The Application of Computational Fluid Dynamics to the Multiscale

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The Application of Computational Fluid Dynamics to the Multiscale Study of Oil-in-Water Emulsions Juan Pablo Gallo-Molina, Dr. Nicolas Ratkovich, and Oscar Alvarez Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03846 • Publication Date (Web): 18 Dec 2017 Downloaded from http://pubs.acs.org on December 23, 2017

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Industrial & Engineering Chemistry Research

The Application of Computational Fluid Dynamics to the Multiscale Study of Oil-in-Water Emulsions 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 widely used in different industries such as oil, food, pharmaceutics and cosmetics. These systems, however, exhibit high degrees of complexity due to the interactions between the dispersed and continuous phase on different levels (i.e. molecular and microscopic) and the emergent properties generated by said interactions. In this work, the interrelationships among macroscopic, microscopic, molecular, process and formulation variables in oil-in-water (O/W) emulsions were analyzed via a multiscale analysis. Furthermore, Computational Fluid Dynamics (CFD) were implemented in order to gain a better understanding of the link between process variables and other relevant responses. Relationships among elastic modulus, mean droplet diameter, zeta potential, stability and incorporated energy measurements could be established. The simulation allowed for the observation of three-dimensional gradients in relative viscosity, droplet diameter and dispersed phase volume fraction, as well as flow details for two of the studied impeller geometries.

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1. INTRODUCTION. Emulsions are metastable colloids made of two immiscible liquids. As these systems are thermodynamically unstable, it is necessary to incorporate energy during its preparation and to add surfactant agents, which reduce interfacial tension and repulsive interactions at the surface1. Even though the range of applications of emulsions is ample (e.g. cosmetics, coating, explosives, oil, pharmaceutics) the complexities caused by the large number of relevant variables and the interrelationships among them have produced a tendency towards the use of empirical methods. It has been determined in the literature that these interrelationships exist among different relevant variables. For example, it has been found that a proportional relation exists between zeta potential and chain size of the dispersed phase in water-in-oil (W/O) emulsions2. Furthermore, Roldan-Cruz et al.3 found that surfactant concentration has a significant impact on this potential and indicated that the ability of nonionic surfactants to stabilize emulsions is related to changes introduced to the interfacial rheology and interactions between molecules at the interface. Wu, et al. 4 pointed out that environmental variables also impact the formation of zeta potential and studied the effects of functional groups on this variable. In his study, Sagis5 established that the molecular level, represented by the dynamics at the interface, affects the macroscopic responses in emulsions and other similar systems. Moreover, Dowding, et al.6 investigated the effect of process variables on particle size distributions, while Kowalska7 studied the relation between the former variable and stability. Likewise, the rheological response of emulsions have been found to be influenced by particle size distribution, environmental factors and volume fraction of the dispersed phase8,9. Considering this large number of relevant variables, multiscale studies have been used by Alvarez et al.10 and Pradilla et al.11 with


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the objective of relating variables at the molecular, microscopic and macroscopic scales with the performance of highly concentrated emulsions as a product. Computational Fluid Dynamics (CFD) are capable of describing multiphase systems such as emulsions and other colloidal suspensions. With the inclusion of rheological, droplet size distribution, break up and coalescence models, it is possible to predict the behavior of these variables and, perhaps more importantly, the nature of the intertwining among them and its influence on the behavior of an emulsion as a whole. Recently, Gallo-Molina et al.12 implemented a CFD model with the objective of complementing a multiscale analysis of W/O emulsions. The use of CFD was found to be valuable for the reason that it yields three-dimensional profiles (which are not easily obtainable via experimentation) that are useful to better understand the effect of macroscopic and microscopic variables. This work represents a continuation of the authors’ previous study. Here, oil-in-water (O/W) emulsions were analyzed using the multiscale approach. As mentioned before, this tool is valuable because it is able to find the links between different scales and the performance of a product. In this case, relations between macroscopic (i.e. elastic modulus), microscopic (i.e. particle size) with the incorporated energy as a transversal factor were studied. As the molecular realm is of critical importance for the understanding of the microscopic and macroscopic behavior, zeta potential measurements were added to the experimental methodology. Stability measurements were analyzed as well. Four types of impeller in a range of concentrations from 10% to 90% were considered. Additionally, a CFD model was coupled with the experimental part of the study with the objective of observing three-dimensional gradients in viscosity, particle size and volume fraction and understanding its influence on the analyzed systems.


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With the exceptions of the addition of zeta potential measurements and an additional impeller geometry to the CFD modelling, the experimental and simulation methodologies were kept equal to the previous work. However, the studied O/W emulsions exhibited significantly different behaviors to W/O systems. For instance, droplet size was not inversely proportional to dispersed phase concentration in the entirety of the studied range of concentrations. The tendencies of all other studied variables diverged from the previous observations for W/O emulsions as well. In this work, different explaining mechanisms are proposed in relation to the studied variables and product and process characteristics.

2. MATERIALS AND METHODS 2.1. Materials. Mili-Q deionized water and USP grade mineral oil were used for preparing oil-in-water (O/W) emulsions. Additionally, Span 80 (sorbitan monooleate, HLB 4.3) and Tween 20 (polisorbate 20, HLB 16.7) were used as surfactants. Simulations were performed with commercial software STAR-CCM+, v. 11.06 (Siemens). The geometric domains were built with Autodesk Inventor 2017. 2.2. Methods. 2.2.1. Experimental methods. 2.2.1.1. Formulation and emulsification process. Emulsions were prepared in a range of concentration from 10 to 90 % and a 4 (wt %) total surfactant mixture concentration. In agreement to usual industry practice13, a HydrophileLipophile Balance (HLB) of 13 was chosen. The surfactant concentration was selected during preliminary tests.


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The preparation process consisted of three steps. In the first place, Tween 20 was added to the aqueous phase and Span 80 was added to the oil phase. Subsequently, each mixture was separately homogenized for 15 min at 300 rpm. The second step consisted in the incorporation of the dispersed phase (oil) into the continuous phase (water). For this, a Fischer Scientific peristaltic pump with a flow rate of 0.5 mL/s was used. The tip velocity of the impeller was 1.7 m/s. During the final step, the emulsions were Figure 1. Schematic of impeller types and dimensions: (a) propeller, (b) straight paddles turbine, (c) Rushton turbine, and (d) pitched blade turbine. permission

from

Reprinted (adapted) with Gallo-Molina,

J.

P.;

Ratkovich, N.; Álvarez, Ó. Multiscale Analysis of Water-in-Oil Emulsions: A Computational Fluid Dynamics Approach. Ind. Eng. Chem. Res. 2017, 56, 7757−7767. Copyright 2017 American Chemical Society.

homogenized for 10 min at the same tip velocity. Lightnin LABMaster L1U10F and Heidolph Hei-TORQUE Precision 400 mixing devices were used for measuring torque. The preparation was made at a temperature of 40ºC. Figure 1 shows the types of impellers used and its dimensions. The impeller-to-tank diameter ratio was 0.78 in all cases. 2.2.1.2. Experimental measurements. A TA instruments DHR1 hybrid rheometer

was used for obtaining rheological information. Three tests were performed: i) a flow sweep with


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the shear rate varying from 1 to 100 s-1; ii) a frequency test at 0.2 Pa and a step of 0.1-300 rad/s; and iii) a stress sweep in a range of 0.1-300 Pa. Temperature was kept at 40 ºC. Measurements of droplet size distributions were performed with a Malvern Instruments Mastersizer 3000. Distribution data is inferred using Mie theory, which predicts the scattering intensity produced by particles (assumed to be spherical) in a sample using Maxwell’s field equations14. Obscuration was kept within manufacturer’s recommended levels in order to avoid that the light scattered by a droplet interacted with other particles before detection. The stability of the samples was evaluated with a Formulaction Turbiscan, which uses temporal changes in transmission and backscattering data produced by a near-infrared source for inferring destabilization kinetics15. Results are presented in the form of the Tubiscan Stability Index (TSI), which is a relative number that compares the stability of a sample at a given time with the status of said sample at the start of the experiment. Tests were performed with a duration of 30 min and scans were done every 25 s. Temperature was kept constant at 40 ºC. Zeta potential was measured with a Malvern Instruments Zetasizer Nano ZS. This equipment estimates the electrophoretic mobility within a cell with a laser light source and an electric field. Then, Henry equation is used for calculating zeta potential16. For this, the dielectric constant of the continuous phase had to be known. 2.2.2. CFD Modelling. 2.2.2.1. Mesh and mesh independence. Autodesk Inventor 2017 was used to reproduce the geometric details of the experimental setup. STAR-CCM+ was used for the discretization of the geometric domain. For this, polyhedral cells were constructed in the bulk of the fluid and a prism layer was used near walls. Considering the complexity of the physical models used and the fact that simulations were conducted in steady


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(a)

(b)

(c)

Figure 2. (a) Geometry mesh, propeller configuration. (b) Geometry mesh, straight paddles turbine configuration. (c) Experimental setup. Reprinted (adapted) with permission from GalloMolina, J. P.; Ratkovich, N.; Álvarez, Ó. Multiscale Analysis of Water-in-Oil Emulsions : A Computational Fluid Dynamics Approach. Ind. Eng. Chem. Res. 2017, 56, 7757−7767 Copyright 2017 American Chemical Society. state, relatively fine meshes were selected. For the propeller setups, the mesh consisted of 602560 cells, while the grid contained 538316 cells for the straight paddles turbine configuration. In Figure 2 the grids and experimental setup can be appreciated. Two factors were considered during mesh independence tests: average velocity after convergence and velocity profiles near the agitator. Mesh independence was considered to be achieved when these variables did not change more than 5%. Tests results for the propeller configuration are reported in a previous publication12, while Figure 3 shows radial velocity profiles for the straight paddles turbine geometry in a 10% emulsion. Three mesh sizes are presented: a coarse mesh consisting of approximately 100000 cells, a fine mesh, consisting in circa 1 million cells and the chosen mesh, which is denoted as ‘medium mesh’. In the same manner, as in the propeller configuration, it was found that the three grids predicted the same forms of the profiles but the coarse mesh generated a noticeable underestimation of velocity magnitudes. On the other hand, the difference between the medium and fine meshes was insignificant. Considering the


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increased computational time required by the later, it was concluded that the medium mesh is acceptable. 2.2.2.2. Simulations. Simulations were conducted for two impellers: propeller and straight paddles turbine. Only the third step of the process described in section 2.2.1.1. (i.e. homogenization) was simulated in steady state. This was deemed to be acceptable due to the reason that preliminary studies showed that the systems become steady immediately after the end of the incorporation phase. Considering this, the impeller motion was simulated with the Moving Reference Frames (MRF) method, which considers the forces associated with a motion without requiring a movement of the cells17,18. The geometric volume discretization was performed with the finite volume method and face fluxes for the transport equations were calculated with a first-order upwind discretization scheme. The algebraic systems of equations resulting from the discretization scheme were solved with GaussSeidel and Algebraic Multi-Grid methods17. Conservation equations were solved in a sequential manner and the pressure-velocity coupling was solved using the SIMPLE algorithm19. Residuals and relevant variables (i.e. torque,

Velocity [m/s]

(a) 0.2

Fine mesh Medium mesh Coarse mesh

relative viscosity, average droplet diameter,

0.1

mean velocity) were used as convergence

0

(b) 0.2 Velocity [m/s]

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

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criteria. Six 10 core Intel Zeon 2.4 Ghz 0.1

processors were used and convergence was 0 -4

-3

-2

-1

0 1 Position [cm]

2

3

4

Figure 3. Radial velocity profiles for the straight

paddles

turbine

geometry

and

different mesh sizes. (a) Above impeller. (b)

achieved after an average of 28.36 h. 2.2.2.3. Mathematical Models. Using the eulerian approach, a set of conservation equations was solved for each

Below impeller.


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phase and additional models were implemented in order to account for interphase interactions. For a phase i, the continuity equation is17,20: 𝜕 ∫ 𝛼 𝜌 𝑥 𝑑𝑉 + ∮ 𝛼𝑖 𝜌𝑖 𝑥 (𝑣𝑖 − 𝑣𝑔 ) . 𝑑𝑎 = ∫ ∑(𝑚𝑖𝑗− 𝑚𝑗𝑖 ) 𝑥 𝑑𝑉 + ∫ 𝑆𝑖𝛼 𝑑𝑉 𝜕𝑡 𝑉 𝑖 𝑖 𝐴 𝑉 𝑉

(1)

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. 𝑆𝑖𝛼 is a mass source term. Similarly, the momentum equation for a phase i is17,20: 𝜕 ∫ 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

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

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. 𝑀𝑖 , the interphase momentum transfer per unit volume, must satisfy equation 3: ∑ 𝑀𝑖 = 0

(3)

The systems were assumed to be isothermal (40 ºC) and density and viscosity for each phase were assumed to be constant as well. The values for the used mineral oil were measured (ρ=851 kg/m3, μ=0.0185 Pa s) and the widely reported values for water at the working temperature were used (ρ=992.2 kg/m3, μ=6.53E-4 Pa s).


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Considering that the flow regimes were laminar (Re, calculated with the Metzner and Otto Method21,22, was of the order of 10 under all conditions) and that a previous study12 found it to be appropriate, no turbulence model was implemented. Furthermore, drag forces was modelled with the Shiller and Naumann expression23 for the reason that it predicts well drag for small spherical particles and it has been found to be adequate for emulsion systems12,24. As it is not relevant in emulsions24, lift force was not taken into account. Similarly, virtual mass forces were not considered because these occur when a dispersed phase has an acceleration relative to a continuous phase. This is relevant only when the dispersed phase density is significantly smaller than the continuous phase density25,26. Additionally, Lotfiyan et al.26 found this approximation to be appropriate for O/W emulsions. Particle size distribution and coalescence and breakup processes were modeled with the Sgamma approximation. This formulation assumes a lognormal distribution and considers transport equations for the moments of the distribution. The lognormal assumption was acceptable because experimental measurements indicated that the samples follow closely this form. The main model equation is: ∞

𝑆𝛾 = 𝑛 ∫ 𝑑 𝛾 𝑃(𝑑)𝑑(𝑑)

(4)

0

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. In order to account for coalescence and break up, source terms must be added to the transport equation of each moment of size distribution. For S0, the following expression was used: 𝜕𝑆0 + ∇. (𝑆0 𝑣𝑑 ) = 𝑠𝑏𝑟 + 𝑠𝑐𝑙 𝜕𝑡

(5)


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Where 𝑣𝑑 is the dispersed phase velocity, 𝑠𝑏𝑟 is the source term for breakup and 𝑠𝑐𝑙 is the term for coalescence. The equation developed by Lo and Zhang27 was used for describing breakup: 𝛾 1−

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

(6)

Where N is the number of small droplets produced when a particle breaks down. Here, 𝑑𝑐𝑟 is the critical diameter and it is described by equation 7.

𝑑𝑐𝑟 =

2𝜎𝛺𝑐𝑟 𝜇𝑐 𝛾̇

(7)

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. This variable is only dependent on the ratio of viscosities between the dispersed and continuous phases1. In equation 6, 𝜏(𝑑) is the timescale for breakup. For the viscous regime (relevant in laminar flows), it can be estimated with the following expression:

𝜏(𝑑) =

𝜇𝑐 𝑑 𝑓(𝜆) 𝜎

(8)

Where 𝜆 is the ratio of viscosities between the dispersed and continuous phases. The definition of the experimental function 𝑓(𝜆) can be found in the work of Hill28. Lo and Zhang27 also developed the coalescence model implemented in this study: 𝛾 𝑑 𝛾 𝑆𝛾 = 𝐹𝑐𝑙 (23 − 2) 𝐾𝑐𝑜𝑙𝑙 𝑃𝑐𝑙 (𝑑𝑒𝑞 )𝑑𝑒𝑞 𝑑𝑡

(9)


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Where 𝐹𝑐𝑙 is a calibration coefficient, 𝐾𝑐𝑜𝑙𝑙 is the collision rate, 𝑃𝑐𝑙 is the probability of collision leading to coalescence. The definition of the equivalent diameter, 𝑑𝑒𝑞 , can be found in the literature27. As in the case of the timescale for breakup, the collision rate depends on the flow regime as well. For the viscous case, it is defined by the following expression: 1

𝐾𝑐𝑜𝑙𝑙

2

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

(10)

Where 𝜙 is the dispersed phase volume fraction. The probability of collision showed in equation 9 represents a comparison of the interaction time of two colliding droplets and the time required to drain away the film of continuous phase that forms between particles27: 𝑃𝑐𝑙 (𝑑𝑒𝑞 ) = exp(−𝑡𝑑 𝛾̇ )

(11)

The drainage time (𝑡𝑑 ) is dependent on the presence of obstacles at the interphase. As surfactants play this role in emulsions, a partially mobile interface model for the drainage time was chosen: 3

𝜋𝜇𝑑 √𝐹𝑖 𝑑𝑒𝑞 2 𝑡𝑑 = ( ) 2ℎ𝑐𝑟 4𝜋𝜎

(12)

Where 𝐹𝑖 is the interaction force during the collision and ℎ𝑐𝑟 is the critical film thickness. The definition of both parameters can be found elesewhere27. The critical film thickness is a function of the Hamaker constant, which was estimated using the values reported in the literature29. The effect of the surfactant is taken into account in equations 7 and 12. In the former, surface tension, which is highly dependent on the action of the chosen surfactant is considered, while the physical obstruction of the interface by surfactant molecules (which is particularly important for non-ionic surfactants) is reflected in the latter.


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Finally, the non-Newtonian behavior of emulsions was described with the Morris and Boulay model30: 𝜙 −1 𝜙 2 𝜂𝑟 (𝜙) = 1 + 2,5𝜙 (1 − ) + 𝐾𝑠 ( ) 𝜙𝑚 𝜙𝑚

(13)

Where 𝐾𝑠 is the contact contribution and 𝜙𝑚 is the maximum packing fraction. The relative viscosity ( 𝜂𝑟 ) is a dimensionless parameter that describes the ratio between the mixture viscosity (𝜂) and the continuous phase viscosity (𝜂𝑐 ): 𝜂𝑟 =

𝜂 𝜂𝑐

(14)

This model is suitable for describing isotropic flows when an identity tensor is used as the anisotropy tensor in the normal stress tensor: 𝜏𝑝,𝑁𝑆 = −𝜂𝑐 (𝜙)𝜂𝑓 𝛾̇ 𝑙 𝑄

(15)

Where 𝛾̇ 𝑙 is the shear rate of the liquid and Q is the anisotropy tensor.

3. RESULTS AND ANALYSIS The first part of this study consists in the experimental multiscale analysis of O/W emulsions prepared with the four previously mentioned impellers. A minimum of three replicate experiments were conducted per data point and each individual measurement was repeated at least three times as well (For example, particle sizes for each concentration were obtained from at least three different samples and each sample was measured at least three times) . For the sake of clarity, error bars are not displayed in the subsequent figures but percent deviation was approximately 5% for incorporated energy measurements, 5-8% for mean droplet diameters, 2-9% for elastic modulus, 8-10% for TSI and 1-6% for zeta potential. Similar deviations were observed by Pradilla et al.11 for highly concentrated emulsions. In the second part, CFD is used in order to gain a better understanding of the experimental observations.


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The incorporated energy during the incorporation and homogenization phases was used as a transversal variable in the multiscale study. The reason for this choice is that it is necessary to add energy in order to create additional interfacial area and to deform the interface with the objective of allowing surfactant molecules to be adsorbed1,31. Previous studies10,12 have found that more energy is incorporated during the homogenization phase and that this difference is exacerbated as the concentration of dispersed phase diminishes due to the reduction in viscosity and required incorporation time. As shown by Figure 4 and Figure 5, an interesting behavior in average droplet size diameter was observed: at low concentrations, it is directly proportional to the incorporated energy and, after reaching an inflection point, the opposite behavior arises. Hadnadev et al.32 reported similar results and pointed out that the dependence of dispersed phase concentration on the droplet diameter is a reflection of complex interactions among different variables. Salager33 reported that, in these systems, the relation between viscosity and stirring efficiency is of importance, while Langevin 34 found that the elasticity at the interface increases with dispersed phase concentration. For this reason, it can be argued that this behavior can be attributed to the dominant set of interactions at each point of dispersed phase concentration. At low concentrations, the elasticity is low, while the effect of the low viscosity of the continuous phase became relevant. This low viscosity allows the impellers to generate more shear forces, which are critical for droplet breakup in a viscous emulsification regime35,36. However, as the concentration increases, the growing interactions among droplets generate an increase in viscosity, which decreases stirring efficiency. Consequently, contacts between droplets became more prevalent and coalescence generates higher droplet diameters. When the inflection point is reached (around 50% wt), the larger amounts of elasticity at the interphases not only keep increasing the incorporated energy but also overcome


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50 40 30

10

Incorporated Energy

8

Propeller Straight Paddles Rushton Pitched Blade

6

20

4

10

2

0 0

20

the trend in droplet diameter generated by the low

12

Mean Diameter Propeller Straight Paddles Rushton Pitched Blade

40 60 Concentration [%]

80

0 100

Figure 4. Mean droplet diameter (D[4,3])

and incorporated energy as functions of

Incorporated Energy [J/mL]

60

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


stirring efficiency of the impeller. As these higher elasticities make droplets more resistant to coalescence and the available space between droplets is reduced, the systems start to tend towards smaller average diameters. Figure 4 illustrates the observed evolution of this

dispersed phase concentration in O/W variable in function of the dispersed phase emulsions prepared with four different concentration: In a step of 10-60% wt, the energy impellers.

increases in an approximate linear form, while at

higher concentrations, an exponential grow was observed. This situation is caused by the increase in elasticity and by the diminishment of space between droplets. As concentration increases, more dispersed phase is added to the system and, after a saturation point is reached, existing droplets must be broken in order to accommodate the droplets that are being added. With higher concentrations, it is necessary to break up more particles, which dramatically increases the energy consumption. This mechanism contributes as well to the observed decrease in mean droplet diameter discussed earlier. Recent studies have found that the impeller geometry is relevant for different variables, such as incorporated energy11,12,37 and stability12,38. In a previous work12, it was discussed that these differences originate from the variance in shear forces and flow characteristics introduced by each impeller geometry. From Figure 4, it can be inferred that the straight paddles and Rushton turbines incorporated the larger amounts of energy and produced the emulsions with the lowest average diameters. On the contrary, the propeller and pitched blade turbines produced emulsions with


15


100

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

higher mean sizes and had lower power draws. Propeller Straight Paddles Rushton Pitched Blade

This results are consistent with the previous

10 % wt

10

Page 16 of 37

literature11,12,37,39,40 but, as discussed by Gallo-

90 % wt

Molina et al.12 and references within, the high 1 1

10

20

sensitivity of the power consumption of the


Figure 5. Mean droplet diameter (D[4,3]) in Rushton turbine to geometric characteristics and function of incorporated energy in O/W the particularities in the power curves at low emulsions using four different impellers. The Reynolds numbers for non-Newtonian fluids, concentration values from the left are 10%, introduce complexities that affect the differences 20%, 30%, 40%, 50%, 60%, 80% and 90% for in power consumption among impellers. the propeller turbine; 10%, 20%, 30%, 50%,

The results reported in Figure 5 are similar to

60%, 80%, and 90% for the straight paddles the observations of Pradilla et al.11 for analogous

turbine; 20%, 30%, 40%, 70% , 80% and 90% O/W emulsions: at high concentrations, the for the Rushton turbine; 10%, 20%, 30%, 40%, differences in mean droplet diameter between 50%, 60%, 70%, 80% and 90% for the pitched impellers tend to be more pronounced. However, blade turbine.

it

was

also

observed

that,

at

lower

concentrations, large dissimilarities in power draw did not translate into comparable divergences in mean droplet diameter. This can be explained by the fact that interactions among droplets are not significant, while other constant variables (e.g. surfactant concentration) play a bigger role. Thus, the coalescence and breakup mechanisms are roughly the same, regardless of the energy that is being added to the system. This phenomenon also helps to explain the similarities in mean diameter growth among different impellers: the decrease in stirring efficiency associated with higher viscosities induced higher droplet sizes, but other mechanisms (probably related to the


16

Page 17 of 37

interfaces) were kept approximately equal. 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



90% wt

Nonetheless, the observed variances indicate that geometry differences do play a role, albeit

1

small, in the growth of droplet diameter at low 0.01

concentrations.

50% wt 1


10

20

Figure 6. Elastic modulus in the linear viscoelastic region as a function of incorporated energy for O/W emulsions prepared with four impeller types. The concentration values in ascending order are 60%, 80% and 90% for the propeller turbine; 50%, 60%, 70%, 80% and 90% for the straight paddles turbine; 70%, 80% and 90% for the Rushton turbine; 50%, 60%, 70%, 80% and 90% for the pitched blade turbine.

The

rheology

of

emulsions

and

its

relationship with microscopic and process variables has been examined in previous publications8,10–12,41–44. Figure 6 shows that higher values of the incorporated energy lead to higher elastic modulus (displayed here in Pa). This behavior was observed in previous studies for both highly concentrated O/W emulsions11 and W/O emulsions12. This is caused by the increases in elasticity associated with higher dispersed phase concentrations. As previously discussed, this makes droplets more

resistant to coalescence. In turn, this allows for more interactions among droplets, which is reflected in larger elastic modulus. Cohen-Addad et al.42 found that elasticity is significantly connected with interfacial energy density. Therefore, it can be concluded that the larger amounts of incorporated energy required to prepare highly concentrated emulsions generated higher elasticities that were macroscopically translated in the elastic modulus.


17


Page 18 of 37

Noticeable differences in the elastic modulus were observed in function of the impeller type. This implies that the impeller geometry plays a role in the final macroscopic characterization of O/W emulsions. However, these divergences are small when the dispersed phase concentration is equal. Therefore, it can be concluded that other factors are more important for the determination of the elastic modulus. Gallo-Molina et al.12 discussed that one of these factors is the amount of interactions among droplets, which is linked with dispersed phase concentration. The stability of emulsions under different conditions has been studied in the literature as well. For example, Almeida et al.45 assessed process and formulation variables in order to obtain stable W/O emulsions. Domian et al.46, Felix et al.47 and Qiao et al.48 inspected the rheology and stability of O/W systems. Aoki et al.49 investigated the influence of environmental conditions on stability while Roldan-Cruz et al.3 explored the relation between surfactant concentration and stability. Figure 7 shows the stability of the emulsions studied here in the form of TSI. At the higher concentrations, the observed behavior is similar to the results presented in a previous work12 for W/O emulsions: more concentrated emulsions exhibited higher stabilities. This is explained by the fact that the smaller droplets associated concentrated emulsions are less sensitive to gravitational effects and are able to equilibrate the differences in Laplace pressure; reducing Ostwald ripening1. In contrast to W/O emulsions, less concentrated systems (10-20%) were more stable than mediumconcentration emulsions. This is related to the previously discussed behavior of mean diameter: at lower concentrations, smaller droplets are favored, which generate more stable emulsions.


18

Page 19 of 37

Impeller geometry was observed to impact

20


TSI

15

stability as well. The higher power draws associated with the Rushton and straight paddles

10

turbines tended to produce smaller mean droplet

5

diameters

0

10

30

50 Concentration [%]

70

and,

consequently,

more

stable

90

Figure 7. TSI after 30 min for different emulsions. As expected, emulsions prepared with less energy-intensive impellers exhibited larger

impeller types.

values of TSI. Zeta potential is commonly used to predict stability in emulsions and it has been considered in previous studies for a variety of purposes2,4,50,51. It is well established that the presence of repulsive forces at the interface is a significant factor for emulsion stability for the reason that they hinder coalescence. Although these repulsive forces cannot be directly measured, they are related to zeta potential, which is defined as the potential difference between the electroneutral region and the bound layer of ions on the droplet surface52. The observed values of zeta potential as a function of oil concentration are showed by Figure 8. The effect of impeller type was found to be insignificant. -20 -25

Zeta Potential [mV]

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


-30

A comparison between figures Figure 4 and Propeller Straight Paddles Rushton Pitched Blade

Figure 8 suggests that a slight relation between droplet diameter and zeta potential exists.

-35 -40

Considering the relatively high total surfactant

-45 -50 0

20


80

100

concentration, this effect is likely caused by the

Figure 8. Zeta Potential in function of

theorized displacement of ions (produced from

dispersed phase concentration for O/W

dissolved atmospheric carbon dioxide and water

emulsions prepared with four impeller dissociation) from the interface that occurs when types.


19


Page 20 of 37

interface coverage is high. This displacement reduces the interfacial charge and thus the magnitude of zeta potential3,53. In this case, the smaller interfacial areas associated with larger droplet diameters allowed the same number of surfactant molecules (as the total mass of surfactant was kept constant) to cover more efficiently each droplet; displacing more ions. Consequently, larger droplet sizes favored smaller magnitudes in zeta potential. In turn, this phenomenon favored the observed instability at medium concentrations due to the smaller repulsive potentials that lead to higher rates of coalescence. Additionally, it can be argued that this phenomenon produced a positive feedback effect below the point of maximum droplet size (around 50% wt): the larger droplet diameters induced by the stirring regime allowed for a reduction in the interfacial repulsive forces, which generated even larger droplet diameters via flocculation and coalescence. As stated before, the relation between droplet diameter and zeta potential is minor. This is to be expected as the use of deionized water suggests that only a relatively small amount of ions could be formed before measurement. Therefore, it can be concluded that dispersed phase concentration is not very influential to the resulting values of zeta potential. This result was also reported by Medrzycka54 and, more recently, by Mirhosseini et al.55. The resulting interfacial potential is much more dependent on the action of the surfactant. As the concentration and type of surfactant were kept constant, this effect could not be observed during this study. Furthermore, the non-ionic surfactants used in this work stabilize emulsions manly by steric repulsion, which implies that electrostatic repulsions are of secondary importance3. Therefore, it can be concluded that the gravitational effects associated with droplet diameter are more important to the stability in the emulsions studied here. CFD have been implemented for the modelling of emulsions under different conditions. Roudsari et al.24 studied the mixing of W/O emulsions in lab-scale conditions, while Oshinowo et


20

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al.56 analyzed the separation of the same type of emulsions in batch gravity separators. Agterof et al57. focused on the prediction of particle size distributions and Lo et al.58 assessed the effect of multiple variables on pressure distributions in W/O emulsions. Furthermore, Vladisavljević et al.59 used CFD to relate microscopic and macroscopic variables in microchannel emulsification, while Lotfiyan26 investigated O/W emulsion microfiltration. Finally, Gallo-Molina et al.12 showed that CFD is a valuable tool in the multiscale analysis of W/O emulsions. In this same manner, a CFD model was implemented in this study with the objective of better understanding the effect of process variables and the resulting three-dimensional gradients in the mixing vessel in the studied microscopic and macroscopic variables. As previously mentioned, only the homogenization phase of the preparation procedure was modelled and two impeller geometries were considered: the propeller turbine, which has a low power draw and the straight paddles turbine, which has a higher energy consumption. The characteristics in flow and other variables for the pitched blade turbine are expected to be similar to the propeller, while analogous similarities are expected for the Rushton and straight paddles geometries.

Simulations were validated with experimental data of relative viscosity and

incorporated energy for the reason that these were deemed as the main variables for analysis in this work. Figure 9 shows that there is good agreement between experimental and CFD results. As expected, the simulations reflected the differences in energy consumption between the studied impeller geometries. Both experimental and CFD results showed that incorporated energy during the homogenization phase is proportional to dispersed phase concentration. As previously discussed, this is caused by the increments in interfacial elasticity and interactions among droplets, which ultimately impact the system hydrodynamics and increases its viscosity; forcing the impeller to add more energy. The relation between concentration and incorporated energy was observed to


21


be approximately linear up until 60%-70%

(a) Incorporated Energy [J/mL]

7 6

Straight Paddles. Experimental Straight Paddles. CFD Propeller. Experimental Propeller. CFD

dispensed phase concentration. From that point

5

onwards,

4

exponential, which suggests that a saturation

3

20

(b)

100

the

behavior

was

roughly

point was reached. This saturation point

2 0

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

Page 22 of 37


80

100

Straight Paddles. Experimental Straight Paddles. CFD Propeller. Experimental Propeller. CFD

conducted to much higher values of viscosity and incorporated energy.

Smaller values of

relative viscosity were reported for the straight 10

paddles impeller because these values of viscosity were calculated at the shear rate 1 0

20

Figure


9.

experimental Incorporated

80

Comparison and energy

CFD in

100

between data.

function

(a) of

dispersed phase concentration. (b) Relative viscosity in function of concentration.

provided near the impeller. As this geometry provides more shear forces and emulsions exhibit strong shear thinning behavior42,60 (this was also observed during the flow tests conducted in this study), this result was to be expected as well. In both cases, there are larger

errors at medium concentrations. This is caused by the fact that this is a transition region that exhibits a complex set of interactions, which the physical models are less able to describe. Velocity profiles for a 10% emulsion are showed in Figure 10. The observed results are typical: the radial flow configuration of the straight paddles turbine produced higher velocities in a perpendicular direction to the blades. Conversely, the axial characteristics of the propeller induced more stratification in the velocity profile in the vertical direction. The increases in viscosity associated with higher dispersed phase concentrations produced a reduction in velocity


22

Page 23 of 37 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


magnitudes and an expansion of dead zones. In turn,

(a)

this viscosity changes are induced by the previously alluded

increases

in

interfacial

elasticity.

Furthermore, the mentioned differences in the

(b)

hydrodynamics caused by impeller geometry are critical for the properties of the studied emulsions. Figure 10.Transversal and axial velocity This was observed in the experimental measurements profiles (m/s) with 10% dispersed phase (which reflect an average over the whole content of concentration.

(a)

Straight

paddles the mixing vessel) and was deemed to be of

geometry. (b) Propeller geometry. Red importance for the particularities of the threezones indicate velocities equal or larger dimensional profiles obtained from the simulations. than the indicated corresponding value.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 11. Profile of Sauter diameter (D[3,2],µm) for different dispersed phase concentrations. (a) 10%, straight paddles. (b) 50%, straight paddles. (c) 90%, straight paddles. (d) 10%, propeller. (e) 50%, propeller. (f) 90%, propeller. Dark red zones indicate diameters equal or larger than the indicated corresponding value.


23


Page 24 of 37

Figure 11 illustrates droplet diameter profiles for three dispersed phase concentrations. Generally larger particle sizes were predicted far from both impellers. This is consistent with the fact that breakup is mainly produced by shear forces in a viscous emulsification regime, which in this case was produced by the low impeller speeds and high viscosities. The larger shear forces existing near the blades of the impeller induce higher breakup rates, which is reflected in smaller droplet diameters. More pronounced gradients were observed when the dispersed phase concentration was 50%. This situation is likely caused by the discussed influence of viscosity and stirring efficiency on droplet diameter. At 50% concentration, the fluid viscosity is high enough to significantly reduce mixing performance, which reduces the breakup rate and perhaps more importantly, exacerbate its dependence to the distance from the impeller. In other words, this low mixing performance further decreases shear forces far from the impeller, which favors larger droplet diameters. Additionally, it can be argued that at this point of concentration, elasticity is not enough to hinder coalescence in a sufficient degree and thus this factor is not able to offset the grow in particle sizes far from the agitators. The lower power draws of the propeller turbine produced an appreciable intensification in diameter gradients. Smaller incorporated energies not only produce higher average droplet sizes but also imply that the impeller is less able to transmit shear to the whole content of the mixing vessel; especially the regions that are far from the blades. Subsequently, the propeller geometry is less efficient at breaking up bubbles far from its blades; producing more pronounced gradients. Relative viscosity profiles show an analogous behavior (Figure 12). For both geometries, larger viscosities were predicted far from the impeller. This situation is caused by the strong shearthinning characteristics of O/W emulsions. Consequently, the lower shears exerted on the fluid far from the impeller generated larger viscosities. The low viscosities and near Newtonian behavior


24

Page 25 of 37 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)

(c)

(d)

(e)

(f)

Figure 12. Profile of relative viscosity for different dispersed phase concentrations. (a) 10%, straight paddles. (b) 50%, straight paddles. (c) 90%, straight paddles. (d) 10%, propeller. (e) 50%, propeller. (f) 90%, propeller. Dark red zones indicate viscosities equal or larger than the indicated corresponding value. of lower dispersed phase concentrations allowed for lesser gradients, while the opposite phenomenon was true for highly concentrated emulsions. At higher concentrations, the large elasticities producing high viscosities and significant non-Newtonian behavior generates a substantial sensitivity to the impeller geometry. As the straight paddles turbine is capable of transmitting shear forces more efficiently to the fluid, a more homogeneous distribution of viscosity was observed. Figure 13 shows that the dispersed phase is reasonably well distributed in the mixing vessel, which suggests that both impeller geometries are capable of generating adequate mixing. This is to be expected considering that O/W emulsions have relatively low viscosities. However, the presence of appreciable gradients indicate that mixing may be inappropriate in a scaled-up operation, which suggests that higher tip velocities are necessary. While considered to be superior to the propeller turbine, the radial configuration of the straight paddles impeller generates some gradients in the vertical direction. For this reason, it may be convenient to use multiple mixers in a coaxial configuration.


25


Page 26 of 37

(a)

(b)

(c)

(d)

(e)

(f)

Figure 13. Profile of oil volume fraction for different dispersed phase concentrations. (a) 10%, straight paddles. (b) 50%, straight paddles. (c) 90%, straight paddles. (d) 10%, propeller. (e) 50%, propeller. (f) 90%, propeller. Dark red zones indicate volume fractions equal or larger than the indicated corresponding value. 4. CONCLUSIONS In this work, CFD were used as a complement to experimental data in a multiscale study of O/W emulsions. The systems were simulated with the Eulerian approach, the S-gamma model for droplet size distribution and the Morris and Boulay formulation for describing non-Newtonian rheology. The experimental part of the work consisted of measurements of rheological data along with incorporated energy, particle size, stability, zeta potential and stability. Incorporated energy was treated as a transversal variable that allowed a better understanding of the relationships among macroscopic (i.e. rheological), microscopic (i.e. droplet size), molecular (i.e. zeta potential) and stability variables. Higher amounts of incorporated energy were related with larger elastic modulus but, unlike W/O emulsions studied previously under the same conditions, an inversely proportional relation to mean droplet diameter was not observed in the entirety of the studied range of concentrations. This phenomenon was attributed to the effect of


26

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viscosity, mixing efficiency and low interfacial elasticity at the lower concentrations. As expected, this situation was reflected in the stability of the emulsions. A minor relationship between zeta potential and droplet diameter was observed. Even though the used surfactants act via steric repulsions, this effect is expected to impact emulsion stability. Impeller geometry was found to play an important role in most of the studied values for the reason that geometry determines the amounts of energy and shear forces transferred to the fluid. After validation with relevant experimental data, CFD simulations provided three-dimensional profiles of droplet diameter, relative viscosity and dispersed phase volume fraction. These results were proven to be useful for the experimental part of this study because the predicted gradients in the analyzed variables are expected to produce significant effect in the macroscopic and microscopic response of the systems; especially in a scaled-up situation. CFD results confirmed the experimentally made assessment that the straight paddles impeller provides superior mixing and emulsion characteristics in comparison to the propeller turbine.

AUTHOR INFORMATION Corresponding Author *Email: [email protected] NOMENCLATURE Latin letters CFD: Computational Fluid Dynamics d: Particle diameter 𝑑𝑒𝑞 : Equivalent diameter 𝑑𝑐𝑟 : Critical diameter


27


Page 28 of 37

Fint: Internal forces g: gravity vector ℎ𝑐𝑟 : Critical film thickness HLB: Hydrophile-Lipophile Balance 𝐾𝑐𝑜𝑙𝑙 : Collision rate m: Mass flow M: Interphase momentum transfer MRF: Moving Reference Frames n: Number of particles O/W: Oil-in-water P: Pressure 𝑃𝑐𝑙 : Probability of collision P(d): Probability function of particle diameter Q: Anisotropy tensor Re: Reynolds number S: Source term 𝑡𝑑 : Drainage time TSI: Tubiscan Stability Index v: Velocity vg: Grid velocity W/O: Water-in-oil X: void fraction Greek letters α: Volume fraction 𝛾̇ : Shear rate 𝜂: Viscosity of mixture 𝜂𝑐 : Viscosity of continuous phase 𝜂𝑟 : Relative viscosity 𝜆: Ratio of viscosities μ: Dynamic viscosity 𝜌: Density 𝜎: Surface tension 𝜏: Molecular stress tensor 𝜏 𝑡 : Turbulent stress tensor 𝜏(𝑑): Timescale for breakup 𝜙: Dispersed phase volume fraction 𝜙𝑚 : Maximum packing fraction 𝛺𝑐𝑟 : Critical capillary number


28

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