On electro-hydrodynamic effects over liquids under influence of corona discharge

Electrohydrodynamic effects over liquids under high voltage electrode are considered in experiments with corona discharge. Simple theory is applied for description of a funnel appearance over a liquid is presented. New types of electrohydrodynamic instabilities are revealed.


Introduction
Present investigations are devoted to formulation and undertaking of experiments with corona discharges realized over surfaces of different liquids. Investigations when a surface of one of the electrodes is covered by a liquid or is an electrode itself are of interest for hydrocarbon fuel activation and search of elimination of undesirable liquids in engines, problems of ecology and disinfection with a help of electric discharge. Such investigations are developing now, that is a reason for undertaking of these investigations. In this work we concentrated on electric-hydrodynamic features of corona discharges which are practically uninvestigated yet. However, there is limited information about any discharges over surfaces of liquids [1,2] and it is obtained mainly for electrolytes or water. From the application point of view it is interesting to know how a surface of a liquid fuel acts under an impact of gas discharges. Therefore our work is devoted to investigations of electric-hydrodynamic (EHD) effects caused by corona discharges over liquid. We made several series of experiments with positive and negative coronas over surfaces of tap water, distilled water, alcohol, glycerin, kerosene, and their mixtures. It consists of a ditch filled with a liquid (water, alcohol, kerosene, etc), and electrical circuit. Upper electrode or a set of electrodes of diameter 0.9 mm (with radius of the tip-0.2 mm) or 2 mm (with radius of the tip-0.4 mm) was located at height 5-15 mm over a liquid surface. A distance between electrodes in upper multi-electrode formulation was 11 mm. Electrodes were under positive or negative potentials. Ditches were either metallic or dielectric. The metallic ditches were: cylindrical  130 mm, height 18 mm, rectangular 3770122 mm; the dielectric plastic ditch was: rectangular 4595130 mm.
A current in a discharge was measured by a milliampere meter A1, a voltage was measured by a chain consisting of resistance R1 and a milliampere meter A2. We measured Ampere and Volt characteristics of the discharge and represented results in A-V2 coordinates typical for corona discharges [2].
Experiments have been carried out with a help of different cavities: rectangulardielectric, cylindricaldielectric and steel. Sizes of the rectangular cavity, were 702015 mm (length, width and depth). Characteristics of cylindrical cavities were 125, 10 mm and 185, 20 mm, respectively. An investigating liquid was poured into a cavity, a negative or positive electrode was located directly over the liquid, a distance between the electrode and the liquid could be varied in a range (1-30) mm. The upper electrode in the case of rectangular cavity was placed at the angle of 50 to the vertical. Its diameter was 3 mm, its angle at the vertex was 30 and a radius of a tip was 0,4 mm. An electrode of another polarity was located directly in the liquid. (A cavity was used as an electrode itself in the case of metallic cavity). It was connected with a feeding source through a hermetic unit. In this case the liquid becomes the second electrode. A high voltage generator was used as the feeding source, it allowed to measure a voltage on the electrodes from 2 kV to 50 kV with a step of 250 V. Typical range of the voltage was 5-25 kV. Appearance of the spark discharge was accompanied with a drop of the voltage at the capacity, which was detected by the voltmeter. In this device we used a ballast resistance, which value was 100 M. Typical values of a current were 50-100A.

Experiments with discharges over tap water surface
Our experiments have shown that application of negative and positive corona discharges over water surfaces in plastic or metallic cavities lead to appearance of a rotating funnel, it was evidently caused by the ion wind, see

Experiments with alcohol
In case of the alcohol in plastic or metallic cavities corona discharges lead to appearances of different EHD effects over the surface of the liquid. Funnels appeared at both polarities of the upper electrode. In Fig.5. we represent such a phenomenon. In case of the negative upper electrode firstly a rotating funnel usually appeared (it was evidently caused by then ion wind). Later some nuclei of jets in a form of tips were observed. Then bursting jets arose from the nuclei. The sprouts develop on sides of the funnel. This finishes either appearance of jets, see Figures 6-9, or liquid columns, see Figure 10-11. Usually this takes place at high applied voltage (20-30 kV). These columns are either standing on a place of the post funnel center or make some rotation motion being on a side of a funnel.
Liquid columns have sometimes widening at tip, sometimes there appears a violet-bleu glow on the column tip, see Figures 10-11. It speaks about breakdown field conditions realization near the tips.
Images were obtained with a help of digital video camera Sony DCR-TRV730 with frame duration 33 ms. Appearance of jets and columns stopped at the upper electrode distance of 17-18 mm from the surface.
Similar phenomena are known in EHD from literature [46]. They are connected with a development of Rayleigh, Taylor, Tonks and Frenkel electrostatic instabilities on surfaces of charged drops and jets when Coulomb forces of accumulated charges become greater than the surface tension.

Short theoretical discussion of obtained results
Let us consider impact of the ion wind to a surface of a liquid, and suppose that the ion wind creates a funnel. A scheme of the corona discharge and a liquid are represented in Fig.4.27.
here  is air density, e-electron charge, E -electric field, ion-a mobility of ions, I -discharge current, A(x)a cross section of air stream at a distance x from the tip of the upper electrode. Taking an area of the ion wind as a cone with a radius of a base Rs, and the cone side surface touches a base of the tip's hemisphere with the radius r0 one can obtain a following equation for a pressure head, see Figure 12, one gets: where d is a distance between a surface of liquid and a tip of the upper electrode. For experimental conditions I ≈ 510 -5 A, d ≈ 10 mm, r0 ≈ 0,2 mm, Rs ≈ 3 mm, ion=210 -4 m 2 V -1 s -1 one obtains from (3): Using a scheme in Figure 12 one obtains the following equation Inserting air density =1,2 kg/m 3 , experimental values of the current I=50 A, the radius of the funnel R=2 mm, the radius of the tip r =0,4 mm of the upper electrode, the distance between the tip and the surface H= 7 mm and air ion mobility ion=210 -4 m 2 V -1 s -1 into (3) one obtains the following value of an average velocity in conditions of our experiment u≈ 7.8 m/s. It is in a reasonable agreement with measurements [7][8] where the values of the ion wind at farer distances from the upper tip were about 3-5 m/s. From another point of view one can find it using a volume of the compressed liquid at a formation of the funnel: where h is a depth of the funnel. In case of water in our experiment h ≈ 3 mm, and  p  30 Pa, it is in reasonable agreement with the estimate given on a basis of the ion wind. So one can conclude that the funnel is created by the ion wind.
According to [1,3] an electric field Emax at a distance x between the tip of the parabolic form with curvature radius r being and the perpendicular plane at a distance d is connected with the voltage V between the tip and a plane by the formulae (4) Electric field in the corona discharge can be described by this formula [3] when there is no developed discharge channel.
One can see that the electric field influences the charged surface of the liquid. It will attract charged surface, against the gravitational force and the force of surface tension, causing the electric instability. It is so called Tonks -Frenkel instability of the charged surface of a liquid [4,6]. A condition for realization of this instability has a form ) /( 2 E is electric field strength near a surface of a liquid,  0 is air dielectric permeability,  is a surface tension of the liquid,  is its density. Using this formula one can obtain thresholds of Tonks-Frenkel instability over different liquids, such estimates for the critical electric fields are represented in Table  1 Looking at the Table one can see that the thresholds for glycerin and distilled water are close to those of the air breakdown, which in real conditions varies in the range E≈2.6-3/0 MV/m. At the same time its threshold in alcohol is E≈1.7 MV/m -much smaller. This shows that the development of air breakdown and formation of plasma channel can damp the development of the instability. However, one can expect a development of this instability in alcohol and kerosene and their mixtures. What we see in our experiments. Using formula (4) and Figure 12 one can understand why jets and columns can be easier originated at the edge of the funnel. Observations show that the edge height reaches 1 mm size. From (4) one obtains a ratio of electric fields between the tip and the funnel bottom and the tip and the edge: where  s1 is the depth of the funnel and s2 is the size of the edge. If s1 ≈1.5 mm, s2≈1,0 mm and d=7 mm then Analysis of Volt 2 -Ampere characteristic of obtained experimental data shows that appearance of jets and columns over alcohol in negative corona take place at voltages when in the positive corona the discharge channel is already realized. So, conditions in the negative corona are similar to those realizing in the capacitor [3,5] with high electric field causing the instability and in the positive corona in the quasi-neutral plasmas with lower electric field, which cannot cause a development of this instability.
Appearance of bursting jets and destruction of columns can be connected with development of instabilities of charged drops (we consider that tips of these structures represent quasi-drops in the case of small deformations, E is electric field strength on the drop surface, air is the dielectric constant of air,  is the surface tension coefficient, R is the radius of the drop. Assuming that the alcohol drop radius is equal to the radius of the column one obtains E 2.6÷4.5MV/m. These values are close to the typical breakdown values realized in air discharge near the electrodes. So we can connect these destruction mechanisms with the phenomena observed in the discharge.
Appearance of jets and columns over a surface in negative corona discharge case can be connected with a time of electric charge relaxation in a liquid. According to electrodynamics this time is , here  liq, 0 are a dielectric constant of a liquid and vacuum, respectively,  liq is electric conductivity of a liquid. For example, inserting values of corresponding values one obtains a typical time of charge relaxation in alcohol ~22 s and ~710-7 s in tap water. So in case of alcohol a state of a quasi-capacitor can be realized, and a surface of liquid can stay charged during a long time. However, ions in the positive corona are transported to the lower electrode quicker than in negative corona, and they will neutralize the charge in the liquid. So the situations with positive and negative coronas are different. It is well known that a liquid is drawn to a region of a high field in a capacitor that can be the reason for appearance of jets and columns in case of negative corona over a surface of alcohol.

Conclusions
Creation of corona discharges of positive and negative polarity has been realized over tap and distilled water, alcohol, glycerin and their mixtures.
Special devices for undertaking of experiments with several electrodes have been developed. Conducted experiments and their analysis show that the corona discharge over different liquids can cause different hydrodynamic phenomena including appearance of the ion wind and different instabilities.
Appearance of funnels is a result of the ion wind this was proved on the basis of the Euler equation. Funnels appear both in positive and negative coronas and independent of the discharge type.
Appearance of liquid jets and columns is a result of the Tonks-Frenkel instability in conditions of negative and positive corona. This phenomenon depends on a value of electric field strength and is better realized in liquids with low density and surface tension.
Separation of these jets and columns in drops are connected with instabilities of charged drops. Experiments show that conditions in the negative coronas in air are more favorable for creation of hydrodynamic phenomena than those in the positive coronas, since in the negative coronas can be achieved higher values of electric fields at which is still no realization of the discharge plasma channel connecting the electrodes.
These experiments helped to clarify modes of discharges realization and their connection with appearance of funnels on the surfaces of liquids and columns in case of alcohol.