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The Electrohydrodynamic mixer for producing homogenous emulsion of dielectric liquids
Colloids and Surfaces A 578 (2019) 123592
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Colloids and Surfaces A journal homepage: www.elsevier.com/locate/colsurfa
The Electrohydrodynamic mixer for producing homogenous emulsion of dielectric liquids R. Heidaria, Alireza R. Khosroshahia, B. Sadrib, E. Esmaeilzadeha, a b
T
⁎
Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran School of Industrial Engineering, Purdue University, 315 N. Grant Street, West Lafayette, IN 47907, USA
G R A P H I C A L A B S T R A C T
Interface instability due to two large recirculation vortex of silicon oil and short recirculation vortex of transformer oil under ground electrode.
A R T I C LE I N FO
A B S T R A C T
Keywords: Electrohydrodynamics mixer Dielectric liquids Miscible Instability Emulsion
This paper experimentally investigates the production of a homogeneous emulsion of two dielectric and immiscible liquids of transformer and silicone oils in an electric field with a high voltage. The aim of this paper is the examination of the effects of the electric field intensity, geometric height of two dielectric liquids and the location of non-uniform electrodes on instability process of two liquids’ interface and the analysis of a homogeneous emulsion production. Experiments are performed within 50 kV, the height ratio of two liquids in a stable h condition is within (H = h1 = 1, 1.25, 1.66, 2.5, 5) and the HV electrode is located in two up and down positions. 2
The interface instability illumination is captured by a high speed digital camera at 1000 f/s using a digital analytic system to a point that a homogeneous emulsion is produced, and the required time to obtain the ultimate goal in different cases is achieved as well. The complete mixing time is calculated till a homogeneous emulsion is obtained which is influenced by a voltage increase and height ratio decrease of two stationary liquids. The results show that both the abovementioned cases lead to a decrease in the complete mixing time. In this context, the way the HV electrodes are located vertically is also effective.
1. Introduction Producing an emulsion of dielectric liquids in smaller-scaled
⁎
systems is of great importance in pharmaceutical, biological and chemical industries as well as in nanofluid productions and miniature systems particularly microfluidics [1–7]. Mechanical systems are not
Corresponding author. E-mail address: [email protected] (E. Esmaeilzadeh).
https://doi.org/10.1016/j.colsurfa.2019.123592 Received 17 March 2019; Received in revised form 18 June 2019; Accepted 20 June 2019 Available online 21 June 2019 0927-7757/ © 2019 Published by Elsevier B.V.
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Fig. 1. Schematic of setup.
various pathways of droplet breaking. Similar study was done on the dynamics of drop formation from submerged orifices under the influence of an external electric field [20]. The computations for leaky dielectric fluids reveal that both prolate and oblate shaped drops can be formed depending on the combination of the fluid conductivity and permittivity ratios. An experimental study on application of an electric field on an oil droplet floated on the surface of a deionized water bath was done [21]. According to the results, when the electric field was ramped up abruptly to a particular voltage, any of the spreading, oscillation or ejection of the droplet could be engendered at lower, intermediate and higher field intensities, respectively. Another study on the application of an electric field across the pressure-driven stratified flow of two miscible fluids inside a microchannel was done by Dutta et al. [22]. The effect of electric field Rayleigh number, linear-onset regime and time-periodic nonlinear regime analogous to the von Kármán vortex street in the downstream was studied. The outcomes reveal that the EHD instabilities of studied system appear only beyond a critical field intensity and these instabilities could be categorized in five distinctive modes. Results reveal that the location of the interface, thickness of the interface, level of charge injection, strength of the applied EHD field, viscosity contrast across the diffused interface and diffusivity across the interface are some of most important parameters for these types of instabilities. As the literature review illustrates, the conducted studies of different researchers have not yet been completely responsive to interface instability of mixed liquids affected by electric fields. In the present study, particular cases of the interface disappearance process have experimentally examined for the purpose of producing a homogeneous emulsion. There are many influential factors among the concerned variables of this study to name a few; the effect of the location of high voltage electrodes and ground, geometric height of two stationary dielectric liquids and electric field intensity.
often used in applications of the mentioned scales. Therefore, applying EHD mixers are highly advantageous. This method requires careful studies so that their high efficiency can be used in different applications. G. I. Taylor [8] investigated the instability resulting from the effects of a vertical electric field on a horizontal interface of a stationary liquid in 1965. He concluded that by increasing the electric field intensity, it is possible to easily overcome the gradient pressure in liquids interface resultant from gravity and surface tension that in turn will lead to interface instability. In an international EHD symposium held on 23–26 September 2012 in Gdansk, Poland, many applications related to EHD were mentioned. Three influential articles by W. Balachandran [1], P. Atten [2] and J. S. Yagoobi [3], the keynote speakers of the seminar; are introduced the importance of Electrhydrodynamic methods in different applications. In 2003, Eow and Gadiri [9] measured the electric current intensity resulting from an electric field perpendicular to two miscible liquids and observed that different regimes govern the phenomenon and bring about instabilities with different patterns and the interface disappearance begins as the Taylor Cone’s regime starts. In 2007, in a review paper, Dela Mora has completely presented Taylor cones instability [10]. Rasin et al. have studied an unstable air-water and oil-water interface and calculated numerically the intensity of the electric current influenced by an electric field [11]. In 2008, Collins et al. examined the geometric shape of the instability cone in the interface and how it was drowned in liquid [12]. They concentrated on the appearance of the Taylor Cone from the beginning of the interface instability and they were able to calculate numerically the critical value of the electric field intensity. In 2011, B. Khorshidi et al. achieved experimental results concerning the mixing quality of two dielectric liquids, drowning of a water drop in oil, its ionization in vertical electric field and its interface instability [13]. In 2010, Uemura et al. examined the technical behavior of singularity of the interface instability of a liquid which was resulted from its rotation and showed different instability regimes due to vertical electric fields [14]. In this regard, P. Atten et al. examined the abovementioned study in the behavior of a circle drop in water-oil interface [15]. In 2010, E. Esmaeizadeh et al. studied mixing of two stationary dielectric liquids with the same height in a non-uniform dielectric field [16]. Results show that by passing the critical intensity field, momentary fluctuations of the two liquids’ interface begin and ultimately result in instability under different patterns in order to achieve a stable emulsion. In addition, the results indicated that the existence of free charges in the interface caused by the dissociation, recombination and breakup of the balance of the electric and hydrodynamic forces are effective. Some numerical and experimental investigations have been carried out to study the deformation and breakup of the droplet inside a microchannel [17–19]. Results show that in the presence of electric field, the interplay between electrostatic, inertial, capillary and viscous forces lead to
2. Methods and materials The present study aims to experimentally investigate the mixing process of two dielectric liquids in a non-uniform vertical electric field in a designed study platform. Fig. 1 illustrates the schematic of the study platform. In this figure, the arrangement of electrodes and the way the electric field is produced, the geometric location of two dielectric liquids and the graphical processing system are shown. In all experiments, two miscible dielectric liquids with thermoelectric properties introduced in Table 1 are used. The two liquids used in the experiments are pure silicone oil and standard transformer oil and they are used in the exact conditions of the study to a point that a homogeneous emulsion is produced. Due to high density of the silicone oil, its height in stationary position is selected to be fixed and equals to 25 mm in all experiments, and the transformer oil above it, is selected in different sizes with the ratio 2
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transformation. To capture the incidents resultant from the electric field in the interface instability and its continuous process to a point that the main objective of the experiment is achieved, a digital camera, EXILIMEX10 Casio at 1000 f/s is used. In the present experiment, due to slowness of the incidents, 400 f/s is enough for the purpose of illumination. Image process toolbox of MATLAB was used for investigation of mixing process and evaluation of the current mixer. For image processing, a video was recorded with high-speed camera for all 20 designed experiments. After that, at certain times specific images were taken out from recorded videos and these images were converted into a gray-scale mode and inserted into image processing toolbox of MATLAB. Then, the intensity of white color is measured for each pixel. This parameter is named ξ and it identifies the efficiency of the local mixing. This parameter is always positive and volatile in the range of 0 ≤ ξ ≤ 256 where it is increased with intensity of white color, i.e. ξ is equal 256 for a completely white pixel. The average of non-dimensional mixing intensity is defined as:
Table 1 Physical and Electrical properties of liquids. Properties
Transformer oil
Silicone Oil
Dynamic viscosity (kg/m.s) Density (kg/m3) Electrical conductivity (S/m) Relative permittivity (εr=εt/ε0) Ion mobility (cm2/V s)
0.02 842 3.3 × 10−12 2.1 5 × 10−6 1.1 × 10−5
0.35 970 14 × 10−13 2.76 9 × 10−7 2 × 10−6
Table 2 Relative height H of two dielectric liquids. H=
1.00
h1 h2
h1 = 25 mm Silicone oil
1.25
1.66
2.50
5.00
h2 = Transformer oil
h
of H = h1 according to Table 2. 2 In all experiments, the non-uniform electric field between the two high voltage electrodes and ground is used in two conditions of a high voltage (in up) and a high voltage (in down). The experiment setup is located in a rectangular cubic enclosure made of highly transparent glass for the purpose of confident capturing. The dimensions of this part are 150 mm × 200 mm and its height is 200 mm which, with respect to the main tank, completely prevents dust and other influencing factors to enter the case. The main section of the experiment is made of a transparent Plexiglas with 60 mm × 80 mm × 150 mm dimensions. The electrodes are made from copper with 30 mm × 40 mm and 10 mm × 20 mm dimensions to produce a non-uniform voltage in two conditions and are located in the main section of the experiment according to Fig. 1. The sharp edges of the electrodes are removed completely as much as possible to prevent ion injection to liquid surroundings. The electrode in the up position, due to observing the relative height H vertically is equipped with a mechanism which can move upwards and downward easily. Applying a voltage with DC voltage generator is done within 50 kV and precision of 0.1 kV. For the purpose of confidence and voltage generator calibration, a high voltage probe is used simultaneously, too. Considering the values in Table 1, in this experiment, pure and standard dielectric liquids are used in both silicone and transformer oils. These properties are used with due attention to buying them from reliable companies and the conditions governing the experiments as well. It is apparent that regardless of this observance, the probability of errors in measurements and impurity of the liquids can slightly influence the experiment results. Different emissivity and mobility can affect transference of positive and negative ions to the interface. Previous experiments conducted by E. Esmaeizadeh et al. show that positive and negative ions can influence instability process by breaking molecules down and recombining them [23]. This transformation follows the equation below:
i
[I ] =
Kr
i × j × ξmax
(2)
Where i, j denotes the horizontal and vertical positions of a pixel, respectively. Fig. 2 illustrates the results of image processing for a sample picture for test No. 1–5. Fig. 2 shows the instability formation in the enclosure and increasing the mixing intensity. 3. Results and discussion The ultimate purpose of this study is to investigate experimentally the interaction effect of electric field and hydrodynamic forces on the interface instability process in dielectric liquids for the purpose of producing a homogenous emulsion. The opposition in both the electric field and hydrodynamic forces has been considered in two cases. Case 1 considers the electric field before it reaches the critical value and in case 2 the electric field reaches the critical value. In case 1, due to interface stability, the hydrostatic forces interact with the electric field forces according to equation below [1]:
Feff . =
1 1 1 ε1 Em2 − T ( + ) − ΔP. g . Zinterfae 2 R1 R2
(3)
Where ε1 is permittivity of dielectric oil in the air vicinity, Em is vertical electric field intensity, T is surface tension in the liquid interface, R1 and R2 are the radiuses of surface curves perpendicular to the interface. Since the present study focuses on the interface of two dielectric liquids, it is necessary that Eq. (3) be corrected in the following way:
Feff . =
1 1 1 (ε1 + ε2) Em2 − T ( + ) − ΔP. g . Zinterfae 2 R1 R2
(4)
In the equation above, ε2 is the second dielectric liquid of the process above. If the electric field intensity exceeds the critical value, the interface instability under different regimes will continue until a homogeneous emulsion is produced. In this case, the interactive forces as well as the effects of both electric and hydrodynamic forces interfere with the instability process. The governing equation of the phenomenon inserted as momentum per unit volume which can be solved numerically.
Kd
A+ B − ↔ A+ + B −
j
ξ ∑imax ∑ jmax =1 = 1 ij
(1)
Where K d and Kr are dissociation and recombination rate constants, respectively [24]. It has been concluded that dissociation rate is dependent on the electric field while recombination rate is independent of it [25]. It has been finally discovered that due to dissociation and positioning of the ions in the interface of two dielectric liquids, they influence the interface instability process as well as counteraction with hydrostatic forces. However, if the electric field exceeds the critical value, the interface instability will be probable. In fact, when the values are less than the critical ones, a static equilibrium between electric and hydrostatic forces govern the phenomenon, while in higher values, the interface stability disappears and electric forces accompany hydrodynamic forces of liquids, especially viscous and surface tension forces, so that a homogeneous emulsion is produced in the process of interface
→ → → → DU → + T. → l = − ∇ P + μ∇2 U + Fe + ρg (5) Dt → Where Fe is the electric forces vector which is generally defined as below [25]: ρ
→ → → 1 →2 Fe = qE − E Δε + ∇ Pst 2
(6)
Because of the incompressibility of the two liquids under investigation, the forces resultant from the changes of ε relative to ρ are 3
Colloids and Surfaces A 578 (2019) 123592
R. Heidari, et al.
Fig. 2. Image processing for 1–5, U, V =30 kV, H = 1.
down; hence, in a time interval of 4 min, a stable homogeneous emulsion is produced as a result of opposition and accompaniment of the hydrodynamic and electric field forces. The main point that should be taken into consideration is that in this figure, applied voltage is nonuniform. When there are no electrical stresses, the liquid/liquid interface is in balance with pressure, surface tension and gravitational forces. As it was observed, by applying a voltage higher than the critical electric field intensity, instabilities begin from the interface fluctuations in 3.91 s after applying high voltage by a gradual creation of an unstable rotating cone from upside to downside of the interface, dragging the dielectric liquid above downwards and their return from ground upwards; thus, mixing happens owing to the creation of vortexes. This process continues as the time passes till it finally results in a homogeneous emulsion of two dielectric liquids in 246 s with uniform color. To produce a stable homogeneous emulsion in different cases of the process for the conducted experiments, different times are derived, the results of which will be examined later by processing the images. It should be noted that critical electric field in all cases is in the order of 1 kV/cm [13]. Fig. 4 illustrates a similar process of imaging and capturing instability moments of producing a homogeneous emulsion except that a high voltage electrode is located in down. In order to analysis the effect of different positions, the location of electrodes is changed. By applying electric field higher than the critical value, transformer oil is penetrated into the silicone oil and moves toward to the down electrode. Here, the key point is that the starting level of instability is about 292 s after applying voltage which is higher than the state that HV electrode is located at up position. As it is observed, the instability effects of the interface begins while the Taylor Cones are created in the interface environment close to symmetric line and are gradually transferred to more distance areas as well as to the walls; moreover, as the Taylor Cones penetration toward the fluid below is weak in initial phases, the interface meets more instabilities and, hence, different Taylor Cones are formed in the interface which finally make the fluid move and interfere with the fluid below. It can be concluded that the main reason for these consequential processes is inequality of mobility of ions because of the dissociation of charges in the interface. In all cases, due to high levels of hydrodynamic forces (static pressure and gravitational force), this
eliminated; consequently, the third term is ignored and, in fact, Coulomb force which is the result of ionic injection is ignored. Therefore, by considering the experiment conditions, the only effective force is dielectrophoresis force.
→ 1 →2 Fe = − E Δε¯ 2
(7)
In the conduction of the experiments, the objectives are as following:
• HV location relative to ground • Applying H in two dielectric liquids according to Table 2 • Applied voltage in electric field Since the illumination of the incidents with 30 kV and 40 kV are clearly evident and analyzable, they are just reported here. Meanwhile, their use is avoided in less value due to lack of instability and higher value due to safety issues as well as the probability of insulation fault. Table 3 illustrates the number of experiments, their governed conditions and through objectives of the study. The location of the HV electrode is defined in two up (U) and down (D) conditions and the relations to H are presented in both conditions. As the momentary imaging in Fig. 3 shows, in order to produce a stable homogeneous emulsion by applying 40 kV, the electric field for the 1–6 conditions indicates the location of HV in up and the ground in Table 3 Test numbers for experimental process. Test No. 1–1 1–2 1–3 1–4 1–5 1–6 1–7 1–8 1–9 1–10
H 5.00 2.50 1.66 1.25 1.00 5.00 2.50 1.66 1.25 1.00
eHV
V (kV)
Test No.
U U U U U U U U U U
30 30 30 30 30 40 40 40 40 40
2–1 2–2 2–3 2–4 2–5 2–6 2–7 2–8 2–9 2–10
H 5.00 2.50 1.66 1.25 1.00 5.00 2.50 1.66 1.25 1.00
eHV
V (kV)
D D D D D D D D D D
30 30 30 30 30 40 40 40 40 40
4
Colloids and Surfaces A 578 (2019) 123592
R. Heidari, et al.
Fig. 3. Time process of instability for producing homogenous emulsion in the case of U, 1–6 and H = 5.
from the first phase, the effects of the electric field of the two mixing dielectric fluids continue till a homogeneous emulsion is produced by eliminating resistance in the interface. It should be taken into consideration that instability is created when electrical stresses overcome the balance between hydrodynamic forces. Based on the fact that one of the effective forces in this phenomenon is pressure gradient which is directed to down electrode, when HV electrode is located at up position, the required time to create instability is less than the state that this electrode is located at down position. The reason is that the direction of liquid flow is the same with pressure gradient.
process is slow in the fluid below and two dielectric fluids are eventually mixed with each other and produce a homogeneous emulsion which, relative to the previous case, goes through a long period of time. This time will be 9250 s which is equal to 2.5 h. As it is illustrated in Fig. 5, in cases which the HV electrode operates from upside in the non-uniform electric field, the formation of the Taylor Cones close to the HV electrode cause the vortexes currents be dragged from the ground towards the interface and, finally, with the diffusion of Taylor Cones to other areas of the interface, the complete interface instability happens. In addition, with a time interval of 18 s
Fig. 4. Time process of instability for producing homogenous emulsion in the case of D, 2–8 and H = 1.66. 5
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R. Heidari, et al.
considered as the suitable criteria for complete mixing point. As it is observed, passing from the critical condition to transform the interface is quicker when 40 kV is used and, thus, the required time to produce a homogeneous emulsion is short, which is almost 250 s whereas the critical period begin with a high index when 30 kV is used and the production of a homogeneous emulsion lasts about 700 s. In general, the performance of mixing is increased based on the increasing of applied voltage. The results of the Fig. 8 show that when the location of the HV electrode and the ground is changed, the effect of the place of HV becomes apparent. But the emulsion is produced approximately in 3000 s when 40 kV is applied; however, this time is increased to 10,000 s when 30 kV is applied. Due to safety issues in both cases as well as the insulation fault, higher voltages are not used and these behaviors are investigated up to 40 kV in this study. In this case, the electric current is about 48 μA. The comparison between Figs. 7 and 8 shows that only difference between figures is the change of the position of HV electrode. As the figures show, the mixing time for applied voltage of 30 kV as a sample, is equals to 700 s when HV electrode is located at upper position. While it is about 10,000 s when HV electrode is located at down position and this is 14 times more than the state in which HV electrode is located at upper position. This number for applied voltage of 40 kV is equal to 12. Another point which is obtained from comparison of Figs. 7 and 8 is that the increasing applied voltage from 30 kV to 40 kV, decreases the required time for completes mixing up to 30 percent, regardless of the position of HV electrode. With regard to the highest voltage capacity of HV transformer which is 50 kV and to show the importance of the relative height of two dih electric liquids (H = h1 ), a series of experiments were conducted in 2 conditions where HV was in up and ground was in down for the five geometric conditions (H = 5, 2.50, 1.66, 1.25, 1.00) and the required time to produce a homogeneous emulsion was studied. It can be observed that, with increasing the height of the transformer oil, the required time to produce an emulsion is increased. Therefore, when the height decreases, this time becomes shorter as well. Accordingly, the relative height parameter has an important role in the process of producing an emulsion, especially if there are some limitations in the mixing of two liquids.
Fig. 5. Taylor Cones formation at interface in the region under HV electrode and its dispersion to the end sides of interface (1–6, U, V =40 kV, H = 5 after 18 s).
Fig. 6. Interface instability due to two large recirculation vortexes of silicone oil and short recirculation vortexes of transformer oil under ground electrode (2–8, D, V =40 kV, H = 1.66 at 6000 s).
According to Fig. 6, in cases that non-uniform electric field resultant from the HV electrode is located in down and the ground electrode is in upper position, rotating vortexes of the fluid below begins to move and cause instability on the interface. Then, close to the ground electrode, gradually forms vortexes of the fluid above which moves downwards, that is, it operates in the opposite direction of the fluid below. Thus, it leads to mixing of two fluids. This process happens in 6000 s from the first applying of the HV and afterwards, these two factors affect other regions far from liquids center which finally result in a homogeneous emulsion. The reason for penetrating the transformer oil into silicone oil is the higher mobility of negative ions of transformer oil in comparison with lower mobility of positive ions of silicone oil (see Table 1). The movement of produced charges causes the formation of liquid flow in which, the flow is from ground to HV in the center of enclosure. As it was discussed, an important parameter affecting these processes is the effect of voltage in similar conditions of a case. In Fig. 7, two conditions of 30 kV and 40 kV in a temporal process of deriving a homogeneous emulsion have been investigated in the case that the HV electrode is located from the above to the ground below. Based on the experimental observations, the condition of [I ] ≥ 0.57 is
4. Conclusion An experimental study was conducted to produce a homogeneous emulsion of two dielectric liquids. The results are as following:
• In a temporal process, there are three key parameters in mixing and •
producing a homogeneous emulsion of two dielectric liquids: electric field intensity, relative height of two liquids and the location of electrodes. Increasing voltage in two cases of locating the HV electrode either in
Fig. 7. Effects of high voltage in the time process of deformation of interface for producing of homogenous emulsion of two dielectric liquids (U, H = 5, V =30 kV & V =40 kV, 1–1, 1–6). 6
Colloids and Surfaces A 578 (2019) 123592
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Fig. 8. Effects of high voltage on the time process of deformation of interface for producing of homogenous emulsion of two dielectric liquids (D, H = 5, V =30 kV & V =40 kV, 2–1, 2–6).
•
•
up or in down leads to a decrease in mixing time to the point that the increasing of voltage doesn’t exceed the allowed level. The allowed voltage of 40 kV was used for this study without any problem. Considering two different regimes of instability, the location of the HV electrode in up or down leads to different time periods. However, if the HV electrode is located above the non-uniform electric field, due to main effect of Taylor Cones on the interface instability of two liquids, mixing happens in a short time. On the other hand, electric field operates in contrast with hydrostatic and hydrodynamic forces with low regime and the production of vortexes at lower fluid. Therefore, the time of producing a homogeneous emulsion becomes too long. In similar conditions, making a comparison of 300 s with 10,000 s is an indicative of this reality. The relative heights of two layers in mixing process have a main effect on mixing time and producing a homogeneous emulsion.
217–243. [11] J. Rasin, J.L. Reboud, P. Atten, Electrically induced deformations of water–air and water–oil interfaces in relation with electrocoalescence, Electrostatics 69 (2011) 275–283. [12] R.T. Collins, J.J. Jones, M.T. Harris, O.A. Basaran, Electrohydrodynamic tip streaming and emission of charged drops from liquid cones, Nat. Phys. 4 (2008) 149–154. [13] B. Khorshidi, M. Jalaal, E. Esmaeilzadeh, Electrohydrodynamic instability at the interface between two leaky dielectric fluid layers, J. Colloids and Surf. A 308 (1–3) (2011) 207–212. [14] T. Uemura, Y. Veda, M. Iguchi, Behavior & an oppositely charged oil-water interface, J. Viscosity 13 (2010) 85–87. [15] P. Atten, F. Aitken, D.K. Nenova, Field-induced deformation and disruption of a planar water-oil interface under the influence of a conducting sphere, IEEE International Conference on Dielectric Liquids, (2005), pp. 166–168. [16] E. Esmaeilzadeh, M. jalaal, B. khorshidi, F. Mohammadi, Characteristics of deformation and electrical charging of large water drops immersed in an insulating liquid on the electrode surface, J. Colloid Interface Sci. 352 (1) (2010) 211–220. [17] M.P. Borthakur, G. Biswas, D. Bandyopadhyay, Dynamics of deformation and pinchoff of a migrating compound droplet in a tube, Phys. Rev. E 97 (4) (2018) pp 043112. [18] J. Chaudhuri, S. Timung, C.B. Dandamudi, T.K. Mandal, D. Bandyopadhyay, Discrete electric field mediated droplet splitting in microchannels: Fission, Cascade, and Rayleigh modes, Electrophoresis 38 (2) (2017) 278–286. [19] S. Timung, J. Chaudhuri, M.P. Borthakur, T.K. Mandal, G. Biswas, D. Bandyopadhyay, Electric field mediated spraying of miniaturized droplets inside microchannel, Electrophoresis 38 (11) (2017) 1450–1457. [20] M.P. Borthakur, G. Biswas, D. Bandyopadhyay, Dynamics of drop formation from submerged orifices under the influence of electric field, Phys. Fluids 30 (12) (2018) pp 122104. [21] S. Kumar, B. Sarma, A.K. Dasmahapatra, A. Dalal, D.N. Basu, D. Bandyopadhyay, Field induced anomalous spreading, oscillation, ejection, spinning, and breaking of oil droplets on a strongly slipping water surface, Faraday Discuss. 199 (0) (2017) 115–128. [22] S. Dutta, A. Ghosh, P.S.G. Pattader, D. Bandyopadhyay, Electric field mediated von Kármán vortices in stratified microflows: transition from linear instabilities to coherent mixing, J. Fluid Mech. 865 (2019) 169–211. [23] J.R. Melcher, G.I. Taylor, Electrohydrodynamics: a review of the role of interfacial shear stresses, Ann. Rev. Fluid Mech. 1 (1969) 111–146. [24] S.I. Jeong, J.S. Yagoobi, Fluid circulation in an enclosure generated by electrohydrodynamic conduction phenomenon, IEEE Trans. Dielectr. Electr. Insul. 11 (2004) 899–910. [25] A. Castellanos, Electrohydrodynamics, CISM International Centre for Mechanical Sciences, Speringer-Verlag, New-York, 1998.
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Colloids and Surfaces A journal homepage: www.elsevier.com/locate/colsurfa
The Electrohydrodynamic mixer for producing homogenous emulsion of dielectric liquids R. Heidaria, Alireza R. Khosroshahia, B. Sadrib, E. Esmaeilzadeha, a b
T
⁎
Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran School of Industrial Engineering, Purdue University, 315 N. Grant Street, West Lafayette, IN 47907, USA
G R A P H I C A L A B S T R A C T
Interface instability due to two large recirculation vortex of silicon oil and short recirculation vortex of transformer oil under ground electrode.
A R T I C LE I N FO
A B S T R A C T
Keywords: Electrohydrodynamics mixer Dielectric liquids Miscible Instability Emulsion
This paper experimentally investigates the production of a homogeneous emulsion of two dielectric and immiscible liquids of transformer and silicone oils in an electric field with a high voltage. The aim of this paper is the examination of the effects of the electric field intensity, geometric height of two dielectric liquids and the location of non-uniform electrodes on instability process of two liquids’ interface and the analysis of a homogeneous emulsion production. Experiments are performed within 50 kV, the height ratio of two liquids in a stable h condition is within (H = h1 = 1, 1.25, 1.66, 2.5, 5) and the HV electrode is located in two up and down positions. 2
The interface instability illumination is captured by a high speed digital camera at 1000 f/s using a digital analytic system to a point that a homogeneous emulsion is produced, and the required time to obtain the ultimate goal in different cases is achieved as well. The complete mixing time is calculated till a homogeneous emulsion is obtained which is influenced by a voltage increase and height ratio decrease of two stationary liquids. The results show that both the abovementioned cases lead to a decrease in the complete mixing time. In this context, the way the HV electrodes are located vertically is also effective.
1. Introduction Producing an emulsion of dielectric liquids in smaller-scaled
⁎
systems is of great importance in pharmaceutical, biological and chemical industries as well as in nanofluid productions and miniature systems particularly microfluidics [1–7]. Mechanical systems are not
Corresponding author. E-mail address: [email protected] (E. Esmaeilzadeh).
https://doi.org/10.1016/j.colsurfa.2019.123592 Received 17 March 2019; Received in revised form 18 June 2019; Accepted 20 June 2019 Available online 21 June 2019 0927-7757/ © 2019 Published by Elsevier B.V.
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Fig. 1. Schematic of setup.
various pathways of droplet breaking. Similar study was done on the dynamics of drop formation from submerged orifices under the influence of an external electric field [20]. The computations for leaky dielectric fluids reveal that both prolate and oblate shaped drops can be formed depending on the combination of the fluid conductivity and permittivity ratios. An experimental study on application of an electric field on an oil droplet floated on the surface of a deionized water bath was done [21]. According to the results, when the electric field was ramped up abruptly to a particular voltage, any of the spreading, oscillation or ejection of the droplet could be engendered at lower, intermediate and higher field intensities, respectively. Another study on the application of an electric field across the pressure-driven stratified flow of two miscible fluids inside a microchannel was done by Dutta et al. [22]. The effect of electric field Rayleigh number, linear-onset regime and time-periodic nonlinear regime analogous to the von Kármán vortex street in the downstream was studied. The outcomes reveal that the EHD instabilities of studied system appear only beyond a critical field intensity and these instabilities could be categorized in five distinctive modes. Results reveal that the location of the interface, thickness of the interface, level of charge injection, strength of the applied EHD field, viscosity contrast across the diffused interface and diffusivity across the interface are some of most important parameters for these types of instabilities. As the literature review illustrates, the conducted studies of different researchers have not yet been completely responsive to interface instability of mixed liquids affected by electric fields. In the present study, particular cases of the interface disappearance process have experimentally examined for the purpose of producing a homogeneous emulsion. There are many influential factors among the concerned variables of this study to name a few; the effect of the location of high voltage electrodes and ground, geometric height of two stationary dielectric liquids and electric field intensity.
often used in applications of the mentioned scales. Therefore, applying EHD mixers are highly advantageous. This method requires careful studies so that their high efficiency can be used in different applications. G. I. Taylor [8] investigated the instability resulting from the effects of a vertical electric field on a horizontal interface of a stationary liquid in 1965. He concluded that by increasing the electric field intensity, it is possible to easily overcome the gradient pressure in liquids interface resultant from gravity and surface tension that in turn will lead to interface instability. In an international EHD symposium held on 23–26 September 2012 in Gdansk, Poland, many applications related to EHD were mentioned. Three influential articles by W. Balachandran [1], P. Atten [2] and J. S. Yagoobi [3], the keynote speakers of the seminar; are introduced the importance of Electrhydrodynamic methods in different applications. In 2003, Eow and Gadiri [9] measured the electric current intensity resulting from an electric field perpendicular to two miscible liquids and observed that different regimes govern the phenomenon and bring about instabilities with different patterns and the interface disappearance begins as the Taylor Cone’s regime starts. In 2007, in a review paper, Dela Mora has completely presented Taylor cones instability [10]. Rasin et al. have studied an unstable air-water and oil-water interface and calculated numerically the intensity of the electric current influenced by an electric field [11]. In 2008, Collins et al. examined the geometric shape of the instability cone in the interface and how it was drowned in liquid [12]. They concentrated on the appearance of the Taylor Cone from the beginning of the interface instability and they were able to calculate numerically the critical value of the electric field intensity. In 2011, B. Khorshidi et al. achieved experimental results concerning the mixing quality of two dielectric liquids, drowning of a water drop in oil, its ionization in vertical electric field and its interface instability [13]. In 2010, Uemura et al. examined the technical behavior of singularity of the interface instability of a liquid which was resulted from its rotation and showed different instability regimes due to vertical electric fields [14]. In this regard, P. Atten et al. examined the abovementioned study in the behavior of a circle drop in water-oil interface [15]. In 2010, E. Esmaeizadeh et al. studied mixing of two stationary dielectric liquids with the same height in a non-uniform dielectric field [16]. Results show that by passing the critical intensity field, momentary fluctuations of the two liquids’ interface begin and ultimately result in instability under different patterns in order to achieve a stable emulsion. In addition, the results indicated that the existence of free charges in the interface caused by the dissociation, recombination and breakup of the balance of the electric and hydrodynamic forces are effective. Some numerical and experimental investigations have been carried out to study the deformation and breakup of the droplet inside a microchannel [17–19]. Results show that in the presence of electric field, the interplay between electrostatic, inertial, capillary and viscous forces lead to
2. Methods and materials The present study aims to experimentally investigate the mixing process of two dielectric liquids in a non-uniform vertical electric field in a designed study platform. Fig. 1 illustrates the schematic of the study platform. In this figure, the arrangement of electrodes and the way the electric field is produced, the geometric location of two dielectric liquids and the graphical processing system are shown. In all experiments, two miscible dielectric liquids with thermoelectric properties introduced in Table 1 are used. The two liquids used in the experiments are pure silicone oil and standard transformer oil and they are used in the exact conditions of the study to a point that a homogeneous emulsion is produced. Due to high density of the silicone oil, its height in stationary position is selected to be fixed and equals to 25 mm in all experiments, and the transformer oil above it, is selected in different sizes with the ratio 2
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transformation. To capture the incidents resultant from the electric field in the interface instability and its continuous process to a point that the main objective of the experiment is achieved, a digital camera, EXILIMEX10 Casio at 1000 f/s is used. In the present experiment, due to slowness of the incidents, 400 f/s is enough for the purpose of illumination. Image process toolbox of MATLAB was used for investigation of mixing process and evaluation of the current mixer. For image processing, a video was recorded with high-speed camera for all 20 designed experiments. After that, at certain times specific images were taken out from recorded videos and these images were converted into a gray-scale mode and inserted into image processing toolbox of MATLAB. Then, the intensity of white color is measured for each pixel. This parameter is named ξ and it identifies the efficiency of the local mixing. This parameter is always positive and volatile in the range of 0 ≤ ξ ≤ 256 where it is increased with intensity of white color, i.e. ξ is equal 256 for a completely white pixel. The average of non-dimensional mixing intensity is defined as:
Table 1 Physical and Electrical properties of liquids. Properties
Transformer oil
Silicone Oil
Dynamic viscosity (kg/m.s) Density (kg/m3) Electrical conductivity (S/m) Relative permittivity (εr=εt/ε0) Ion mobility (cm2/V s)
0.02 842 3.3 × 10−12 2.1 5 × 10−6 1.1 × 10−5
0.35 970 14 × 10−13 2.76 9 × 10−7 2 × 10−6
Table 2 Relative height H of two dielectric liquids. H=
1.00
h1 h2
h1 = 25 mm Silicone oil
1.25
1.66
2.50
5.00
h2 = Transformer oil
h
of H = h1 according to Table 2. 2 In all experiments, the non-uniform electric field between the two high voltage electrodes and ground is used in two conditions of a high voltage (in up) and a high voltage (in down). The experiment setup is located in a rectangular cubic enclosure made of highly transparent glass for the purpose of confident capturing. The dimensions of this part are 150 mm × 200 mm and its height is 200 mm which, with respect to the main tank, completely prevents dust and other influencing factors to enter the case. The main section of the experiment is made of a transparent Plexiglas with 60 mm × 80 mm × 150 mm dimensions. The electrodes are made from copper with 30 mm × 40 mm and 10 mm × 20 mm dimensions to produce a non-uniform voltage in two conditions and are located in the main section of the experiment according to Fig. 1. The sharp edges of the electrodes are removed completely as much as possible to prevent ion injection to liquid surroundings. The electrode in the up position, due to observing the relative height H vertically is equipped with a mechanism which can move upwards and downward easily. Applying a voltage with DC voltage generator is done within 50 kV and precision of 0.1 kV. For the purpose of confidence and voltage generator calibration, a high voltage probe is used simultaneously, too. Considering the values in Table 1, in this experiment, pure and standard dielectric liquids are used in both silicone and transformer oils. These properties are used with due attention to buying them from reliable companies and the conditions governing the experiments as well. It is apparent that regardless of this observance, the probability of errors in measurements and impurity of the liquids can slightly influence the experiment results. Different emissivity and mobility can affect transference of positive and negative ions to the interface. Previous experiments conducted by E. Esmaeizadeh et al. show that positive and negative ions can influence instability process by breaking molecules down and recombining them [23]. This transformation follows the equation below:
i
[I ] =
Kr
i × j × ξmax
(2)
Where i, j denotes the horizontal and vertical positions of a pixel, respectively. Fig. 2 illustrates the results of image processing for a sample picture for test No. 1–5. Fig. 2 shows the instability formation in the enclosure and increasing the mixing intensity. 3. Results and discussion The ultimate purpose of this study is to investigate experimentally the interaction effect of electric field and hydrodynamic forces on the interface instability process in dielectric liquids for the purpose of producing a homogenous emulsion. The opposition in both the electric field and hydrodynamic forces has been considered in two cases. Case 1 considers the electric field before it reaches the critical value and in case 2 the electric field reaches the critical value. In case 1, due to interface stability, the hydrostatic forces interact with the electric field forces according to equation below [1]:
Feff . =
1 1 1 ε1 Em2 − T ( + ) − ΔP. g . Zinterfae 2 R1 R2
(3)
Where ε1 is permittivity of dielectric oil in the air vicinity, Em is vertical electric field intensity, T is surface tension in the liquid interface, R1 and R2 are the radiuses of surface curves perpendicular to the interface. Since the present study focuses on the interface of two dielectric liquids, it is necessary that Eq. (3) be corrected in the following way:
Feff . =
1 1 1 (ε1 + ε2) Em2 − T ( + ) − ΔP. g . Zinterfae 2 R1 R2
(4)
In the equation above, ε2 is the second dielectric liquid of the process above. If the electric field intensity exceeds the critical value, the interface instability under different regimes will continue until a homogeneous emulsion is produced. In this case, the interactive forces as well as the effects of both electric and hydrodynamic forces interfere with the instability process. The governing equation of the phenomenon inserted as momentum per unit volume which can be solved numerically.
Kd
A+ B − ↔ A+ + B −
j
ξ ∑imax ∑ jmax =1 = 1 ij
(1)
Where K d and Kr are dissociation and recombination rate constants, respectively [24]. It has been concluded that dissociation rate is dependent on the electric field while recombination rate is independent of it [25]. It has been finally discovered that due to dissociation and positioning of the ions in the interface of two dielectric liquids, they influence the interface instability process as well as counteraction with hydrostatic forces. However, if the electric field exceeds the critical value, the interface instability will be probable. In fact, when the values are less than the critical ones, a static equilibrium between electric and hydrostatic forces govern the phenomenon, while in higher values, the interface stability disappears and electric forces accompany hydrodynamic forces of liquids, especially viscous and surface tension forces, so that a homogeneous emulsion is produced in the process of interface
→ → → → DU → + T. → l = − ∇ P + μ∇2 U + Fe + ρg (5) Dt → Where Fe is the electric forces vector which is generally defined as below [25]: ρ
→ → → 1 →2 Fe = qE − E Δε + ∇ Pst 2
(6)
Because of the incompressibility of the two liquids under investigation, the forces resultant from the changes of ε relative to ρ are 3
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Fig. 2. Image processing for 1–5, U, V =30 kV, H = 1.
down; hence, in a time interval of 4 min, a stable homogeneous emulsion is produced as a result of opposition and accompaniment of the hydrodynamic and electric field forces. The main point that should be taken into consideration is that in this figure, applied voltage is nonuniform. When there are no electrical stresses, the liquid/liquid interface is in balance with pressure, surface tension and gravitational forces. As it was observed, by applying a voltage higher than the critical electric field intensity, instabilities begin from the interface fluctuations in 3.91 s after applying high voltage by a gradual creation of an unstable rotating cone from upside to downside of the interface, dragging the dielectric liquid above downwards and their return from ground upwards; thus, mixing happens owing to the creation of vortexes. This process continues as the time passes till it finally results in a homogeneous emulsion of two dielectric liquids in 246 s with uniform color. To produce a stable homogeneous emulsion in different cases of the process for the conducted experiments, different times are derived, the results of which will be examined later by processing the images. It should be noted that critical electric field in all cases is in the order of 1 kV/cm [13]. Fig. 4 illustrates a similar process of imaging and capturing instability moments of producing a homogeneous emulsion except that a high voltage electrode is located in down. In order to analysis the effect of different positions, the location of electrodes is changed. By applying electric field higher than the critical value, transformer oil is penetrated into the silicone oil and moves toward to the down electrode. Here, the key point is that the starting level of instability is about 292 s after applying voltage which is higher than the state that HV electrode is located at up position. As it is observed, the instability effects of the interface begins while the Taylor Cones are created in the interface environment close to symmetric line and are gradually transferred to more distance areas as well as to the walls; moreover, as the Taylor Cones penetration toward the fluid below is weak in initial phases, the interface meets more instabilities and, hence, different Taylor Cones are formed in the interface which finally make the fluid move and interfere with the fluid below. It can be concluded that the main reason for these consequential processes is inequality of mobility of ions because of the dissociation of charges in the interface. In all cases, due to high levels of hydrodynamic forces (static pressure and gravitational force), this
eliminated; consequently, the third term is ignored and, in fact, Coulomb force which is the result of ionic injection is ignored. Therefore, by considering the experiment conditions, the only effective force is dielectrophoresis force.
→ 1 →2 Fe = − E Δε¯ 2
(7)
In the conduction of the experiments, the objectives are as following:
• HV location relative to ground • Applying H in two dielectric liquids according to Table 2 • Applied voltage in electric field Since the illumination of the incidents with 30 kV and 40 kV are clearly evident and analyzable, they are just reported here. Meanwhile, their use is avoided in less value due to lack of instability and higher value due to safety issues as well as the probability of insulation fault. Table 3 illustrates the number of experiments, their governed conditions and through objectives of the study. The location of the HV electrode is defined in two up (U) and down (D) conditions and the relations to H are presented in both conditions. As the momentary imaging in Fig. 3 shows, in order to produce a stable homogeneous emulsion by applying 40 kV, the electric field for the 1–6 conditions indicates the location of HV in up and the ground in Table 3 Test numbers for experimental process. Test No. 1–1 1–2 1–3 1–4 1–5 1–6 1–7 1–8 1–9 1–10
H 5.00 2.50 1.66 1.25 1.00 5.00 2.50 1.66 1.25 1.00
eHV
V (kV)
Test No.
U U U U U U U U U U
30 30 30 30 30 40 40 40 40 40
2–1 2–2 2–3 2–4 2–5 2–6 2–7 2–8 2–9 2–10
H 5.00 2.50 1.66 1.25 1.00 5.00 2.50 1.66 1.25 1.00
eHV
V (kV)
D D D D D D D D D D
30 30 30 30 30 40 40 40 40 40
4
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Fig. 3. Time process of instability for producing homogenous emulsion in the case of U, 1–6 and H = 5.
from the first phase, the effects of the electric field of the two mixing dielectric fluids continue till a homogeneous emulsion is produced by eliminating resistance in the interface. It should be taken into consideration that instability is created when electrical stresses overcome the balance between hydrodynamic forces. Based on the fact that one of the effective forces in this phenomenon is pressure gradient which is directed to down electrode, when HV electrode is located at up position, the required time to create instability is less than the state that this electrode is located at down position. The reason is that the direction of liquid flow is the same with pressure gradient.
process is slow in the fluid below and two dielectric fluids are eventually mixed with each other and produce a homogeneous emulsion which, relative to the previous case, goes through a long period of time. This time will be 9250 s which is equal to 2.5 h. As it is illustrated in Fig. 5, in cases which the HV electrode operates from upside in the non-uniform electric field, the formation of the Taylor Cones close to the HV electrode cause the vortexes currents be dragged from the ground towards the interface and, finally, with the diffusion of Taylor Cones to other areas of the interface, the complete interface instability happens. In addition, with a time interval of 18 s
Fig. 4. Time process of instability for producing homogenous emulsion in the case of D, 2–8 and H = 1.66. 5
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considered as the suitable criteria for complete mixing point. As it is observed, passing from the critical condition to transform the interface is quicker when 40 kV is used and, thus, the required time to produce a homogeneous emulsion is short, which is almost 250 s whereas the critical period begin with a high index when 30 kV is used and the production of a homogeneous emulsion lasts about 700 s. In general, the performance of mixing is increased based on the increasing of applied voltage. The results of the Fig. 8 show that when the location of the HV electrode and the ground is changed, the effect of the place of HV becomes apparent. But the emulsion is produced approximately in 3000 s when 40 kV is applied; however, this time is increased to 10,000 s when 30 kV is applied. Due to safety issues in both cases as well as the insulation fault, higher voltages are not used and these behaviors are investigated up to 40 kV in this study. In this case, the electric current is about 48 μA. The comparison between Figs. 7 and 8 shows that only difference between figures is the change of the position of HV electrode. As the figures show, the mixing time for applied voltage of 30 kV as a sample, is equals to 700 s when HV electrode is located at upper position. While it is about 10,000 s when HV electrode is located at down position and this is 14 times more than the state in which HV electrode is located at upper position. This number for applied voltage of 40 kV is equal to 12. Another point which is obtained from comparison of Figs. 7 and 8 is that the increasing applied voltage from 30 kV to 40 kV, decreases the required time for completes mixing up to 30 percent, regardless of the position of HV electrode. With regard to the highest voltage capacity of HV transformer which is 50 kV and to show the importance of the relative height of two dih electric liquids (H = h1 ), a series of experiments were conducted in 2 conditions where HV was in up and ground was in down for the five geometric conditions (H = 5, 2.50, 1.66, 1.25, 1.00) and the required time to produce a homogeneous emulsion was studied. It can be observed that, with increasing the height of the transformer oil, the required time to produce an emulsion is increased. Therefore, when the height decreases, this time becomes shorter as well. Accordingly, the relative height parameter has an important role in the process of producing an emulsion, especially if there are some limitations in the mixing of two liquids.
Fig. 5. Taylor Cones formation at interface in the region under HV electrode and its dispersion to the end sides of interface (1–6, U, V =40 kV, H = 5 after 18 s).
Fig. 6. Interface instability due to two large recirculation vortexes of silicone oil and short recirculation vortexes of transformer oil under ground electrode (2–8, D, V =40 kV, H = 1.66 at 6000 s).
According to Fig. 6, in cases that non-uniform electric field resultant from the HV electrode is located in down and the ground electrode is in upper position, rotating vortexes of the fluid below begins to move and cause instability on the interface. Then, close to the ground electrode, gradually forms vortexes of the fluid above which moves downwards, that is, it operates in the opposite direction of the fluid below. Thus, it leads to mixing of two fluids. This process happens in 6000 s from the first applying of the HV and afterwards, these two factors affect other regions far from liquids center which finally result in a homogeneous emulsion. The reason for penetrating the transformer oil into silicone oil is the higher mobility of negative ions of transformer oil in comparison with lower mobility of positive ions of silicone oil (see Table 1). The movement of produced charges causes the formation of liquid flow in which, the flow is from ground to HV in the center of enclosure. As it was discussed, an important parameter affecting these processes is the effect of voltage in similar conditions of a case. In Fig. 7, two conditions of 30 kV and 40 kV in a temporal process of deriving a homogeneous emulsion have been investigated in the case that the HV electrode is located from the above to the ground below. Based on the experimental observations, the condition of [I ] ≥ 0.57 is
4. Conclusion An experimental study was conducted to produce a homogeneous emulsion of two dielectric liquids. The results are as following:
• In a temporal process, there are three key parameters in mixing and •
producing a homogeneous emulsion of two dielectric liquids: electric field intensity, relative height of two liquids and the location of electrodes. Increasing voltage in two cases of locating the HV electrode either in
Fig. 7. Effects of high voltage in the time process of deformation of interface for producing of homogenous emulsion of two dielectric liquids (U, H = 5, V =30 kV & V =40 kV, 1–1, 1–6). 6
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Fig. 8. Effects of high voltage on the time process of deformation of interface for producing of homogenous emulsion of two dielectric liquids (D, H = 5, V =30 kV & V =40 kV, 2–1, 2–6).
•
•
up or in down leads to a decrease in mixing time to the point that the increasing of voltage doesn’t exceed the allowed level. The allowed voltage of 40 kV was used for this study without any problem. Considering two different regimes of instability, the location of the HV electrode in up or down leads to different time periods. However, if the HV electrode is located above the non-uniform electric field, due to main effect of Taylor Cones on the interface instability of two liquids, mixing happens in a short time. On the other hand, electric field operates in contrast with hydrostatic and hydrodynamic forces with low regime and the production of vortexes at lower fluid. Therefore, the time of producing a homogeneous emulsion becomes too long. In similar conditions, making a comparison of 300 s with 10,000 s is an indicative of this reality. The relative heights of two layers in mixing process have a main effect on mixing time and producing a homogeneous emulsion.
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