Multiscale Analysis of Water-in-Oil Emulsions: A Computational Fluid

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MULTISCALE ANALYSIS OF W/O EMULSIONS: A CFD APPROACH Juan Pablo Gallo-Molina, Dr. Nicolas Ratkovich, and Oscar Alvarez Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02246 • Publication Date (Web): 21 Jun 2017 Downloaded from http://pubs.acs.org on June 24, 2017

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Industrial & Engineering Chemistry Research

MULTISCALE ANALYSIS OF W/O EMULSIONS: A CFD APPROACH Juan Pablo Gallo-Molina*‡, Nicolás Ratkovich‡ and Óscar Álvarez‡. ‡

Process and Product Design Group (GDPP), Department of Chemical Engineering, Universidad

de los Andes, Bogotá, Colombia.

ABSTRACT: Emulsions are a type of metastable colloids composed by two or more immiscible liquids. These systems are widely used in a variety of applications, such as cosmetics, drug delivery, food, etc. Although there exist theoretical foundations which offer insights into these systems, industry practices often favor empirical methods. In this work a multiscale approximation is used for the study of water-in-oil (W/O) emulsions. This approach allows for the analysis of interrelationships among macroscopic, microscopic, process and formulation variables. Additionally, the emulsions were modelled with CFD, which permitted a better understanding of the role process variables plays. It was possible to establish relationships among incorporated energy, elastic modulus, mean droplet diameter and stability measurements. In addition, differences in impeller geometry were found to have an effect in the aforementioned variables. Finally, the CFD model allowed for the observation of gradients in relative viscosity, droplet diameter, and dispersed phase volume fraction.

ACS Paragon Plus Environment

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1. INTRODUCTION. Emulsions are thermodynamically unstable colloids composed by immiscible liquids. Due to this instability, its preparation necessitates the addition energy and surfactant agents 1. These systems are broadly used in diverse industrial applications (e.g. cosmetics, pharmaceutics, food, oil recovery, etc.) which suggests that an adequate knowledge of its behavior is of importance. There is, however, a large number of variables that affect the final properties of an emulsion product. Among these variables, disperse phase concentration, continuous phase characteristics and process variables (i.e. mixing velocity, impeller type, etc.) are of special importance. Several authors have indicated that numerous factors on different levels (i.e. molecular, microscopic and macroscopic) intertwine in the process of determining the properties of an emulsion. For instance, rheological properties are highly influenced by microscopic variables such as fraction of dispersed phase and droplet size distribution2,3. Additionally, Azodi and Nazar4 studied the interrelationship between viscosity, stability and surface tension, while Acedo-Carrillo et al5 analyzed the influence of zeta-potential on droplet diameter. On the other hand, Roldan-Cruz et al6 pointed out that environmental conditions, droplet size distribution and interfacial phenomena affect stability; a crucial property in industrial applications. Taking this into consideration, a multiscale approach is an adequate approximation for studying emulsion systems. This approach consists in the building of relations between the internal dynamics of a system and its performance as a product7. In this case, a link between the emulsification process variables and rheological and microscopic properties may be constructed. Recently, Pradilla et al7 and Alvarez et al8 implemented this approximation into emulsions and found both numerical and qualitative relations among process (i.e. type of propeller), macroscopic (i.e. rheological characteristics), microscopic (i.e. particle size distribution) and molecular (i.e.


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near infrared spectroscopy measurements) variables. Incorporated energy was used as a transversal factor. Taking into account that emulsification process variables are arguably among the most easily controllable factors, it is convenient to gain insight into its effects on other relevant variables. As mentioned above, this endeavor can be accomplished via a multiscale study. However, one possible shortcoming is the fact that experimental measurements often cannot reflect the conditions in the entire volume of the studied system, but instead offer average results. In turn, this could hide important factors such as particle size gradients in the mixing vessel. For this reason, this work sought to couple Computational Fluid Dynamics (CFD) with a multiscale analysis in order to analyze the relationships between formulation, impeller type, rheological properties, particle size distribution and stability in W/O emulsions and to better understand both the link to process variables and the three-dimensional behavior of macroscopic and microscopic responses. CFD is a technique that allows for the description of the behavior of one or more fluids under several conditions. It solves numerically physical equations and uses a discretization of a geometric domain via the finite volume method. Besides conservation equations, it is possible to couple, among others, rheological and phase interaction models9. In the field of emulsions, several approaches have been proposed for the modelling of particle size distribution and the phenomena affecting it (e.g. coalescence and break-up). Among those, population balances models (PBM) are, arguably, the most rigorous but other statistically based models such as S-gamma are also viable10,11. In the first part of this work, relationships between rheology, droplet size, concentration of dispersed phase and energy incorporated during the emulsification process were stablished. Four types of impellers were used in a range of concentrations from 10 to 90%. The second part of this


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work analyses the influence of mixing during the emulsification process on the rheological properties, incorporated energy and particle size. For this endeavor, CFD results were used for concentrations of disperse phase ranging from 10 to 90% and one type of impeller. 2. MATERIALS AND METHODS 2.1. Materials Water-in-oil (W/O) emulsions were prepared using mineral oil (USP-grade) and mili-Q deionized water. Two commercial non-ionic surfactants were used: Span 80® (Sorbitan Monooleate), oil soluble, HLB 4.3 and Tween 20® (polisorbate 20), water soluble, HLB 16.7. CFD modelling was conducted using commercial software STAR-CCM+, v. 11.04 (Siemens®). CAD geometry was constructed using Autodesk® Inventor 2017. 2.2. Methods 2.2.1. Experimental 2.2.1.1. Formulation and emulsification process. W/O emulsions (10 to 90% dispersed phase concentration) were prepared using a 1.5 (w.t. %) total surfactant mixture concentration and a HLB of 5. The choice of emulsifiers and HLB was made in accordance to common industry practice12, while the concentration was found to be appropriate during preliminary studies. The interfacial tension (measured using the pendant drop technique in an Attension® Theta optical tensiometer) was 9.51 mN/m, which was within the reported ranges in the literature13,14 for similar systems. A semibatch process consisting of three steps was used. Initially, Span 80® was added to the continuous phase (oil) and Tween 20® was added to the dispersed phase (water). Both mixtures were separately homogenized for 15 min at 300 rpm. During the second step, the dispersed phase was added to the continuous phase at a constant flow rate of 0.5 mL/s. A Fischer Scientific®


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peristaltic pump was utilized. The tip velocity of the impellers was kept at 1.7 m/s. Finally, the emulsions were homogenized at the same tip velocity for 10 min. Torque vs time data was recorded using a Lightnin® LabMaster (a)

(b)

L1U10F mixing device. Temperature was kept at 40ºC. Four types of impellers were used: propeller, straight paddles turbine, 45º pitched blade turbine and Rushton turbine (Figure 1). The impeller-to-tank diameter

(c)

(d)

Figure 1. Schematic of impeller types and dimensions. (a) Propeller. (b) Straight paddles turbine. (c) Rushton Turbine. (d) Pitched blade

ratio was kept constant at 0.78. 2.2.1.3. Experimental Measurements Rheological

measurements

were

performed using a TA Instruments® DHR1

turbine.

hybrid rheometer with a temperature of 40 ± 0.1 ◦C. The first test was a flow sweep with the shear rate varying in a range of 1 to 100 1/s. Subsequently a frequency sweep with a step of 0.1-300 rad/s at 0.2 Pa was implemented. The final test was a stress sweep with a step of 0.1-300 Pa. Droplet size distributions were measured using a Malvern Instruments® Mastersizer 3000. This instrument permits particle size measurements in the range of 0.01 to 3500 μm and uses Mie theory for calculation size distributions. This theory uses Maxwell’s field equations and predicts scattering intensity produced by particles in a sample. It assumes spherical particles and takes into


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consideration diffraction, refraction and absorption, for which optical properties of both dispersant medium (mineral oil) and particle material (water) must be known15. In order to avoid that light scattered by one particle interacted with other droplets before detection, the samples were diluted in such a way that obscuration was maintained within the limits suggested by the equipment manufacturer. Stability tests were performed with a Formulaction® Turbiscan. Sample scans were done every 25 seconds for a period of 30 min with a temperature of 40 °C. This equipment analyzes transmission and backscattering in a cylindrical sample cell produced by a near infrared light source. Destabilization kinetics are inferred by analyzing changes in transmission and light scattering as a function of the different destabilization mechanisms in play (e.g. flocculation and sedimentation). Results are presented in a form of the Turbiscan Stability Index (TSI), which is a relative number that reflects the variations in time of stability in comparison with the status of the sample at the start of the analysis16. 2.2.2. CFD Modelling 2.2.2.1. Mathematical Models The Eulerian approach was utilized during simulations. This means that a set of equations is solved for each phase, alongside models that account for phase interactions. The continuity equation for a phase i is 17,18 : 𝜕 ∫ 𝛼𝑖 𝜌𝑖 𝑥 𝑑𝑉 + ∮ 𝛼𝑖 𝜌𝑖 𝑥 (𝑉𝑖 − 𝑉𝑔 ) . 𝑑𝒂 = ∫ ∑(𝑚𝑖𝑗− 𝑚𝑗𝑖 ) 𝑥 𝑑𝑉 + ∫ 𝑆𝑖𝛼 𝑑𝑉 (1) 𝜕𝑡 𝑉 𝐴 𝑉 𝑉 𝑖≠𝑗

Where α is the volume fraction of phase i, 𝜌𝑖 is the density of phase i, x is the void fraction, 𝑉𝑖 is the velocity of phase i, 𝑉𝑔 is the grid velocity, 𝑚𝑖𝑗 is the mass flow from i to j and 𝑚𝑗𝑖 is the mass flow from j to i.


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Momentum equation for phase i is17,18: 𝜕 ∫ 𝛼 𝜌 𝑥 𝑑𝑉 + ∮ 𝛼𝑖 𝜌𝑖 𝑥 (𝑉𝑖 − 𝑉𝑔 ) . 𝑑𝑎 𝜕𝑡 𝑉 𝑖 𝑖 𝐴 = − ∫ 𝛼𝑖 𝑥 𝛻𝑃 𝑑𝑉 + ∫ 𝛼𝑖 𝜌𝑖 𝑥 𝑔 𝑑𝑉 + ∮ [𝛼(𝜏𝑖 − 𝜏𝑖𝑡 )] 𝑥. 𝑑𝒂 + ∫𝑀𝑖 𝑥 𝑑𝑣 𝑉

𝑉

𝐴

𝑣

+ ∫(𝐹𝑖𝑛𝑡 )𝑖 𝑥 𝑑𝑣 + ∫𝑆𝑖𝑣 𝑑𝑣 + ∫ ∑(𝑚𝑖𝑗 𝑣 − 𝑚𝑗𝑖 𝑣)𝑥 𝑑𝑣 𝑣

𝑣

(2)

𝑣

Where P is pressure, which is equal for both phases, g is the gravity vector, 𝜏𝑖 is the molecular stress tensor of phase i, 𝜏𝑖𝑡 is the turbulent stress tensor of phase i,, (𝐹𝑖𝑛𝑡 )𝑖 represents internal forces at phase i, 𝑆𝑖𝑣 is the phase momentum source term and 𝑀𝑖 is interphase momentum transfer per unit volume, where: ∑ 𝑀𝑖 = 0

(3)

No turbulence model was implemented for the reason that flow regimes were considered to be laminar under all conditions (Re≪ 1000). Additionally, the system was taken to be isothermal (40ºC) and each phase was assigned constant density and viscosity values. These properties were measured for the continuous phase (𝜌 = 851 kg/m3, 𝜇=0.0185 Pa s) and the widely reported values for the dispersed phase at the working temperature were used. Drag was modeled using the well-known Schiller and Naumann expression19 because it is well suited for cases in which fluid particles are small and can be considered spherical such as in this study. Additionally, recent works in the literature have shown that it is adequate for systems similar to the emulsions studied here (For example, see the work of Roudsari et al10 and references within). Lift force was not considered for the reason that it is not significant in comparison to drag force in emulsions20. Virtual mass forces were not considered due to the reason that they occur when the dispersed phase accelerates relative to the continuous phase and this is significant only when the dispersed phase density is considerably smaller than the continuous phase density20,21.


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Even though the studied emulsions are composed by two Newtonian fluids, non-Newtonian behavior arises due to interaction between particles and particles and the continuous phase22. For this reason, an emulsion rheology model was implemented as well. The mentioned model uses relative viscosity for describing the mixture viscosity: 𝜂𝑟 =

𝜂 𝜂𝑐

(4)

Where 𝜂 is the mixture viscocity and 𝜂𝑐 is the viscosity of the continuous phase. In turn, relative viscosity was described using the Morris and Boulay model23: 𝜙 −1 𝜙 2 𝜙 −2 𝜂𝑟 (𝜙) = 1 + 2,5𝜙 (1 − ) + 𝐾𝑠 ( ) (1 − ) 𝜙𝑚 𝜙𝑚 𝜙𝑚

(5)

Where 𝐾𝑠 is the contact contribution, ϕ is the disperse phase volume fraction and 𝜙𝑚 is the maximum packing fraction. Although this model was originally developed for flows with anisotropic components, it can describe isotropic flows if an identity tensor is used as the anisotropy tensor in the normal stress tensor: 𝜏𝑝,𝑁𝑆 = −𝜂𝜂 (𝜙)𝜂𝑓 𝛾̇ 𝑙 𝑄

(6)

Where 𝜂𝜂 is the continuous phase viscosity, 𝛾̇ 𝑙 is the shear rate of the liquid and Q is the anisotropy tensor. Particle size distribution as well as coalescence and break up was described with the S-gamma formulation24,25. This method assumes a lognormal distribution, which was deem acceptable because experimental measurements showed that actual distributions are close to the lognormal form. The method is statistical in nature and is based in the resolution of transport equations for moments of the size distribution: ∞

𝑆𝛾 = 𝑛 ∫ 𝑑 𝛾 𝑃(𝑑)𝑑(𝑑)

(7)

0


8

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Where 𝑛 is the number of particle per unit volume, 𝑑 is the particle diameter and P(d) is the probability function of particle diameter. Coalescence and breakup were modeled within the S-gamma framework by adding source terms to the transport equation for each moment of size distribution. For instance, the transport equation for 𝑆0 adopts the following form: 𝜕𝑆0 + ∇. (𝑆0 𝑣𝑑 ) = 𝑠𝑏𝑟 + 𝑠𝑐𝑙 𝜕𝑡

(8)

Where 𝑣𝑑 is the dispersed phase velocity and 𝑠𝑏𝑟 and 𝑠𝑐𝑙 are the terms for breakup and coalescence, respectively. For breakup, the equation formulated by Lo and Zhang25 was implemented: 1−

𝛾

∞ (𝑁(𝑑) 3 − 1) 𝑑 𝑆𝛾 = ∫ 𝑛𝑃(𝑑) 𝑑 𝛾 𝑑(𝑑) 𝑑𝑡 𝜏(𝑑) 𝑑𝑐𝑟

(9)

Where N is the number of small droplets produced when a particle breaks down and 𝑑𝑐𝑟 is the critical diameter: 𝑑𝑐𝑟 =

2𝜎𝛺𝑐𝑟 𝜇𝑐 𝛾̇

(10)

Where 𝜇𝑐 is the continuous phase dynamic viscosity, 𝜎 is the surface tension, 𝛾̇ is the local shear rate and 𝛺𝑐𝑟 is the critical capillary number, which only depends on the ratio of viscosities between the dispersed and continuous phases 1. The timescale for breakup (𝜏) depends on the breakup regime (i.e. viscous or inertial). For this study, only the viscous case was relevant due to the fact that only laminar flows were considered. Thus, the mentioned time scale is25: 𝜏(𝑑) =

𝜇𝑐 𝑑 𝑓(𝜆) 𝜎

(11)


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Where 𝜆 is the ratio of viscosities between the dispersed and continuous phases. 𝑓(𝜆) is an experimentally derived function, the details of which can be found elsewhere26. The implemented coalescence model based on the work of Lo and Zhang25 as well. The source term for coalescence is given by equation 12: 𝛾 𝑑 𝛾 𝑆𝛾 = 𝐹𝑐𝑙 (23 − 2) 𝐾𝑐𝑜𝑙𝑙 𝑃𝑐𝑙 (𝑑𝑒𝑞 )𝑑𝑒𝑞 𝑑𝑡

(12)

Where 𝐹𝑐𝑙 is a calibration coefficient, 𝐾𝑐𝑜𝑙𝑙 is the collision rate, 𝑃𝑐𝑙 is the probability of collision leading to coalescence and 𝑑𝑒𝑞 is an equivalent diameter defined by the authors25. For the viscous case, the collision is defined as follows: 1

𝐾𝑐𝑜𝑙𝑙

2

8𝜋 2 6ϕ 2 = ( ) (𝛾̇ 𝑑𝑒𝑞 )𝑑𝑒𝑞 ( 3 ) 3 𝜋𝑑𝑒𝑞

(13)

According to Lo and Zhang25, the probability of collision depends on the shear rate and the drainage time of the film of continuous phase between colliding droplets. Consequently, this probability represents a comparison of the interaction time of the droplets and the required time for the film to drain away. Equation 14 defines the probability of collision. 𝑃𝑐𝑙 (𝑑𝑒𝑞 ) = exp(−𝑡𝑑 𝛾̇ )

(14)

The mentioned drainage time (𝑡𝑑 ) depends on the presence of blockages at the interphase. Considering that surfactants act as barriers at the interphase, a partially mobile interface model for the drainage time was selected: 𝜋𝜇𝑑 √𝐹𝑖 𝑑𝑒𝑞 3/2 𝑡𝑑 = ( ) 2ℎ𝑐𝑟 4𝜋𝜎

(15)


10

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Where 𝐹𝑖 is the interaction force during the collision and ℎ𝑐𝑟 is the critical film thickness. The definition of both parameters can be found in the literature25. The critical film thickness depends on the Hamaker constant, which was estimated using the work of Bergström27.

2.2.2.2. Mesh The

3D

computational

domain

was

modelled using Autodesk ® Inventor 2017. The

geometrical

experimental

parameters

setup

were

of

the

reproduced.

Subsequently, it was discretized using STARCCM+. Polyhedral cells were used for the bulk of the fluid and, in order to facilitate (a)

convergence and improve accuracy, a prism layer mesh was implemented near walls. Taking into consideration that mixing was simulated in steady state and possible convergence problems occasioned by the multiple physics models applied, a relatively dense mesh consisting of 602560 cells was used. Figure 2 shows the used geometry grid

(b) Figure 2 (a) Geometry mesh. (b) Experimental used set-up.

during

simulations

and

the

corresponding experimental set-up.


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1 0.8 Velocity [m/s]

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Mesh independence tests were conducted Above impeller. Fine mesh Above impeller. Medium mesh Above impeller. Coarse mesh Below impeller. Fine mesh Below impeller. Medium mesh Below impeller. Coarse mesh

taking two factors into account: average velocity

0.6

after

0.4

velocity profiles near the agitator, where

0.2

gradients are expected to be larger10. The

0 -4

convergence

and,

more

importantly,

simulations were considered to be mesh -2

0 Position [cm]

2

4

Figure 3. Radial velocity profiles for different

the average velocity and the velocity profiles near

mesh sizes Table 1. Comparison of average variables for different mesh sizes Variable Coarse Mesh Incorporated 2.311 Energy [J/mL] Mean Sauter 1.972 diameter [μm] 1.615 Relative viscosity

independent when additional cells did not change

the impeller by more than 5%. Figure 3 shows the velocity profiles in the x

Medium Fine Mesh Mesh 1.737 1.738

direction for both 5 mm above and below the impeller blades for a 10% emulsion. Three grid sizes are displayed: a coarse mesh, consisting of

1.999

2.001 approximately 100000 cells, the chosen mesh

1.272

1.274

(denoted ‘medium mesh’) and a fine mesh, consisting of approximately 1 million cells. It can

be seen that that the use of the coarse mesh resulted in generally equal forms of the profiles but generated an underestimation of the velocity magnitudes. The variance between the fine and medium grids was negligible. Table 1 illustrates that a similar behavior was encountered for the average values of relevant variables. Considering that the fine mesh required a significant increase in computational time, the medium mesh was deemed to be acceptable.


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2.2.2.3. CFD Simulations Only the third step of the emulsification process (i.e. homogenization) previously described was simulated. Considering preliminary experimental results (not presented) showed that a steady state develops immediately after the incorporation phase ends, simulations were performed in this same manner. Impeller motion was incorporated using the Moving Reference Frames (MRF) approximation. This approach avoids changing the positions of cells but instead simulates the forces associated with motion, thus giving time-averaged results with lower computational effort 18,28

.

Walls were treated with a no-slip condition and convergence was checked monitoring the residuals of conservation equations and evolution of relevant variables like relative viscosity, velocity, average mean droplet diameter and torque. Two 10 core Intel Xeon 2.4 Ghz processors were utilized. Convergence was achieved after an average of 50.13 h. 3. RESULTS AND ANALYSIS As mentioned before, the first part of the discussion will focus on the multiphase analysis of the studied W/O emulsions, using incorporated energy during the incorporation and homogenization process as a transversal factor. This energy corresponds to the work done by the impellers and is critical for the final properties of an emulsion, for the reason that it is responsible for the creation of additional interfacial area and the deformation of said interface, which allows for the adsorption of surfactant molecules1,29. In their study Alvarez et al8 found that, in highly concentrated emulsions (above 80% w.t.), the incorporated energy during homogenization is larger than the added energy during the incorporation of the dispersed phase. As could be expected, this situation occurs in less concentrated emulsions as well. However, as the amount of dispersed phase to incorporate diminishes, it was observed that the difference in magnitudes experimented a growth.


13


This can be explained by the fact that less

D[4,3] µm

15

Incorporated Energy [J/mL]

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10

concentrated

emulsions

increases

viscosity

experiment

lower

5 0 20

Propeller Straight Paddles Pitched Blade Rushton

in

and

requires

less

incorporation time.

10

Figure 4 shows the evolution of mean droplet 0 0

20

40 60 Concentration [%]

80

100

Figure 4. Average droplet size (D[4,3]) and

incorporated

energy

during

homogenization phase as functions of dispersed phase concentration in W/O emulsions prepared using four different impellers.

size the dispersed phase. It can be seen that the former

is

inversely

proportional

to

concentration, while the latter exhibits the opposite behavior. Langevin30 showed that an increase in concentration of the dispersed phase generates an increment in the elasticity of the interphases, which increments the amount of

energy that the impeller must incorporate. Additionally, the increasing amounts of dispersed phase reduces the available space between droplets, while the mentioned increase in elasticity makes droplets more resilient to coalescence. As mentioned by Pradilla et al7, this allows for more interactions between droplets, which generates larger elastic modules as the concentration grows. Recently, Alvarez et al8 and Pradilla et al7 established that tip velocity is a fundamental factor during the emulsification process. Additionally, Torres and Zamora31 investigated the influence of impeller type on incorporated energy during an emulsification process. It was found that different impeller geometries add different quantities of energy into the system. On the other hand, Ghannam32 concluded that the choice of impeller can affect the stability of an emulsion. This phenomenon can be explained by the fact that impeller geometry affects the shear generated during the homogenization, as well as the flow characteristics of the system. Figure 4 illustrates


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


differences among impellers in mean diameter and incorporated energy. Generally, the pitched blade impeller contributed with the lower amounts of energy, while generating the emulsions with larger mean diameters. Conversely, Rushton turbine incorporated larger amounts of energy, while its emulsions tended to have significantly smaller mean diameters. The observed differences in power consumption of the studied impellers were generally in accordance with the literature7,31,33,34 but, as suggested above, the Rushton turbine tended to incorporate more energy than the straight paddles impeller, which would not have been expected. However, Chapple et al.33 found that the Rushton turbine power draw is highly sensitive to geometric characteristics. For instance, a significant inversely proportional relationship between blade thickness and power number was observed due to the influence of this variable on flow separation and trailing vortex formation. Subsequently, the fact that the blade thickness of the used Rushton turbine (approximately 1 mm) was significantly smaller than that of the straight paddles turbine and that other geometric parameters such as blade length and width were not equal can explain the higher energy consumption of the Rushton impeller. Furthermore, it is noteworthy that recent studies34–38 have found that the power curves for non-Newtonian fluids and different types of impellers may exhibit pronounced inflexion points and even minima at low Reynolds numbers (In this study, Re for all systems, calculated using the Metzner and Otto Method35,39, was of the order of 10). Considering the complexities introduced by non-Newtonian flow, it is expected that these peculiarities in the power curves are dependent on impeller geometry and fluid properties as well as the Reynolds number, which may further explain the observed differences in power consumption among impellers and dispersed phase concentrations. Even though this may deserve further research, it can be concluded that impeller geometry is a major process variable during the emulsification process, since it modifies shear and incorporated energy.


15


1000

100

G' [Pa]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Page 16 of 31

The effects of different microscopic and 90% wt

process variables on rheological behavior has been investigated by several authors. For

10

example, Derkach3 discussed the proportional 1

relationship

50% wt

0.1 0.1

10

20


Figure 5. Elastic modulus in the linear viscoelastic region incorporated

as

energy

a function of during

the

homogenization phase for W/O emulsions using

four

different

impellers.

The

concentration values in ascending order are: 60%, 70%, 80 % and 90% for the propeller turbine; 60%, 70% and 80% for the straight paddles turbine; 50%, 60%, 70% and 80% for the Rushton and pitched blade turbines.

between

concentration

and

relative viscosity and the non-Newtonian behavior arising by close packing and droplet interactions.

Furthermore,

it

has

been

stablished that elasticity in emulsions is strongly related to interfacial energy density and both are connected with dispersed phase concentration40. Liu et al41 found that a transition from Newtonian to non-Newtonian regimes occurs in function of dispersed phase concentration and established that highly concentrated O/W emulsions exhibit shear-

thinning behavior, which can be well represented by a power law. Pradilla et al7 reported a directly proportional relationship between the elastic modulus in the linear viscoelastic region and incorporated energy in O/W emulsions. As shown by Figure 5, a similar behavior was observed for W/O emulsions, which implies that, for these systems, larger amounts of incorporated energy also leads to more elasticity in the interphase. As suggested before, this elasticity is reflected in the values of the elastic modulus.


16

Page 17 of 31

20

10


Moreover, the appreciable differences in

10% wt

elastic modulus when the concentrations are

D[4,3] µm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


equal show that the impeller type may be an important factor in the emulsion formulation. 90% wt

For instance, there exist an order-of1 1

10

20


Figure 6. Mean droplet diameter as a function of incorporated energy during the homogenization phase for W/O emulsions using four different impellers. The concentration values in descending order are: 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90% for the propeller turbine; 30%, 40%,

60%, 70% and 80% for the straight paddles turbine; 30%, 40%, 50%, 60%, 70% and 80% for the pitched blade; 20%, 30%, 40%, 60%, and 80% for the Rushton turbine.

magnitude difference between the elastic modulus of 50% emulsions prepared with the Rushton turbine and the pitched blade turbine. Less dramatic differences for higher concentrations were observed. As previously discussed, these divergences can be explained by the shear and energy incorporated by the different impellers which, in turn, is determined by its geometry when all other factors are kept equal. It is noteworthy, however, that in most cases the differences

between elastic modulus values are relatively small when the concentration is equal. For this reason, it can be concluded the amount of interactions amongst droplets –which is highly dependent on concentration- is critical for the determination of the elastic modulus. Figure 6 shows a behavior consistent with the results previously reported by Pradilla et al7 for O/W emulsions. That is: an increase in incorporated energy generates a decrease in average droplet diameter and elasticity in the studied systems. Furthermore, it was observed that divergences in mean diameter among impeller types are more pronounced for higher values of incorporated


17


energy (i.e. higher concentrations). This is explained by the fact that, at lower concentrations, the interactions between droplets are negligible, the flow regime is essentially Newtonian and the viscosities are relatively low41. In turn, this causes that the differences introduced by the different geometries became less important than the factors that were kept constant (i.e. homogenization time and surfactant concentration). Conversely, when the concentration of dispersed phase increases, the larger amounts of elasticity and interactions between droplets cause the differences in impeller geometry to play a bigger role, which generated the observed difference in mean diameter. Previous publications have investigated the effect of dispersed phase concentration in the stability of emulsions42,43, as well as the influences of surfactant concentration and environmental variables in the same variable44,45. Figure 7 shows the TSI of the studied emulsions for different concentrations and impeller types. As expected, more concentrated emulsions exhibited lower values of the TSI (i.e. higher stabilities), for the reason that at lower concentrations, the larger droplets are more sensitive to gravitational effects causing sedimentation and creaming. Furthermore, at higher concentrations, the osmotic pressure within the droplets can equilibrate the differences in Laplace pressure, which reduces Ostwald ripening 1. 10


8

A comparison between figures Figure 4, Figure 6 and Figure 7 shows that impeller

6

type also has an influence on stability. As

4

discussed before, the pitched blade tended to

2

incorporate lower amounts of energy during

TSI

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 31

0

10%

30% 50% Concentration

90%

Figure 7. TSI after 30 min for different

the homogenization stage, which created emulsions

with

generally

larger

mean

concentrations and impeller types.


18

Page 19 of 31

diameters.


(a)

(b)

10

CFD Experimental

Consequently,

this

made

emulsions less stable than those prepared

8

with impellers that tended to incorporate

6

more energy (e.g. Rushton).

4

Although

2 0 0

200

Relative Viscosity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


abundant

than

experimental studies, previous literature 20


80

100

have focused on the CFD modelling of emulsions

CFD Experimental

under

different

circumstances10,11,46–49. In this study, CFD

150

simulations were conducted with the

100

objective 50

0 0

less

of

studying

the

three-

dimensional profile of relevant variables as 20


80

100

a way of gaining better insight into the

Figure 8. Comparison between experimental data influence of process variables in the and CFD results. (a) Incorporated energy versus observed macroscopic and microscopic dispersed phase concentration. (b). Average responses. relative

viscosity

concentration.

versus

dispersed

phase simulations

As were

mentioned limited

before, to

the

homogenization phase with the propeller

turbine. In order to validate the simulations, measured cumulative distributions of droplet size, as well experimental data of incorporated energy and relative viscosity (calculated at the shear rate of the impeller) were compared with the results of the simulations. As shown by Figure 8 and Figure 9, there is good agreement between experimental and simulated results. Larger errors were


19


(b) Cumulative Probability [%]

Cumulative Probability [%]

(a) 100 10 1 0.1 0.01 0.001 0.5

1

1.5

2

2.5

3

3.5

100 10 1 0.1 0.01 0.001

0

0.5

1

1.5

2

2.5

3

3.5

Size [m]

Size [m]

(c) Cumulative Probability [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 31

100

Experimental. 10% 10

CFD. 10% Experimental. 50%

1

CFD. 50% Experimental. 90%

0,1 0,01 0.001

CFD. 90% 0

0.5

1

1.5

2

2.5

3

3.5

Size [m]

Figure 9. Comparison between experimental and CFD cumulative probability of droplet Sauter diameter distributions for different dispersed phase concentrations. (a) 10%. (b) 50%. (c) 90%. observed in the zone of medium concentrations, due to the fact that it constitutes a transition zone, where the used physical models are less capable to describe the complex behavior of the dispersed system and the distribution of size diverges more from the lognormal form. Figure 10 shows the velocity profiles for an emulsion with a concentration value of 10%. As it could be expected, higher velocities were observed in the vicinity of the impeller, while lower magnitudes occurred in the edges of the tank. Simulations showed a decrease in the average velocity and an enlargement of dead zones as the water concentration increased. This behavior was caused by the higher viscosities exhibited by more concentrated systems. As discussed before, this is generated by the increments in elasticity associated with more droplet interactions in the emulsions. Several authors have discussed the effects of the emulsification flow regime on the resulting droplet size distribution: Maggioris et al50 and Roudsari et al10 for the inertial case and Baldyga and Podgórska51 and Vankova et al52 for the viscous case. In the latter regime, which was


20

Page 21 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

Figure 10. Velocity profile (m/s) with 10% dispersed phase concentration. (a) Transversal profile. (b). Axial profile predominant in the studied emulsions, due to the relatively low impeller speeds and large viscosities, it has been reported that shear forces are directly responsible for droplet break-up. As shown by Figure 11, larger droplet diameters were predicted to exist far from the agitator for all concentrations but with greater differences being observed in more concentrated emulsions. This behavior is caused by the higher shear forces exerted on the fluid in the vicinity of the impeller, which favors a larger break-up rate than in the far reaches of the mixing vessel. Although both the CFD model and the experimental measurements showed a relatively narrow size (a)

(b)

(c)

Figure 11. Profile of Sauter diameter (D[3,2], μm) for different dispersed phase concentrations. (a) 10%. (b) 50%. (c) 90%. Red zones indicate diameters equal or larger than 2.5 μm.


21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 31

distribution, the existence of the mentioned gradients in droplet diameter suggests that mixing is critical for this variable in scaled-up applications; especially when highly concentrated emulsions are being prepared. Figure 12 shows a somewhat more dramatic behavior in the case of the viscosity of the product. The flow tests performed during the experimental phase of this study as well as several authors have shown that W/O emulsions exhibit a strong shear-thinning behavior3,40,41,53. In accordance to this, the CFD model predicted smaller viscosities near the impeller, with larger differences in more concentrated systems. In the same manner as with the particle size profiles, the lower shear rates experienced by the emulsions far from the propeller induced higher viscosities in those zones. There were less significant gradients in less concentrated emulsions because those systems exhibit less pronounced non-Newtonian effects and lower viscosities. Incidentally, this phenomenon was evident during the preparation of highly concentrated emulsions, as the flow of the fluid was clearly diminished far from the impeller during the incorporation and homogenization phases. This situation is expected to be greatly exacerbated in a scaled-up situation.

(a)

(b)

(c)

Figure 12. Profile of relative viscosity for different dispersed phase concentrations. (a) 10%. (b) 50%. (c) 90%. Different scales were used due to the large differences in magnitude. Red zones indicate viscosities equal or larger than the indicated corresponding value


22

Page 23 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Dispersed

phase

volume

fraction

profiles (Figure 13) showed that the chosen impeller is capable to produce a relatively even distribution of water droplets at the preferred tip velocity (1.7 m/s).

Analogously to the previously

discussed profiles, more concentrated

(a)

systems exhibited larger gradients. This is explained by the fact that, at higher concentrations, the viscosity of the emulsions makes mixing difficult and generate

effects

on

other

variables

associated with inappropriate mixing. For

(b)

this reason, higher tip velocities and/or other impeller geometries may be more appropriate for the homogenization of

(c)

highly concentrated emulsions. 4. CONCLUSIONS In this study an experimental multiscale

(c)

analysis of W/O emulsions was coupled

Figure 13. Profile of water volume fraction for

with the CFD modelling of the same

different concentrations. (a) 10%. (b) 50%. (c).

systems.

Rheological,

90%. Different scales were used due to the large

stability

and

particle

incorporated

size, energy

differences in magnitude.


23


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Page 24 of 31

measurements were taken in the laboratory, while the simulations were conducted using an Eulerian model with the S-gamma approach for the droplet size distribution and the Morris and Boulay model for the rheology of the emulsions. Using the incorporated energy during the incorporation and homogenization steps as a transversal variable, it was possible to find relationships among macroscopic (i.e. rheological), microscopic (i.e. particle size) and stability variables. Larger amounts of incorporated energy tended to generate more stable emulsions with lower average droplet diameters and higher elastic modulus. A comparison among different impeller types showed that the agitator geometry plays an important role in the rheology, size distribution and stability of the final emulsions by virtue of different impellers being capable of adding different amounts of energy and shear to the mixture. The CFD simulations were validated (Figure 8 andFigure 9) with the obtained experimental results and resulting three-dimensional profiles were proven to be useful as a complement to the multiscale approach used in this study. Gradients in droplet diameter, relative viscosity and dispersed phase volume fraction were found to exist in the mixing tank, which indicated that the chosen impeller and tip velocity don’t provide optimal mixing, while generating effects in the final macroscopic and microscopic properties of the product. In sum, the combination of an experimental multiscale study and CFD modelling of emulsions appears to be a useful tool for the analysis of the various variables affecting the final properties of these complex systems. Additionally, the use of computational methods may be useful for connecting laboratory results to full-scale observations. AUTHOR INFORMATION Corresponding Author *Email: [email protected]


24

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Author Contributions The manuscript was written through contributions of all authors. All authors have given approval ACKNOWLEDGMENT The authors gratefully acknowledge Alejandra Barrera (Process and Product Design Group (GDPP), Department of Chemical Engineering, Universidad de los Andes, Bogotá, Colombia) for measuring the interfacial tension. REFERENCES (1)

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8





6

TSI

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4 2 0

10%

30% 50% Concentration

90%





 

For Table of Contents Only


31

Multiscale Analysis of Water-in-Oil Emulsions: A Computational Fluid

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