continuous phase can change to a bimodal distribution in an organic continuous one. They also found that an increase in impeller speed changed a bimodal distribution to a unimodal distribution. Ryan et al. (2018) performed an emulsification process in a pilot scale Sonolator with four different oil viscosities with sodium lauryl ether sulphate (SLES) as surfactant. They obtained DSDs using laser scattering measuring technique in order to develop a correlation between Sauter mean diameter and input parameters.
Among available droplet size measurement techniques, focused beam reflectance measurement (FBRM) has some advantages, such as the capability of on-line and in-situ measurements, ease of use, and minor calibration requirements (Li et al., 2005). In a study conducted by Wang et al. (2013), FBRM was used to evaluate the droplet size in an oil in water dispersion system and also to investigate the phase inversion for oil volume fractions of 10–60%. Greaves et al. (2008) found that FBRM-measured sizes are smaller than the ones measured by particle video microscope (PVM). Hu et al. (2006) introduced empirical models to explain the relationship between the distribution of chord lengths obtained by needle probe and DSD in a liquid–liquid dispersion. However, converting the chord length distribution (CLD) into corresponding DSD is not a straight-forward task due to the lack of theoretical analysis of the measurement principles as well as the dependency of the measurements on the particles’ shapes (Langston, 2002; Langston and Jones, 2001; Li et al., 2005). In most of these studies, the particles are assumed to be spherical, allowing for the particle chord length and diameter to be considered equal (Liu and Clark, 1995; Tadayyon and Rohani, 1998). However, this assumption is not valid for all case studies, since the droplet size measurement using laser diffraction, ultrasonic attenuation spectroscopy (UAS), and FBRM are influenced by droplet shape (Endoh et al., 1998; Heath et al., 2002; Xu and Di Guida, 2003; Li et al., 2005). The non-sphericity of droplets causes discrepancies in results. Therefore, detailed information about the shape of droplets is required (Xu and Di Guida, 2003).
To save time and costs associated with experimental studies (Boxall et al., 2010; Rueger and Calabrese, 2013), the experimental studies can be supplemented by numerical studies through population balance modeling (PBM) combined with computational fluid dynamics (CFD). Schütz et al. (2009) employed the mixture model and the Lehr’s breakage model in water-diesel separation in a hydro-cyclone. Their DSD results indicated that the Lehr’s model can successfully describe a droplet’s breakage in a liquid–liquid dispersion. Coupling CFD with PBM was done by Håkansson et al. (2009) to study breakage phenomenon in the emulsification process in a homogenizer. Srilatha et al. (2010) included the DSD results for a mixing tank used for two different emulsion systems. However, they assumed that aggregation and the breakage phenomena occurred only among droplets with equal diameter. In a study by Hermann et al. (2011), it was found that droplet breakage probability is lower for more stable droplets (increasing viscosities and interfacial tensions), while it increases at regions far beyond the impeller blade. Roudsari et al. (2012) used the Luo’s model coupled with the Eulerian approach and k-epsilon turbulence model for mixing a water in oil emulsion. They successfully validated the model using an experimental study by Boxall et al. (2010). Vonka and Soos (2015) used CFD and PBM for a liquid–liquid stirred tank equipped with a Rushton turbine. They found that the critical Weber number is dependent on droplet viscosity and independent of interfacial tension and local energy dissipation rate. The dependency of Sauter mean diameter on impeller tip speed was also predicted by their model. Ryan et al. (2017) measured the droplet size and model the flow field within a pilot scale Sonolator for the first time, using particle image velocimetry (PIV) and CFD, respectively. They concluded that CFD can be used for simulation of Sonolator devices if the bounds for the energy dissipation values are defined accurately.
The objective of our study was to investigate the effect of impeller speed, volume fraction, and viscosity of the dispersed phase on mixing hydrodynamics and droplet size in an oil in water dispersion system with the oil volume fraction less than 10% (i.e. a dilute oil in water dispersion system). We discuss the development of a CFD model, which we validated with the experimental data of ERT and FBRM under different operational conditions. The measured CLDs by FBRM were used to assess the effect of mixing on droplet shape in our dispersion system. In this regard, CLDs of two different droplet shapes, i.e. spherical and spheroidal, were modeled using the Python coding language.
Section snippets
Experimental setup and procedure
Experiments were conducted in a transparent flat-bottomed cylindrical tank of 200 mm liquid height and 200 mm inner diameter as shown in Fig. 1a. The tank was equipped with the A200 impeller (refer to Fig. 1b) with a 95 mm off-bottom clearance in a downward mode. The A200 impeller has been placed with an equal distance away from each ERT measuring sensor planes. The impeller with 95 mm diameter was driven using a 0.2 hp direct driven motor. The canola oil and linseed oil were used as a
CFD model development
The rotation of the impeller in the tank was modeled by multiple reference frame (MRF) (Roudsari et al., 2012). The geometry of the mixing system and the mesh were generated in ANSYS Design Modeler and ANSYS Mesh (version 17.2), respectively. The sweep method was applied to mesh the mixing tank. In this method, the MRF volume was discretized with tetrahedral cells however the rest volume was meshed with hexahedral cells. We used biased-edge sizing to have a smooth increase in the size of
Results and discussion
The results are discussed in two sections, starting with the effect of oil volume fraction, impeller speed, and oil type on the mixing index and droplet size distribution. Following this discussion is the analysis for the droplet shape.
Conclusion
In this study, the effect of impeller speed, volume fraction of the dispersed phase, and the viscosity of the dispersed phase on hydrodynamic mixing as well as chord length distribution (CLD) of a dilute oil in water dispersion were investigated by means of electrical resistance tomography (ERT) and focused beam reflectance measurement (FBRM). The experimental results were used to validate the CFD results, allowing a more comprehensive understanding of the mixing of liquid–liquid dispersions.
Acknowledgement
The financial support of Natural Sciences and Engineering Research Council of Canada (NSERC) provided for this research is gratefully acknowledged. The author would like to appreciate the high-performance facilities of the Centre for advanced computing (formerly HPCVL) for running intense simulations of this study. The authors wish to thank Dr. Pedram Fatehi who gave the FBRM probe to be used in this study.
References (99)
- et al.
Simulation of the population balances for liquid–liquid systems in a nonideal stirred tank. Part 1 Description and qualitative validation of the model
Chem. Eng. Sci.
(1999) - et al.
Predicting the sizes of toluene-diluted heavy oil emulsions in turbulent flow. Part 2: Hine–Kolmogorov based model adapted for increased oil fractions and energy dissipation in a stirred tank
Chem. Eng. Sci.
(2006) - et al.
The use of electrical resistance tomography for the characterization of gas holdup inside a bubble column bioreactor containing activated sludge
Chem. Eng. J.
(2015) - et al.
Analysis of gas phase characteristics and mixing performance in an activated sludge bioreactor using electrical resistance tomography
Chem. Eng. J.
(2015) - et al.
Description of interaction processes in agitated liquid–liquid dispersions
Chem. Eng. Sci.
(1977) - et al.
Factors governing emulsion droplet and solid particle size measurements performed using the focused beam reflectance technique
Colloids Surf. Physicochem. Eng. Asp.
(2001) - et al.
Dispersion of silicone oil in water surfactant solution: effect of impeller speed, oil viscosity and addition point on drop size distribution
Chem. Eng. Process. Process Intensif.
(2009) - et al.
Impact attrition of particulate solids. Part 1: a theoretical model of chipping
Chem. Eng. Sci.
(2002) - et al.
Measuring the particle size of a known distribution using the focused beam reflectance measurement technique
Chem. Eng. Sci.
(2008) - et al.
A model for turbulent binary breakup of dispersed fluid particles
Chem. Eng. Sci.
(2002)