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In the presence of an electric field two patterns of drop-interface coalescence may occur: complete coalescence and partial coalescence. The former is obviously the desirable pattern for industrial coalescers. However in practice, the process of coalescence could actually produce smaller droplets, which become more difficult to remove, and hence undesirable. This is caused by either necking or reaction to fast and energetic coalescence. This is referred to as partial coalescence. The volume of the small droplet formed in this way is a function of the initial drop size (d), electric field strength (E) and the distance between the drop and the interface (Î»). Also it was shown the expansion speed of the narrow channel () connecting the drop and interface at the beginning of the pumping process is much faster than the two other velocity i.e. the peak () and equator () velocity of the drop and in about 1 ms after beginning of the pumping process the two later velocity are zero and drop volume is increasing in this period so according to mass conservation law there must be a mass flow into the drop that the only source for this mass is drop bulk phase under the interface layer. Moreover decreases rapidly in a continuous manner and this shows the driving force to expand the channel between drop and interface is the most at the first of the pumping process.
Keyword: complete coalescence, partial coalescence, detached body, peak velocity, equator velocity, channel expansion velocity
In the chemical processing and manufacturing industries, immiscible liquids are often mixed such that one phase becomes fully dispersed in the other, e.g. in extraction and leaching. The aim is to get a large interfacial area for the enhancement of mass transfer between the two immiscible liquids . Examples of liquid-liquid mixing processes can be found in the mining and solvent extraction industries [2-4] and crude oil extraction , where in the latter the aqueous phase is often well-dispersed in the crude oil. However these emulsions or dispersions have to be separated into their constituent phases before the next operating steps or as required by process requirements, environmental regulations and customer specifications as in the case of crude oil industry . There are several techniques for enhancing the separation of water-in-oil emulsions, such as the addition of chemical demulsifier , pH adjustment and filtration , gravity or centrifugal settling, heat treatment and electrostatic demulsification[10,11]. In terms of energy efficiency, electrical demulsification is considered to be the best among the above methods , and the state of the art has been reviewed by Eow and Ghadiri .
Gravity settlers are one of the most common unit operations to separate immiscible liquid/liquid [3,4]. They are based on the drop-drop and drop-interface coalescence. The coalescence between drops in an immiscible liquid medium, or between a drop and interface occurs in three stages [9,12,13]. In the first stage, the drops approach each other and are separated by a film of the continuous phase. The second stage involves the thinning of this film. The thinning rate is affected by the capillary pressure and disjoining pressure, and can be retarded due to the Marangoni effect if any surfactant is present [14,15]. When the film reaches a certain critical thickness any disturbance or instability will cause it to rupture and coalescence occurs [14,16]. Film thinning is often the overall controlling step in absence of an electric field. In order to increase the separation rate, it is desired to reduce the residence time of the dispersion in a gravitational settler. This can be achieved by increasing the settling speed of the dispersed aqueous drops towards the interface and/or reducing the time the drops sit on the interface prior to drop-interface coalescence. High electric fields have been used to separate water-in-oil dispersions in the crude oil and extraction industries . To apply this method, continuous phase needs to be much more electrically insulating compared with the dispersed phase, in order to facilitate the setting up an electric field. The current understanding of the electrocoalscence phenomenon has been reviewed by Eow et al. . The bottleneck of the coalescence process between an aqueous drop and its own bulk liquid phase is generally the drainage of the thin organic phase film trapped between the drop and the interface [2,15,17]. By applying an electric field, the drainage rate of the organic phase film and the subsequent drop-interface coalescence can be significantly enhanced .
The effect of applied electric field on drop interface coalescence
By applying an electric field acting as an additional external force, the mean rest-time value of a drop at an interface can be significantly decreased because of increasing the rate of film thinning . Charles and Mason [19,20] and Brown and Hanson  also reported that the drop's rest-time on the interface reduces rapidly with increasing applied electric field strength because an applied electric field produces an attractive force between a drop and an interface, which can be much larger than available gravitational force.
This results in an increase in the film thinning rate and drop distortion, producing a significant decrease in the stability of the drop, eventually leading to rapid drop-interface coalescence [17,22]. An uncharged water drop will be attracted to a water/oil interface by dielectrophoresis forces. The point of maximum field strength lies between the drop and the interface, and the drop moves towards this point. The attraction force may be much larger than the gravitational force during the drainage of the film, reducing the time required by the continuous phase film to drain to the rupture thickness . The coalescence of a drop at a liquid_liquid interface often produces a smaller drop as observed by Charles and Mason [19,20]. During the rupture of the continuous phase film between the main drop and the interface, the excess internal pressure from the curved interface produces a cylindrical liquid column leading to a secondary drop. The radius of this column decreases due to the excess pressure until its circumference becomes smaller than its height. As a result of a Rayleigh disturbance, due to drainage and the necking process, the resultant secondary drop size is determined . It has been reported that in the presence of an external electric field, the generation of the secondary drop does not occur [19,20,22]. However Brown and Hanson  report that secondary drops do form depending on the electric field strength. The size of the secondary drop has been observed to be inversely proportional to the electric field strength and moreover at higher applied fields, the coalescence of the main drop becomes instantaneous and single-staged. This is of course before reaching a critical electric field strength at which the drop disintegrates.
Objectives of the present work
For the separation of water-in-oil emulsions, the smaller dispersed phase drop size the more difficult separation would be. An important problem in this separation process is the formation of the secondary drop by partial coalescence. This leads to a lowering of the separation efficiency as the much tinier drops are more difficult to separate. Therefore basically it is better to prevent these secondary drops from being formed in the first place. In this work our observations on the formation of the secondary drops during the electro-coalescence of the primary drops are reported and the parameters that affect the process are quantified.
Experimental set-up and procedure
The experimental cell used for investigation of the secondary drop formation in drop-interface coalescence has been shown in Fig. 1. The cell was made of Perspex to facilitate visualisation of the phenomenon. The electrodes were polished brass plates. The plates had dimensions of 90 mmÃ-25 mm. The distance between the electrodes was 53 mm in all experiments. The high voltage electrode was attached to the moveable upper part of the cell. The distance between the two electrodes could, therefore, be varied by moving the upper part up or down. Furthermore, this part was supported on the upper surface of the Perspex cell with two cylindrical Perspex pin supports.
Fig. 1. Details of the Prespex test-cell
The Perspex block had a thickness of about 6 mm. There is a small hole through the middle point of the moveable upper part of the cell and the brass plate for a hypodermic needle going through it. The needle attached to a syringe (Hamilton micro liter syringe), was used to produce small aqueous drops in the cell. The high voltage electrode was connected to a positive polarity high voltage direct current source (Model: PS/EH60R01.5-22, manufactured by Glassman High Voltage Inc). The bottom electrode was grounded. A high-speed digital video camera (Photron FASTCAM SA5 32GB), equipped with a micro lens (NAVITARA 12X Zoom Lens) was used to observe the phenomena taking place during the drop-interface coalescence. Using this camera a framing speed of up to 62000 fps was used to record the coalescence process. The video camera was focused on the centre of the liquid_liquid interface. A halogen lamp (Dedolight DLHM4-300) with four flexible fiber optic heads was used for lighting. The intensity of the lighting could be accurately adjusted to facilitate focusing. de-ionized water was used to produce drops, while the organic phase was sunflower oil that was obtained from Morrisons (UK)Ltd. The properties of the liquids used in this research are given in Table. 1.
Table. 1 The properties of the liquid used in the experiment
Conductivity (Î¼sm-1) (±5%)
Viscosity (Pa s) (±5%)
Surface tensiona (mN m-1) (±5%)
Density (kgm-3) (±5%)
a The measured surface tension is with respect to air at 1 atm and 20 0C
The densities of sunflower oil and de-ionized water are quite close and this facilitates experimentation because it allows water drops falling slowly towards the liquid_liquid interface, giving ample time for managing the recording process. De-ionized water drops of different sizes were produced using hypodermic needles by pressing the syringe piston so that it changes the volume of the fluid inside the syringe and by this method it was possible to have a droplet diameter range between 576±1µm to 1196±4µm. The glassware and needles were cleaned by several washing by acetone and distilled water to prevent any pollution that my affect the coalescence phenomenon. The drops were released gently from the needle to avoid oscillation of the drops and interface and were allowed to settle through the oil phase towards the aqueous/oil interface. The drops were introduced at the middle of the planar interface which is far away from the edge where the interface is curved and the electric field is not uniform. The diameter of the drops was measured with an accuracy better than ±5 µm by the use of Image-Pro and PFV (Photron Fastcam Viewer) software. The diameter of the needle was measured by a microscope and was used for the calibration of the drop size. The experiments were done at 20±2 0C.
Results and discussion
The mechanism of drop-interface coalescence under electric field
The coalescence events of water drops at an oil/water interface recorded at 20000 fps are shown in the sequence of images in Figs 2 and 3. In these figures, the scale is the same for all images, facilitating the comparison between the primary drop and the secondary drops (Fig. 3). The deformation of the drop and interface and before coalescence in the absence of the electric fields has been reported before  but deformation is notable only when the drop is resting on the interface. Applying the electric field results in the deformation of interface and falling drop whilst they are still far from each other, in contrast to the case where the electric field is absent. (See Fig. 4(b)). An uncharged drop subject to an electric field is polarized and When the deformed drop is approaching the deformed interface the electric field strength increases exponentially at small separations the extent that electroclamping phenomenon becomes operative  giving rise to the neck formed and shown in Fig. 4(b). The high speed of video recording has made this observation very clear. When the drop is sufficiently close to the interface (a few micro meters distance) in a time period less than 16 µs the high strength electric field in the space of drop and interface causes clamping between drop and interface (Fig. 4(b)), resulting in the formation of a narrow channel. The drop will now be acquiring the same charge as the adjacent electrode and will be experiencing a repelling Coulombic force. At the same time, the surface tension will be pushing the liquid in the drop into the continuous phase via the channel formed, and rapidly enlarging the neck. It is likely that the current constriction causing the electrical clamping ruptures the thin film (oil phase) between the drop and its own bulk phase, whereby the formation of a hole the most important factor inhibiting the initiation of the coalescence i.e. this thin film, is removed, thus the start of coalescence. The hole expands very rapidly and the liquid is pumped rapidly into its bulk phase. Two patterns of coalescence are observed: "complete coalescence" and "partial coalescence", as shown in Figs 2 and 3, respectively.
Fig. 2. Sequence of a complete coalescence for a drop with a diameter of 984±2µm under electric field strength of 56 V/mm
In the absence of an electric field, when a partial coalescence occurs there is a race between drainage of the drop content into its bulk phase and necking process. Also by applying an electric field there will be a balance between pumping of drop into its bulk phase (due to surface tension) and the necking process (due to interaction between surface tension and attractive columbic force between the negatively charged drop and positive electrode), the outcome of which determines the volume of the detached body. The electric force between upper side of the drop (that negative charges has accumulated on it as a result of polarization) closer to positive electrode and the positive electrode will help necking process and finally detaching of the secondary drop. Predominance of each of these processes i.e. necking and pumping depends on some parameters as discussed later.
5.2 Complete and partial coalescence patterns
It can be seen from the Fig. 2 that with start of drop pumping into its bulk phase any necking process does not occur so that the pumping process leads to a complete coalescence pattern. In this coalescence pattern in some stages (Fig. 2. (l) and (m)), the peak of the drop while progress of the process becomes sharp but finally as a result of surface tension the process leads to a flat area without any detached bodies. This means in this condition there is such a fast rate of pumping that can prevent from initiation of a necking process resulting to separate a secondary body. Although the drop experiences an attractive columbic force by the positive electrode (due to contact with the interface and being negatively charged) but this force in not strong enough (in the case of complete coalescence occurrence) to help the occurrence of necking process and eventually resulting in secondary droplet. In fact the surface tension force attempts to keep the drop shape continuous and uniform while pumping process whereas attractive columbic force attempts to detach a secondary droplet by development of necking process. In another case as shown in Fig. 3, the two same drops subjected to different electric field strengths led to secondary drop formation. Here as a result of drop size and electric field strength it can be seen a necking process appears. In fig. 3. (b), as a result of faster development of necking process in comparison with (a), the volume of secondary drop is bigger. In case (b) because of more electric field strength, attractive force between drop and positive electrode is stronger than for case (a) so that it can help necking process to develop faster and detach a bigger secondary drop. In both cases (a) and (b) the pumping process is in progress to drain the content of the primary drop into its bulk phase but necking process and its rate determines the volume of secondary drop. Thus under a given condition leading to a partial coalescence, the necking process (trying to prevent the primary drop from complete pumping) and pumping process (trying to cause the drop drain into its bulk phase) are in competition with each other. Another point should be noted is that the difference between the tail length in Fig. 3 (a) and (b). In Fig. 3(b) the drop is subjected to higher electric strength the detached body has longer tail than the other case. The reason for longer tail is because of the higher electrical stress on the drop and more elongation of the drop under higher electric strength. As detached body is going up it can be seen the longer tail is broken into several much fine droplets being added to continuous phase and it is highly undesirable.
Factors affecting the volume of the secondary drop
High speed video observations indicate that three parameters are influential in determining the coalescence pattern: drop size (d), electric field strength (E) and the height of falling drop from interface while (Î»). In this work the dispersed phase is de-ionised water and does not contain any surfactants which could affect the interfacial tension.
Fig. 3. Partial coalescence of a drop with a diameter of 1196±4µm under two electric field strengths: (a): 124(V/mm); (b): 181 (V/mm)
Fig. 4. Deformation and start of coalescence of a 1196±4 µm drop with an interface under the electric field strength of 181 V/mm, showing the formation of a narrow channel.
The effect of primary drop size
The effect of drop size in the range 576±1µm to 1196±4µm on the volume of the secondary drop has been investigated for constant electric field strength and Î». The results are shown in Figs 5 to 13.
Fig. 6. The effect of drop size on detached body Volume under various electric field strengths for Î»=101±10 µm
Fig. 5. The effect of drop size on detached body Volume under various electric field strengths for Î»=53±7 µm
Fig. 7. The effect of drop size on detached body Volume under various electric field strengths for Î»=150±11µm
Fig. 8. The effect of drop size on detached body Volume under various electric field strengths for Î»=200±14µm
Fig. 9. The effect of drop size on detached body Volume for various Î» under E=56 V/mm
Fig. 10. The effect of drop size on detached body Volume for various Î» under E=90 V/mm
Fig. 12. The effect of drop size on detached body Volume for various Î» under E=158 V/mm
Fig. 11. The effect of drop size on detached body Volume for various Î» under E=124 V/mm
Fig. 13. The effect of drop size on detached body Volume for various Î» under E=181 V/mm
As indicated in these graphs in any electric field strength (E) and any height of drop from interface (Î»), by increasing the primary drop size (d) the volume of detached body increases. In figures 5 to 8 this result has been shown for various height of falling drop from the interface and for simplicity the figure relating to Î»=0 has not been shown because for this special value of Î» there is no detached body for any drop size and electric field strength. It means when the drop sit on the interface there will not be any detached body and all coalescence processes lead to a complete coalescence pattern that is an ideal pattern and if the efficiency of the single drop coalescence is defined as the following:
The efficiency for this pattern of coalescence is unique and for a partial coalescence leading to detached body that is a value less than unique. so the bigger detached body in terms of volume the lee efficiency there is. It can be seen by increasing the primary drop size the volume of detached body is getting higher as a power law and this result is very sensible when the Î» is getting bigger in any electric field strength or when electric field strength is getting higher in any constant Î». Production of bigger detached body by increasing the primary drop size for a constant Î» and/or electric field strength can be explained by considering the effect of interfacial tension. According to Yang-Laplace equation, where , and are internal pressure, interfacial tension and the radius of the drop, it is obvious for the bigger droplets the internal pressure is less that means the rigidity for the smaller droplet will be higher and in other words the bigger drops are more formable. Higher rigidity and less formability for smaller droplets means under a given electric field strength and Î», the smaller drops resist production of a detached body. In another point of view as mentioned before the polarized drop subjected to an electric field is experiencing an attractive force being applied by positive electrode above the drop and the intensification of the polarization for a bigger drop is more than for a smaller one. Thus less rigidity and more attractive force by positive electrode for a bigger drop result in detaching a bigger volume of primary drop.
5.3.2 The effect of electric field strength
The effect of electric field strength on the production of detached body has been illustrated in the fig. 14 to 22. It can be seen when the falling drop is subjected to higher electric field strength the volume of the detached body will increase. In all graphs the drop size and the height of falling drop from interface has been kept constant so it is clearly seen that the results are valid for any given drop size and any quantity of Î». As mentioned the volume of detached body is being controlled by the mutual interaction between necking and pumping process. Eow and el.  have been shown by increasing the electric field strength the deformation of a given drop size will increase and in fact for a given drop size the more electric field the more deformation (the term "deformation" used here refers to the ratio of the major diameter to minor diameter of a prolate aqueous drop).
Fig. 14. The effect of electric field strengths on detached body Volume for various drop size and Î»=53±7µm
Fig. 15. The effect of electric field strengths on detached body Volume for various drop size and Î»=101±10µm
Fig. 17. The effect of electric field strengths on detached body Volume for various drop size and Î»=200±14µm
Fig. 16. The effect of electric field strengths on detached body Volume for various drop size and Î»=150±11µm
Fig. 19. The effect of electric field strengths on detached body Volume for various Î» and d=829±1µm
Fig. 18. The effect of electric field strengths on detached body Volume for various Î» and d=576±1µm
Fig. 21. The effect of electric field strengths on detached body Volume for various Î» and d=1100±2µm
Fig. 20. The effect of electric field strengths on detached body Volume for various Î» and d=984±2µm
Fig. 22. The effect of electric field strengths on detached body Volume for various Î» and d=1196±4µm
As illustrated in Fig. 23 and table. 2, by increasing the strength of electric field from 90 V/mm to 181 V/mm the deformation of the drop with the diameter of 984±2µm has been increased and that side of drop close to the interface gets more elongated in higher electric field.
Fig. 23. Different deformations degree for the same drop diameter of 984±2µm under different electric field strength
Table. 2. The deformation of the same drop diameter of 984±2µm under different electric field strength quantitatively
Electric field strength (V/mm)
When the drop is more elongated as a result of higher electric field it means in the moment of contact between drop and interface there is less contact area between them than contact area for a less elongated drop and interface in a lower electric field. As the narrow channel formed between drop and interface is the only way of pumping of the drop content into its bulk phase and moreover in high electric field strength the drop is feeling a higher attractive force caused by the positive electrode located above of it, so the pumping process is not able to overcome the necking process and in this state the volume of detached body in higher electric field will be bigger than for lower electric field for a given drop size and given height of falling.
In other words in high electric field strength the attractive force exerted by positive electrode on the drop coalescing with its bulk phase is very strong and this probably causes some of the bulk phase move inside the drop via narrow channel. So at the same time there are probably two flows into and out of the drop via narrow channel and moreover in high electric field the flow into the drop is more significant than for a low electric field. To prove that there is a flow from bulk phase into the drop the speed of three key points (Fig. 24) of a given drop has been considered while coalescing. These speeds have been shown in Fig. 25.
Fig. 24. Three key points on a typical drop to monitor the speed of them
Fig. 25. Speed of the channel expansion, equator deduction and peak falling for a drop with diameter 984±2µm under E=181 V/mm
It can be a good estimate to assume the coalescence of the drop under electric field is a highly symmetric process so in anytime the remaining volume of the primary drop is a symmetric volume about the axis going through the center of the volume. In Fig. 25, "channel expansion" radial speed shows the radial change () of the narrow channel connecting the drop and interface and the terms "Equator reduction" () and "Peak falling" () are showing the radial reduction and falling of peak point of drop respectively. To understand the pumping behavior of the drop these three speeds should be considered at the same time. As it can be seen in Fig. 25, at the beginning of the coalescence by formation of the narrow channel between drop and interface, the speed of channel expansion is very fast (in this case about 245 mm/sec) and it decreases continuously. Moreover before about 1ms the speed of equator reduction () and peak falling () are zero. As the channel is the only way of pumping of the drop content into bulk phase and both of and do not change in the time period from zero to 1 ms, this probably implies there must be a flow from bulk phase into the drop resulting in an increase in the drop volume in this period. An explanation for this upward flow can be because of a high attractive force by the positive electrode and bulk phase under the interface which has been negatively charged. Thus bulk phase moves toward the positive electrode via the only channel that is less viscose than continuous oil phase surrounding the channel. This flow into drop probably intensifies the circular flow inside the coalescing drop. Moreover it should be noted because of high speed of channel expansion and inertia of the drop and are much less than. Following this time period and start increasing slowly. In fact the net pumping into bulk phase and subsequent reduction of coalescing drop volume will start from this time. and approach a maximum in about 6.5ms after the beginning of the coalescence and after that start reducing. This reduction is because of the start of a necking process and subsequent separation of a detached body. Another point is that is reduces so fast and this means the driving force to expand the channel is reducing so fast as well. Thus the highest driving force to expand the channel and subsequent pumping of the drop into bulk phase is available at the beginning of the coalescence.
5.3.3 The effect of height of drop from interface (Î»)
This effect has been shown in fig. 26 to 35. According to these figures by increasing the height of falling drop from interface for a given drop size and under a constant electric field strength, the volume of detached body will increase.
Fig. 27. The effect of height of drop from interface on detached body volume for various drop sizes under E=90 V/mm
Fig. 26. The effect of height of drop from interface on detached body volume for various drop sizes under E=56 V/mm
Fig. 29. The effect of height of drop from interface on detached body volume for various drop sizes under E=158 V/mm
Fig. 28. The effect of height of drop from interface on detached body volume for various drop sizes under E=124 V/mm
Fig. 30. The effect of height of drop from interface on detached body volume for various drop sizes under E=181 V/mm
Fig. 32. The effect of height of drop from interface on detached body volume for various electric field strengths and d=829±1µm
Fig. 31. The effect of height of drop from interface on detached body volume for various electric field strengths and d=576±1µm
Fig. 34. The effect of height of drop from interface on detached body volume for electric field strengths various EF and d=1100±2µm
Fig. 33. The effect of height of drop from interface on detached body volume for various electric field strengths and d=984±2µm
Fig. 35. The effect of height of drop from interface on detached body volume for various electric field strengths and d=1196±4µm
It can be seen in all charts for small Î», the volume of detached body is very small and by increasing the Î» the detached body volume increases rapidly especially for bigger drop size and electric field strength. Bigger Î» means the drop is closer to the positive electrode and as mentioned the drop subjected to the electric field is polarized in such a way that on the pole of drop close to the positive electrode negative chares accumulate, so the drop feels more attractive force than a drop closer to the interface (less Î»). According to the graphs the effect of drop size is significant because bigger drops have less rigidity and are more deformable against the electric stress applied by electric field and moreover intensity of the polarization is higher for them so the bigger drops located in further Î» are experiencing more attractive columbic force ( where the r is the distance between charges sources) exerted by positive electrode. So the less rigidity and the more columbic force help necking process significantly. As a result of these events there will be a bigger detached body for a bigger drop under higher electric field strength. In addition the falling velocity for a drop further from interface is more than one for a drop closer to the interface in a uniform electric field. More falling velocity of the drop gives more momentum to it at the moment of the contact with interface and as a result of a stronger strike between drop and interface a wave is made on the liquid column that goes up and helps the necking process and detachment of a secondary drop. Hence in such a condition described above it seems the necking process rate is significant.
In consideration of the coalescence phenomenon without application of the electric field most of the researchers assume three main stages for it including approach of the drop to interface, and then rest of the drop on the interface for a long time and after thinning and drainage of the thin continuous phase film between drop and interface finally rupture and pumping of the drop into its bulk phase. Most of the research has been focused on the second stage as the most time-consuming stage in the absence of an electric field. But by application of a relevant strength of the electric field the second stage is going to be removed in practice. But drop-interface coalescence under electric field usually leads to the production of a detached body. By production of the detached body the coalescence process is not complete and so-called partial coalescence. By occurrence a partial coalescence instead of complete coalescence the efficiency of the single drop coalescence decreases that means whole volume of the drop does not coalescence in a single-stage and the separation of the current emulsion including added much fine droplets resulting from partial coalescence will be even much more difficult than primary emulsion. So it is highly desirable to consider the parameters resulting in production of detached body. As in real electrocoalescer, some of the most important parameters to control of the separation of dispersed phase include drop size distribution, electric field strength and moreeverd emulsion drops are located in different positions in terms of closeness and nearness to the interface or electrodes so in this research the effect of three parameters as drop size, electric field strength and the height of drop from interface have been considered. The results show by increasing any of these parameters or all of them at the same time the volume of detached body increases. Also it has been shown that while pumping of the drop into its bulk phase there is a mutual flow from the bulk phase to drop and vice versa. Moreover the velocity of three key points on the peak () and equator () of the drop and channel connecting the drop and interface () determined and it was shown is much faster than two other velocities (245 mm/sec) for a typical drop size of 984±2µm under 181 V/mm that this value is clearly showing the speed of pumping process and this is the reason in the literature this process has been described as an instantaneous process.