K Adamiak
email: kadamiak@eng.uwo.ca

P Atten

Keywords: Corona discharge, electrohydrodynamics, electrostatic precipitation, particle charging, fine particles removal

A numerical model for simulating precipitation of submicrometer particles in a single-wire electrostatic precipitator is discussed in this paper. It includes all essential phenomena affecting the process: electric field, space charge density, gas flow, including the secondary electrohydrodynamic flow caused by the corona discharge and charged particles, and particle transport. A simplified corona model assumes just one ionic species and neglects the ionization zone. The fully coupled model for the secondary EHD flow, considering the ion convection, has been implemented. The dust particles are charged by ionic bombardment and diffusion. The gas flow pattern is significantly modified by the secondary EHD flow, which depends on the particle concentration. As for fine particles the drift velocity is small and particles practically follow the gas streamlines, the particle concentration has a very strong effect on the precipitation efficiency.

I. INTRODUCTION

HILE the concept of electrostatic precipitator (ESP) is relatively old and for many years these devices have been used to protect our atmosphere, the whole process is still not completely understood in details. Mutual interaction between an electric field, space charge density, gas flow, its modification by the secondary electrohydrodynamic (EHD) flow and particle transport makes analysis of the entire precipitation process rather complicated. Despite of wealth of literature on this subject the effects of different factors and criteria for optimum precipitator configurations continue to be a subject of discussion and sometimes contradicting conclusions.

One of the first interesting issues was the electrohydrodynamic origin of turbulence in ESPs [START_REF] Atten | The electrohydrodynamic origin of turbulence in electrostatic precipitators[END_REF]. Action of the electric field on the space charge results in the Coulomb force producing gas motion, which, in turns, affects the charge transport. This effect can lead to a much more intense turbulence than caused due to an interaction with the precipitation walls. Increased turbulence changes aerodynamic conditions in the precipitation channel and, according to many researchers, is detrimental to the particle transport [START_REF] Davidson | EHD flow visualization in the wireplate and barbed plate electrostatic precipitator[END_REF]. However, some initial research results also seem to indicate improvement in the precipitation efficiency due to the EHD flow under certain conditions [START_REF] Withers | Augmentation of single-stage electrostatic precipitation by electrohydrodynamic instability[END_REF].

Numerical simulation is a natural choice for investigating the effect of different factors on the precipitation efficiency. Yamamoto and his co-workers have clearly been the leaders in this field. Even though their corona discharge models were quite simplistic, it was emphasized from the very beginning that non-uniform electric field and gas flow distributions are crucial for the complete description of particle transport. As the negative corona discharge occurs in the form of discrete tufts, it was necessary to consider 3-D models of the process, even for smooth discharge electrodes [START_REF] Yamamoto | Numerical simulation of threedimensional tuft corona and electrohydrodynamics[END_REF]. Improved models of the same authors presented later [START_REF] Yamamoto | Three-dimensional ionic wind and electrohydrodynamics of tuft/point corona electrostatic precipitator[END_REF] still accepted some common idealizing assumptions, for example the point charge injection zone and negligible ion convection, but were able to show detailed 3-D distributions of potential, electric field, space charge and secondary gas flow for the two-wire and four-wire ESP geometries. Severe interaction between primary and secondary flows was observed with pairs of spiral vortices formed between the corona tufts in the direction of the gas flow.

The effect of secondary EHD flow depends of course on the primary flow magnitude: the size of spiral rings is reduced by the increased primary velocity. Similar investigations were subsequently performed for barbed-electrode multi-wire precipitators [START_REF] Fujishima | Numerical simulation of three-dimensional electrohydrodynamics of spikedelectrode electrostatic precipitators[END_REF] and for turbulent flow models [START_REF] Yamamoto | Threedimensional EHD simulation for point corona electrostatic precipitator based on laminar and turbulent models[END_REF]. It has been observed that the distance between spikes is critical for the flow pattern: for larger distances a well-organized spiral flow is formed, while at the reduced distance a turbulent flow arises. These agreed with the earlier experimental observations: for the positive corona discharge, which is uniform along the corona wire, the flow turbulence increases only slightly whereas the negative corona discharge strongly reinforces the turbulence intensity [START_REF] Leonard | An experimental study of the electrohydrodynamic flow in electrostatic precipitators[END_REF][START_REF] Kallio | Interaction of electrostatic and fluid dynamic fields in wire-plate electrostatic precipitator[END_REF].

W

A very detailed study of the effect of secondary EHD flow on the overall flow pattern in the electrostatic precipitator was presented by Soldati [START_REF] Soldati | Turbulence modification by large-scale organized electrohydrodynamic flow[END_REF], who investigated 3-D, timedependent, fully developed channel flow interacting with the EHD vortices. The corona model was again rather simple, as the Finite Difference discretization was not able to accurately represent the ionic transport close to the discharge wires. However, Direct Numerical Simulation (DNS) technique provided a very clear picture of the flow field, which was examined using a triple decomposition into a mean field, an organized EHD flow and a turbulent flow. It has been confirmed that pairs of counter-rotating EHD vortices are advected downstream by the main flow. Continuing his research, the same author also examined the particle transport and deposition in the wire-plate precipitator by performing Lagrangian simulation of particle trajectories [START_REF] Soldati | On the effects of electrohydrodynamic flows and turbulence on aerosol transport and collection in wire-plate electrostatic precipitators[END_REF]. The final conclusions were rather surprising, indicating that the EHD flow has a negligible influence on the overall particle collection efficiency: EHD flow contributes to a particle reentraining in the central region of the channel, but also sweeps them towards the walls in other regions.

The numerical model of the secondary EHD flow in ESP presented in [START_REF] Zhao | Electrohydrodynamic flow in a single wireplate electrostatic precipitator[END_REF] focused on accurate prediction of the charge transport. All calculations were performed for a 2-D turbulent flow model assuming infinitely long discharge wires and collection plates, but the fine discretization of the corona wire area made it possible to predict the total ionic current for a given wire voltage. The ionic drift was simulated using the Method of Characteristics, which is immune to the numerical diffusion and can easily incorporate the ion convection. Detailed analysis of different external flow and wire voltage levels revealed that at least eight flow patterns are possible. Recent experimental investigations using the method of Particle Image Velocimetry (PIV) confirmed a significant interaction between the electric field, space charge and flow fields [START_REF] Podlinski | Electrohydrodynamic gas flow in a positive polarity wire-plate electrostatic precipitator and the related dust particle collection efficiency[END_REF].

Collection efficiency of the conventional ESPs is usually satisfactory for large particles, but is much poorer for submicron particles. The drift velocity of such particles is small and they practically follow the gas streamlines [START_REF] Dumitran | Numerical simulation of fine particles charging and collection in an electrostatic precipitator with regular barbed electrodes[END_REF]. In this situation the effect of secondary EHD flow is much more pronounced. What is more important, the charged particles can significantly contribute to the magnitude of EHD flow. Experimental investigations published in [START_REF] Podlinski | ESP performance for various dust densities[END_REF] indicate that the mean values of the dust and ionic space charge densities can be comparable. In this situation the flow velocity and the level of its turbulence strongly depend on the dust density, especially in the region close to the corona wire.

This paper presents the results of numerical investigations of the gas flow and particle trajectories in a simple twodimensional model of ESP. The problem is simulated using a hybrid numerical algorithm, in which the electric field is calculated using the Finite Element Method, the ion drift by the Method of Characteristics and the gas flow by the Finite Volume Method. The flow simulation is done in the FLUENT commercial software, with other parts coded as the User Defined Functions.

I. PRECIPITATOR MODEL

As most of industrial ESPs are the wire-plate devices, this model is investigated in the paper. A single discharge electrode (cylindrical wire) is located symmetrically between two collecting plate electrodes (Fig. 1). Gas flows in the direction parallel to the ground plates, but is modified by the ionic wind. Neutral sub-micron particles, with spherical shape, are injected at the precipitator entrance and are charged by the field and diffusion charging as they move along the channel and cross the ionic space charge zone. Affected by the electric and aerodynamic forces some of these particles are deposited on the walls, while others exit the precipitation channel on the other side. The deposited particles are removed from the model and they don't contribute to the electric field distribution or to the flow pattern.

II. MATHEMATICAL MODEL

A. Electric Field and Space Charge

A simple single-species stationary corona discharge model is implemented in this paper. The ionization layer is neglected and just one ionic species is injected from the corona electrode surface. These ions drift with an average mobility until they are deposited on the surface of the grounded electrodes. The mathematical description involves the equations for the electric potential and current continuity 0 2

ε p i q q Φ + - = ∇ (1) 0 ) ) ( ) (( = + + + ⋅ ∇ p p i i q u E k q u E k r v r r (2)
where Φ (V) is the electric potential, q i (C/m 3 ) -space charge density of ions, q p (C/m 3 ) -space charge density of particles, ε 0 (F/m) -ambient gas permittivity, k i (m 2 /Vs) -ion mobility, k p (m 2 /Vs) -particle mobility, u r (m/s) -vector of gas velocity and Φ E ∇ = r -the electric field vector. Eq. ( 2) is valid assuming that the ion diffusion can be neglected.

Formulation of the boundary conditions is trivial for the potential Φ: the surfaces of corona wire and ground plates are equipotential (Dirichlet conditions). No exact boundary condition can be specified for the channel inlet and outlet. However, these parts are sufficiently far from the most critical region around the corona wire, so zero normal derivative of the electric potential (homogeneous Neumann conditions) is usually sufficiently accurate. The boundary conditions for the space charge are more problematic. As the ionization layer has been neglected in this model, exact formulation of these boundary conditions is not possible. Kaptzov's hypothesis is usually accepted, stating that for voltages above the onset level the electric field remains constant at the value given by the empirical Peek's formula

) 5 . 0 308 . 0 1 ( 10 1 . 3 6 0 r E ⋅ + ⋅ = ( 3
)
where r is the corona wire radius in cm. While this formula is theoretically valid for 1-D wire-cylinder geometry, where the electric field on the corona wire surface is constant, it has been proved [START_REF] Adamiak | Corona discharge in the hyperbolic point-plane configuration: direct ionization criterion versus approximate formulations[END_REF] that accuracy of the simulation is preserved for non-uniform electric fields, too. The charge transport equation ( 2) is of the first order, so that no boundary condition is needed on other domain boundaries.

B. Gas flow

Under the assumption of incompressible ambient air, the gas has constant density and viscosity; the air flow has to satisfy the continuity and the conservation of momentum equations [START_REF] Zhao | Electrohydrodynamic flow in a single wireplate electrostatic precipitator[END_REF]:

0 = ⋅ ∇ u r (3)
F u P u u t u f r r r r r + ∇ + -∇ = ∇ ⋅ + ∂ ∂ 2 ] ) ( [ η ρ (4)
where ρ f (kg/m 3 ) is the gas density, P (Pa) -the static pressure, η (kg/m•s) -the air viscosity, and F r (N/m 3 ) -the body force, in this case equal to the Coulomb force

E q q F p i r v ) ( + = .
The flow velocity vector u r must vanish on all solid surfaces (corona electrodes and channel walls); it takes a specific profile at the channel inlet and the pressure at all points of the outlet has the same value.

C. Particle Concentration

The particles injected into the precipitation channel are assumed to be spherical, to be electrically neutral and to move with a uniform initial velocity equal to the gas velocity. As soon as they enter the region where the ionic space charge exists, they become electrically charged. There are two mechanisms responsible for imparting charge onto the particles: field charging (ionic bombardment) and diffusion charging.

The first effect occurs only if the actual particle charge Q p is smaller than the saturation charge Q s , given by the formula

E d Q p s 2 0 2 2 πε ε ε + = (5)
where ε is the particle relative permittivity. Diffusion charging can occur even for Q p above the saturation level, but its practical contribution is most often minimal. The overall charging rate is given as [START_REF] Lawless | Modeling particulate charging in ESPs[END_REF]: A moving particle experiences inertial, air drag and electrical forces. All are balanced in the Newton equation, which needs to be solved in order to determine the particle trajectory. For sub-micrometer particles, inertia is very small and can be neglected. In this situation, the so-called particle migration velocity can be calculated first

           > - - < + - = s p p B p s s p q s p p B s p q s p Q Q Td kk Q Q e Q Q Q Q e Td kk Q Q Q dt dQ for ) 2 ) ( exp( ) ( 4
E d Q Cu v p p d r r πη 3 ⋅ = ( 7
)
where Cu is the Cunningham factor, calculated as When the migration velocity is known, the particle trajectory is calculated by a simple integration

d p v u t x r r r + = ∂ ∂ (8)
where p

x r -is a vector defining particle position along the trajectory.

III. NUMERICAL ALGORITHM

The numerical algorithm is based on the Finite Element Method (FEM) and FLUENT flow dynamics commercial software. The whole domain is discretized into approximately 9500 triangular elements distributed in a very non-uniform way with smallest elements close to the corona wire and much larger elements near the inlet and outlet of the precipitation channel. The laminar flow model has been assumed and the Navier-Stokes equation ( 4) is solved in time domain by FLUENT. The electric body force has to be determined separately using so-called User-Defined-Functions (UDF). Before this is done the electric field and space charge distributions are determined. This is done in another UDF, which is based on FEM for the electric field and on the Method of Characteristics for the space charge. A double iterative loop is employed, in which the space charge density on the corona wire surface and in the entire precipitation space is iterated until convergence is reached for all involved variables. The corona model includes the convection current, as far from the corona wire, it can visibly modify the ion trajectory and the space charge density [START_REF] Zhao | Electrohydrodynamic flow in a single wireplate electrostatic precipitator[END_REF].

A given number of spherical particles are injected at every time step from the channel inlet. All of them are electrically neutral and have the same size and initial velocity. They start from uniformly distributed rectangular cells with random initial particle position inside of each cell. The super-particle approach is used, in which each particle moves as a single particle with real parameters. However, this super-particle carries a charge of some number of particles. The particle distribution is sufficiently dilute, so they do not affect the air velocity field. The particle charge is calculated by integrating the charging equation ( 6).

IV. RESULTS AND DISCUSSION

The above numerical algorithm has been applied for simulating a single-wire EPS precipitator, assuming that the diameter of corona wire is 1 mm, collecting plates are 10 cm apart, average gas velocity at the inlet is 0.4 m/s and 30 kV is applied to the corona wire. Injected dust particles are spherical in shape with the diameter of 0.3 µm. Their concentration is expressed in terms of the reference value of c 0 = 2•10 +12 particles/m 3 .

A. Electric Field and Space Charge

Electric potential distribution follows an expected pattern: close to the equipotential wire the equipotential lines are practically circular. Large concentration of lines indicates strong electric field in this area. The lines deform as the distance to the corona wire increases showing an oval shape. Eventually, the equipotential line becomes completely flat at the ground plate.

Gas ionization occurs in a thin corona sheet surrounding the corona wire. The maximum space charge density in this region is about 190 µC/m 3 , but this density sharply decreases towards the ground plate. Close to the inlet and outlet of the precipitation channel the space charge density decreases to a very small value.

B. Flow Velocity Streamlines

Without the action of electrical forces the gas flow follows regular laminar path lines shown in Fig. 2a. Depending on the Reynolds number, von Karman vortices can be created behind the corona wire, but they are too small to be visible. When the wire voltage is above the corona onset level, the corona discharge generates the secondary EHD flow. Without external flow four doubly symmetrical vortices are created [START_REF] Zhao | Electrohydrodynamic flow in a single wireplate electrostatic precipitator[END_REF]. The presence of charged dust particles also contributes to the generation of EHD flow, but this pattern is not symmetric with respect to the vertical plane: upstream the corona wire the particles are not fully charged yet, so in this region the electric body force is much smaller than in the downstream region, where the particles are fully charged and much stronger EHD flow can be expected. The final flow distribution results from the balance of all three components.

Without the presence of charged dust particles the flow pattern is practically dominated by the external gas flow (Fig. 2b). The two upwind vortices generated by the corona discharge are shifted towards the walls and two downwind vortices are squeezed towards the channel plane of symmetry forming an elongated wake. The charged dust presence dramatically changes aerodynamic conditions in the channel: time dependent vortices grow in size with increased particle concentration until they eventually occupy the major part of the channel downstream the corona wire (Fig. 2e). The flow is not steady and it exhibits violent oscillations.

C. Particle Concentration

Fig. 3 shows the dust particle distribution for different dust densities. As expected, the dust particles are mostly affected by the air drag force with a rather weak contribution of the electric force. When the dust concentration is very small (Fig. 3a) the particle charge doesn't affect the flow pattern and particle trajectories basically follow the gas streamlines shown in Fig. 2b. The dust particles are swept from the area of two upwind vortices. Also, a thin trail downwind of the corona wire exists, where the dust particles are removed by the electric force. Increased dust concentration changes the flow structure and the dust concentration pattern.

With an increased dust concentration the region with the negligible particle concentration spreads out towards the collecting plates, what can be seen as a factor improving the dust collection, because the particles are driven towards the collecting plates. However, vortex formation downwind the corona wire drives the dust particles again towards the channel centre. This kind of flow might even re-entrain particles already deposited on the walls. The particle re-entrainment is not included in the presented algorithm; so calculated values of the deposition efficiency improve with the dust concentration. This is contrary to the experimental observations, where the collection efficiency is actually deteriorated, when the dust concentration is increased [START_REF] Atten | Turbulence generation by charged fine particles in electrostatic precipitators and its effect on collection efficiency[END_REF].

D. Voltage-current characteristics

The presence of charged dust particles influences the corona discharge. The dust-generated space charge adds to the ionic space charge. As the total space charge produces the same effect on the electric field on the wire, an increase in dust concentration reduces the ions concentration and, therefore, the total corona current under the same voltage [START_REF] Podlinski | ESP performance for various dust densities[END_REF].

Numerical simulations confirm this picture (Fig. 4). Under 30 kV, without dust the total corona current is I ≅ 200 µA; this current decreases with c and at c = 20 c 0 we obtain I ≅ 120 µA, i.e. a reduction of about 40 %. This estimate fairly well agrees with measurements presented in [START_REF] Podlinski | ESP performance for various dust densities[END_REF], although exact comparison of the concentration levels is not possible, as in the experiments the dust has a poly-dispersed size distribution.

E. Charging level of dust particles

The dust particles are charged mainly by the field charging with a small addition by the diffusion charging. The charging level is a function of the maximum electric field the particle

c = 0.2 c0, c) c = c0, d) c = 8 c0, e) c = 12 c0, f). c = 20 c0
has been exposed to; therefore, different particles are charged differently depending on their trajectories: those passing in close proximity of the corona wire are charged to a much higher level than the ones migrating close to the collecting walls.

Fig. 5 shows examples of the dust charge distribution both for the collected and uncollected particles. It may be first surprising to see that the uncollected particles are charged to a much higher level than the collected ones. However, it is obvious that the electric forces play a minor role in the dust precipitation: collected particles were injected close to the wall and were deposited by the mechanical forces: migrating close to the ground electrodes they were exposed to a weak electric field and didn't gain significant electric charge. There are two humps on this graph: the first one corresponds to precipitation in the area of upwind vortices, the second one -to precipitation in the area downwind the corona wire.

V. CONCLUSIONS

The results presented in the paper show the effect of particle concentration on the gas flow streamlines, on the particle distribution pattern and on the current-voltage characteristics of the single-wire ESP. Increasing the particle concentration significantly affects the flow pattern which becomes more and more non-uniform and exhibits stronger and stronger agitation. Increasing the particle concentration also increases the space charge due to particles, what results in a reduction of the corona current. Obtained results qualitatively agree with the experimental data [START_REF] Podlinski | ESP performance for various dust densities[END_REF].

Kazimierz Adamiak and Pierre Atten 6 ème

 6 Conférence de la Société Française d'Electrostatique, Paris & Gif-sur-

Fig. 1 .

 1 Fig. 1. Schematic configuration of the investigated precipitator.

  q being the charging time constant, k B -Boltzmann coefficient and T -temperature.

  g = 6.5 10 -8 m -the mean free path of the gas molecules.

Fig. 2

 2 Fig. 2 Gas path lines for different dust particle concentrations (corona wire voltage equal to 30 kV, input gas velocity 0.4 m/s). a). no corona discharge, c = 0, b).corona discharge, c = 0, c). corona discharge, c = c0, d). corona discharge, c = 8c0, e). corona discharge, c = 12 c0, f). corona discharge, c = 20 c0.

Fig. 3

 3 Fig. 3 Dust particle pattern for different dust particle concentrations (corona wire voltage equal to 30 kV, input gas velocity 0.4 m/s). a) c ≈ 0, b) c = 0.2 c0, c) c = c0, d) c = 8 c0, e) c = 12 c0, f). c = 20 c0

Fig. 4 Fig. 5

 45 Fig. 4 Corona current versus dust concentration (corona wire voltage -30 kV, gas velocity -0.4 m/s)

This work was supported in part by CNRS (trough invitation of K.A. in GE2 Lab) and the Natural Sciences and Engineering Research Council (NSERC) of Canada.


T Ogier

J M Bassat

F Mauvy

S Fourcade

J C Grenier

K Couturier

M Petitjean

J Mougin

Enhanced Performances of Structured Oxygen Electrodes for High Temperature Steam Electrolysis

Introduction

For economical and ecological reasons, hydrogen is considered as a potential energy vector for future. Before becoming an available alternative fuel, the main problem still to be solved is its massive production via clean processes with low or no CO 2 emissions. High temperature steam electrolysis (HTSE) is one of the most promising ways to reach this target, with a high efficiency when compared to the conventional low temperature processes. It consists in splitting water molecules into hydrogen and oxygen gases using electricity and heat [START_REF] Dönitz | Electrochemical Hydrogen Technologies. Electrochemical Production and Combustion of Hydrogen[END_REF], which can be provided by renewable energy sources or nuclear power plants for example [START_REF] Elder | [END_REF]. To reduce the required energy, the development of highly efficient systems is necessary. Each system component has to be optimized, in particular the single solid oxide electrolysis cell (SOEC) where the electrochemical reactions occur. At the cell level, electrode polarizations induce large voltage losses that should be reduced to increase the total efficiency [START_REF] Ivers-Tiffée | High Temperature Solid Oxide Fuel Cells. Fundamentals, Design and Applications[END_REF]. More precisely, improving the oxygen electrode performances is of crucial interest since this electrode contributes to a large extent to the cell polarization resistance. Compared to oxygen electrodes with pure electronic conduction, the use of a mixed electronic and ionic conducting (MEIC) oxygen electrodes (either as composite or as single phase) is especially relevant as such kind of materials is expected to extend the reaction zones all over the gas/electrode interface.

Most current studies reported on HTSE consider solid oxide cells containing perovskite-type oxygen electrodes as generally for SOFCs [START_REF] Herring | [END_REF]5]. The present study focuses on alter--~Paper presented at the 10th European SOFC Forum 2012, June 26-29, 2012 held in Lucerne, Switzerland. Organized by the European Fuel Cell Forum -www.efcf.com

Abstract

The present study is focused on alternative structured oxygen electrodes for solid oxide electrolysis cells (SOEC). The Ln 2 NiO 4+d (Ln = La or Pr) nickelate oxides were selected as innovative electrode materials with respect to their mixed electronic and ionic conductivity. A thin interfacial ceriabased layer was added in between the electrode and the zirconia-based electrolyte to improve mechanical and electrochemical properties and to limit the chemical reactivity. These structured cells were characterized by electrochemical impedance spectroscopy on symmetrical cells, under zero dc conditions and anodic polarization. Low polarization resistance R P and improved anodic overpotential g A versus current density curves were obtained for the Pr 2 NiO 4+d electrode with Ce 0.8 Y 0.2 O 2-d interlayer: R P is decreased down to 0.06 X cm 2 at 800 °C, under air and zero dc conditions. Then, complete hydrogen electrode-supported cells including Pr 2 NiO 4+d as oxygen electrode were electrochemically characterized. At 800 °C, when the inlet gas composition is 90 vol.% H 2 O-10 vol.% H 2 at the hydrogen electrode, air being swept at the oxygen electrode, the current density determined at 1.28 V reaches -0.9 A cm -2 , the corresponding steam to hydrogen conversion ratio being 58%. These results are compared to those obtained with a reference cell including the oxygen deficient perovskite La 0. native structured oxygen electrodes. The Ln 2 NiO 4+d (Ln = La or Pr) rare-earth nickelate oxides (with K 2 NiF 4 -type structure) have been selected as oxygen electrode materials with respect to their electrocatalytic activity. Indeed, their ability to accommodate oxygen over-stoichiometry and their MEIC properties when operating under oxidizing conditions [6] explains the strong interest in these compounds as solid oxide fuel cell (SOFC) cathode material [7]. Moreover, it appears that these materials show an extremely high flexibility for being used as oxygen electrode in very different conditions in terms of oxygen partial pressure or/and water content [8,9]. In this way, it was reported that, under anodic polarization (HTSE conditions), this rare-earth nickelate oxide-type exhibits a lower polarization resistance than under cathodic polarization [10]. In addition, in SOFC devices, it has been shown several times that adding a thin doped ceria buffer layer with optimized microstructure, between the oxygen electrode and the zirconia-based electrolyte significantly increases the electrochemical properties of the cells [11][START_REF] Jordan | Solid State Ionics[END_REF][START_REF] Van Berkel | [END_REF][14].

In this work, such a ceria-based interfacial layer has been deposited to improve electrochemical interfacial properties and to limit the chemical reactivity between the electrode material and the electrolyte. In this frame, two different interfacial layers were compared. The corresponding structured electrodes were screen-printed and sintered, then characterized using electrochemical impedance spectroscopy (EIS) measurements performed on symmetrical electrolyte-supported cells, under zero dc conditions and also anodic polarization. Then, complete hydrogen electrode-supported cells, including Pr 2 NiO 4+d structured oxygen electrode, were characterized in terms of electrochemical performances, in electrolysis working conditions.

Experimental

Powder Preparation and Cell Manufacturing

The Ln 2 NiO 4+d (Ln = La or Pr) powders were prepared by the nitrate-citrate route, as previously described [8]. The powders were then ball milled to decrease the median particle size down to about 0.5 lm. The selected interfacial materials were made of ceria doped with 20 mol.% yttrium or gadolinium, leading to the formula Ce 0.8 Y 0.2 O 2-d (YDC) and Ce 0.8 Gd 0.2 O 2-d (GDC) provided by Praxair ® and Rhodia ® , respectively. Both median particle sizes were about 0.2 lm. Terpineolbased slurries with YDC or GDC, then Ln 2 NiO 4+d (Ln = La or Pr) powders were successively screen-printed on both sides of dense 8 mol.% yttria-doped zirconia (8YSZ) electrolyte pellets (about 1.2 mm thick). YDC and GDC layers were sintered in air at 1,400 and 1,350 °C, respectively for 1 h resulting in 3-5 lm thick layers. The Ln 2 NiO 4+d (Ln = La or Pr) electrodes were annealed for 1 h, in air, at 1,100 °C for La 2 NiO 4+d and at 1,180 °C for Pr 2 NiO 4+d . These sintering temperatures were beforehand optimized to obtain a controlled homogenous porous electrode microstructure. Figure 1 shows a typical example of the SEM micrographs of the cross-section for La 2 NiO 4+d /8YSZ interface with or without YDC barrier layer.

In order to characterize the electrochemical properties of these structured electrodes on symmetrical cells, two geometries were used: (i) both electrodes cover all the electrolyte surface, in the case of impedance spectroscopy measurements performed under zero dc conditions (ii) a Pt reference electrode is set on one side of the electrolyte, the electrodes covering one-half of the electrolyte surface, for samples used for measuring the polarization curves (i dc ≠ 0) [15].

Finally, to prepare complete electrolysis single cells, a Pr 2 NiO 4+d electrode was screen-printed on a planar commercial hydrogen electrode-supported half-cell. The 5-10 lm thick hydrogen electrode functional layer consists in a porous nickel and 8 mol.% yttria-doped zirconia cermet (Ni -8YSZ) supported by a 500 lm thick porous nickel and 3 mol.% yttria-doped zirconia cermet (Ni -3YSZ). The electrolyte is a 3-5 lm thick layer of 8 mol.% yttria-doped zirconia (8YSZ). The commercial half-cell comprises a relatively dense 3 lm thick YDC interlayer deposited on the oxygen electrode side. The hydrogen electrode diameter was 50 mm and the oxygen electrode diameter was 20 mm. The Pr 2 NiO 4+d electrode was sintered for 1 h, in air, at 1,180 °C.

Electrochemical Characterizations

Investigations on Symmetrical Cell

In order to characterize the electrochemical properties of the Ln 2 NiO 4+d (Ln = La or Pr) oxygen electrodes, EIS measurements were carried out under air, on symmetrical cells, in the temperature range 600-800 °C. Current collectors on both cell sides were gold grids (1,024 mesh cm -2 ). The impedance diagrams were recorded after reaching steady state, under potentiostatic control with 50 mV ac amplitude, from 10 6 Hz down to 10 -2 Hz, using a frequency response analyzer module Autolab FRA2, coupled with a potentiostat/galvanostat PGSTAT 302N. The complex impedance diagrams were fitted using an equivalent circuit by means of the Zview™ software (Scribner Associates). The polarization resistance R P values (corresponding to the sum R P = R HF + R LF ) were calculated from the difference between the low and the high frequencies diagram intercepts with the Z′-axis of the Nyquist representation.

The polarization curves were obtained by voltamperometry measurements using a three-electrode configuration, with the same apparatus and the same potentiostatic control. For each point, a constant voltage polarization E was applied between the working and the reference electrodes and the resulting current I between the working and the counter electrodes was recorded after steady state. Measurements were carried out step by step from zero dc voltage up to the highest polarization of 1 V, then back to zero dc voltage, in order to check reversibility. The impedance value obtained at the diagram -Z′-axis intercept at high frequencies, represents the series resistance R S . The ohmic drop R S I was deduced from the impedance diagram carried out at each investigated voltage step, which allowed determining the working electrode anodic overpotential g A , according to Eq. (1):

g A E À R S I (1

Single Cell Set-up and Measurements

The single cell characterizations were carried out using a two-atmosphere set-up (cf. Figure 2) [START_REF] Mansuy | 10th European Solid Oxide Fuel Cell Forum[END_REF]. The inlet gas composition was composed of 90 vol.% H 2 O-10 vol.% H 2 for the hydrogen electrode while air flew in the oxygen electrode. The area normalized flow was 12 NmL min -1 cm -2 on the standard ambient temperature and pressure conditions, on both anode and cathode sides. The percentage of steam-tohydrogen conversion (SC) of the SOEC during the experiments is calculated as the produced molar amount of hydrogen divided by the molar amount of water in the inlet gas. The produced hydrogen amount was calculated using the Faraday law assuming 100% current efficiency. Current collectors were gold and platinum grids for the anode, nickel grids for the cathode, in order to improve contact with the ceramic electrodes. Moreover, the current collection was optimized through the control of the compression effort. The current density i was calculated from the normalization of the recorded dc current I with respect to the geometrical oxygen electrode surface area (about 3.14 cm 2 ). The polarization curves were performed under galvanostatic control, from 0 A cm -2 to -1 A cm -2 , then back to zero current, using an Autolab PGSTAT 302N.

Results and Discussion

Symmetrical Cell Characterizations

Polarization Resistance Measurements under Air

The symmetrical cells were characterized by EIS under air. Typical diagrams measured at 800 °C are shown in Figure 3 in the Nyquist representation. They are normalized by the geometrical electrode surface area (about 1.7 cm 2 ) divided by two to take into account the fact that two symmetrical electrodes are surrounding the electrolyte and to obtain the electrochemical properties of one single electrode.

All the measured diagrams have been fitted using the equivalent circuit show in Figure 3,i contribution R HF when a GDC interlayer is present. On the contrary, the resistance of the low frequency contribution R LF seems constant at 800 °C whatever the interface. The thermal evolutions of R HF and R LF are given in Figure 4. It can be noticed the simultaneous decrease of the high and low frequency resistances with temperature. According to previous works, the large decrease of R HF can be explained by the beneficial effect of the GDC barrier layer [14]. Indeed, SEM pictures of the corresponding cells have shown that the adhesion between materials and the quality of the electrode/electrolyte interface are improved when the interlayer is present. According to the literature, the low frequency resistance R LF is generally assigned to the electrode reaction processes [START_REF] Mauvy | [END_REF]18]. In this way, R LF is supposed to be only slightly changed when adding a GDC barrier. This assumption is in good agreement with our experimental results, especially in the lowest temperature range. However, at high temperature (700-800 °C), the activation energy of R LF is lower, with the value of 0.19 eV, which could indicate a modification of the reaction rate-determining step.

The polarization resistances values obtained for the structured Ln 2 NiO 4+d (Ln = La or Pr) electrodes are plotted in Figure 5.

The GDC or YDC interlayer leads to a significant decrease of the R P , for both La 2 NiO 4+d and Pr 2 NiO 4+d electrodes. For instance, for Pr 2 NiO 4+d /YDC half-cell, the R P is decreased by a factor of two, down to 0.06 X cm 2 at 800 °C, under air and zero dc conditions. A similar value is also obtained with Pr 2 NiO 4+d /GDC, at 800 °C. These values correspond to the lowest obtained R P value in the set of data. It can be concluded that ceria-based barrier layer (and optimized sintering process and power preparation) leads to a drastic improvement of the electrode polarization resistance.

Polarization Curves

With the aim to characterize the electrochemical properties under dc current conditions, electrode polarization curves g A = f(i) have been measured step by step under steady state on symmetrical cells based on Ln 2 NiO 4+d (Ln = La or Pr) materials with or without an additional GDC or YDC interfacial layer. Anodic current conditions, representative of electrolysis operation have been selected. Examples of polarization curves recorded at 800 °C, under air, are given in Figure 6.

As observed under zero dc conditions, adding a ceriabased interlayer leads to significant improvement of the polarization curves. Similar anodic overpotential g A versus current density curves are obtained when a GDC or YDC interlayer is applied. Finally, because of better electrochemical properties of Pr 2 NiO 4+d compared to La 2 NiO 4+d , this electrode was selected for further characterizations as single electrolysis cells.

Electrolysis Single Cell Operation

The polarization curve recorded on a single cell including Pr 2 NiO 4+d oxygen electrode was compared at 800 °C to the ones obtained with two commercial hydrogen electrode-supported cells of the same type, including the -reference -oxygen deficient perovskite La 0.6 Sr 0.4 Fe 0.8 Co 0.2 O 3-d , as oxygen electrode (Figure 7). All cells had an identical YDC barrier layer. They were studied using the same experimental set-up and similar gas conditions. However, the difference observed in the polarization curves of the commercial cells likely results from disparity in their manufacture. From the analysis of Figure 7, the i-V curves may be divided into three parts. Firstly, the low current density range (i > -0.2 A cm -2 ) is the domain where activation overvoltage dominates. In this part, the kinetics is mainly governed by the charge transfer process. The evolution of the voltage at low current densities shows that the area specific resistance (ASR) decreases as the current density increases. At the OCV, the ASR value of cell based on Pr 2 NiO 4+d /YDC oxygen electrode is about 0.71 X cm 2 while for i = -0.2 A cm -2 , the ASR is equal to 0.40 X cm 2 . Secondly, in the intermediate part (-0.6 A cm -2 < i < -0.2 A cm -2 ), the i-V plot is quasi-linear. In this part, the ASR is nearly constant and minimal. This behavior is mainly assigned to the ohmic drop located in the solid electrolyte. At i = -0.5 A cm -2 , the ASR is 0.37 X cm 2 . Finally, under high negative current densities (i < -0.6 A cm -2 ), concentration overpotentials appear which reflect the problems for the reactants to access to the active sites and the products to be evacuated from them. The kinetics is then limited by the mass transport properties. These phenomena can be divided into two processes: the diffusion of the involved species to the catalytic sites and the removal of produced hydrogen and oxygen. On the i-V curve, this domain characterized by diffusion leads to an abrupt increase of the voltage and ASR when the current density increases. For i = -0.8 A cm -2 , the ASR is 0.66 X cm 2 and for i = -0.9 A cm -2 the ASR is close to 1.20 X cm 2. On the major part of the polarization curves, i.e. until -0.8 A cm -2 , the studied cells show similar performances. The current density determined at thermo-neutral potential 1.28 V reaches -0.9 A cm -2 , the steam conversion being about 58%.

It can be noticed that the boundaries of the three domains described for Figure 7 are valid for the experimental conditions used to obtain these data. Indeed, the borders of these domains depend for a given single cell on the gas flow rates and on the working temperature as shown in Figure 8 where the i-V polarization curves recorded in the range 800-650 °C are reported. In particular, at 650 °C, the mass transport limitation domain is no more observable. It is due to the fact that the SC values are lower as well as the current densities in these conditions, minimizing the problems of reactant access and products evacuation to and from the active sites, respectively. The properties of the cell are mainly governed by the increase of the ohmic drop through the cell, the ASR in the linear part is 1.0 X cm 2 at 650 °C. It can be noticed that Pr 2 NiO 4+d can operate as oxygen electrode down to 650 °C, leading to a promising current density close to -0.3 A cm -2 for a cell voltage equals to 1.28 V.

Conclusion

MEIC materials Ln 2 NiO 4+d (Ln = La or Pr) have been investigated as oxygen electrodes for HTSE. Two interfacial ceria-based layers (YDC and GDC) have been studied and both yield significant improvements. At first, the structured electrodes were characterized by EIS measurements performed on symmetrical electrolyte-supported cells, under zero dc conditions and anodic polarization. The Pr 2 NiO 4+d / YDC and Pr 2 NiO 4+d /GDC structured electrodes lead to enhanced electrochemical properties compared to the electrode without any interlayer.

Then, a complete hydrogen electrode supported cell, including the Pr 2 NiO 4+d /YDC structured oxygen electrode, was characterized in terms of electrochemical performances and compared to reference cells including the oxygen deficient perovskite La 0.6 Sr 0.4 Fe 0.8 Co 0.2 O 3-d as oxygen electrode and the same YDC interlayer. At 800 °C, when the inlet gas composition is 90% H 2 O-10% H 2 at the hydrogen electrode, and flowing air at the oxygen electrode, the current density reaches -0.9 A cm -2 at 1.28 V, the steam to hydrogen conversion ratio being 58%. One can consider that this alternative cell shows similar performances than the commercial cells. According to these promising results, the Ln 2 NiO 4+d (Ln = La or Pr) nickelates associated with a ceria-based interlayer can be considered as good candidates for oxygen electrode materials of HTSE cells. However, long-term durability should be studied for both kinds of cells; the tests are in progress.

Fig. 1

 1 Fig. 1 Typical SEM micrographs (transverse cross-section view after fracture) for the La 2 NiO 4+d /8YSZ interface (a) and the La 2 NiO 4+d /YDC/8YSZ interface (b).

Fig. 2 Fig. 3

 23 Fig. 2 Schematic representation of the experimental set-up for the single cell measurements.

Fig. 4 Fig. 5

 45 Fig. 4 Thermal variation of the resistances R HF and R LF measured for Pr 2 NiO 4+d / 8YSZ and Pr 2 NiO 4+d /GDC/8YSZ symmetrical half-cells, under air. The activation energy is indicated for each resistance.

Fig. 6 Fig. 7 Fig. 8

 678 Fig. 6 Polarization curves recorded under air at 800 °C on structured symmetrical cells: Pr 2 NiO 4+d , Pr 2 NiO 4+d /GDC, and Pr 2 NiO 4+d /YDC (a), La 2 NiO 4+d , La 2 NiO 4+d /GDC, and La 2 NiO 4+d /YDC (b).

  6 Sr 0.4 Fe 0.8 Co 0.2 O 3-d as oxygen electrode.

	Keywords: Barrier Layer, Hydrogen Production, K 2 NiF 4
	Structure, Overpotential, Oxygen Electrode, SOEC, SOFC

-

[ * ] Corresponding author, mauvy@icmcb-bordeaux.cnrs.fr DOI: 10.1002/XXXXXXXXXXX

Acknowledgments

Authors gratefully acknowledge the French Research National Agency (ANR) through "H2 and Fuel Cells program" (project FIDELHYO n°ANR-09-HPAC-005) for supporting parts of this work. We also thank Benoit Sommacal for technical assistance on electrochemical experiments.


F Martins

S Faniel

B Rosenow

M G Pala

H Sellier

S Huant

L Desplanque

X Wallart

V Bayot

B Hackens
email: benoit.hackens@uclouvain.be.

Scanning Gate Spectroscopy of transport across a Quantum Hall Nano-Island

Keywords: numbers: 73.43.Jn, 73.43.-f, 73.23.Hk

We explore transport across an ultra-small Quantum Hall Island (QHI) formed by closed quantum Hall edge states and connected to propagating edge channels through tunnel barriers. Scanning gate microscopy and scanning gate spectroscopy are used to first localize and then study a single QHI near a quantum point contact. The presence of Coulomb diamonds in the spectroscopy confirms that Coulomb blockade governs transport across the QHI. Varying the microscope tip bias as well as current bias across the device, we uncover the QHI discrete energy spectrum arising from electronic confinement and we extract estimates of the gradient of the confining potential and of the edge state velocity.

INTRODUCTION

Most peculiar properties of quantum Hall systems stem from the propagation of electrons along one-dimensional edge channels, emerging wherever a Landau level crosses the Fermi energy [START_REF] Halperin | [END_REF]. The so-called Edge States (ES), that mainly form at the borders of a two-dimensional sheet of electrons in a high perpendicular magnetic field B, provide a powerful model that describes the behavior of quantum Hall nano-devices [2]. Since scattering is topologically prohibited, ES offer a natural protection to electrons, so that they constitute ideal models of quantum wires, whose manipulation is particularly fruitful. Indeed, various device geometries can be carved from two-dimensional electron systems thanks to lithography techniques, and the position of ES within a device can then be tuned using voltages applied on metallic gates deposited on top of the device.

In this context, a strong interest recently emerged for interferometer geometries, where counterpropagating ES are brought close enough to interact, and electron loops can be formed at will. Tuning the coupling between ES leads to a large variety of situations. In open systems, i.e. when the conductance of the device σ is much larger than 2e 2 /h, electronic analogs of Mach-Zehnder [3][4][5] and Fabry-Pérot [6][7][8][9][10][11] interferometers allowed to study and control electron dephasing processes within ES and to estimate the electron phase coherence length [4,5,12]. In particular, ref. [7] used interference checkerboard patterns generated in a Fabry-Pérot geometry to determine the edge state velocity in the quantum Hall regime.

In the other extreme, σ << 2e 2 /h, Quantum Hall Islands (QHIs) created by patterned quantum dots [13] or antidots [14][15][16][17][18] lead to the observation of a fractional electric charge [18][19][20] and to the characterization of localized states' confining potential [15][16][17].

These pioneering experiments succeeded in evidencing electron interferences in model ES geometries, as well as signatures of charge tunneling through lithographically-patterned QHIs. Such phenomena can also occur in unpatterned two-dimensional electron systems: since the electron confining potential is never perfectly flat, electrons can be trapped in QHIs, pinned around potential "hills" and "dips". The contribution of these QHIs to electron transport depends on their coupling to propagating ES. It is therefore important to devise methods to explore electron transport at the local scale in such systems, and new scanning probe techniques, derived from Atomic Force Microscopy (AFM) are now used for that purpose. The microscopic picture of electron localization was particularly investigated: com-pressibility measurements on quantum Hall localized states using a scanning single electron transistor revealed deviation from the single-particle picture [21,22]. Moreover, localized states as well as the electrostatic potential confining the two-dimensional electron systems could be imaged by monitoring the charging of a moving 'bubble' of electrons created in a two-dimensional electron system [23,24]. Finally, Scanning Gate Microscopy (SGM) [25][26][27][28][29][30][31][32][33][34], directly relates the microscopic structure of a quantum Hall system to its transport properties. At the starting point of the present work is the discovery that SGM allows to precisely locate QHIs connected to propagating ES through tunnel barriers, and to decrypt the complex magnetoresistance oscillations patterns to which they give rise [35,36].

Here, we go beyond SGM and apply Scanning Gate Spectroscopy (SGS) [35,37] to access the discrete energy spectrum of an individual QHI pinned around a potential inhomogeneity.

Unexpectedly, the QHI is located near one constriction of the quantum ring rather than around the central antidot. In SGS, the microscope tip is used as a local gate whose bias tunes the energy levels inside the QHI that is coupled to propagating ES by tunneling.

Around filling factor ν = 6, the magnetoresistance of the quantum ring displays periodic oscillations. Thanks to SGM, we decrypt that they originate from Coulomb Blockade (CB) of electrons tunneling across a single ultra-small QHI. The CB interpretation is confirmed by the presence of Coulomb diamonds in the SGS spectrum. Importantly, lines parallel to the sides of Coulomb diamonds are associated with excited states arising from confinement.

Using their energy spacing, we estimate the gradient of the confining potential and the associated edge state velocity around the QHI.

EXPERIMENTAL SETUP AND SAMPLE PROPERTIES

Our experiments are carried out inside a 3 He/ 4 He dilution refrigerator at temperature T = 100 mK. The cryostat is equipped with a superconducting coil that provides a magnetic field up to 15/17 T. A home made cryogenic AFM is attached at the bottom of the mixing chamber. The movement of the tip is detected via a piezoelectric tuning fork to which a conductive cantilever is glued [35]. Using this setup, we perform measurements on a quantum ring patterned in an InGaAs/InAlAs heterostructure using e-beam lithography followed by wet etching. The two-dimensional electron gas is located 25 nm below the surface. In figure 1 With the AFM tip connected to the ground, and retracted, around ν = 6 (measured in the Hall bar), the magnetoresistance of the device, shown in figure 1(c), displays oscillations with various periods which correspond to different QHIs being successively "active" [35], i.e.

tunnel-coupled to the propagating ES. A close up of a set of periodic oscillations is shown in the inset of figure 1(c). These magnetoresistance oscillations are not related to coherent electron interferences since their amplitude is inversely proportional to temperature which is consistent with pure Coulomb blockade [35]. For the rest of our work, we focus on the orange-shaded region of figure 1(c), zoomed in figure 1(d), which displays periodic peaks with ∆B = 1/ 180 T ∼ 5.6 mT as evidenced by the fast Fourier transform displayed in figure 1(e). This magnetic field range was chosen after reviewing the full trace and picking one region where the magnetoresistance was characterized by one dominant frequency, and where the resistance minima were the closest to zero so that the edge state picture, i.e. essentially no backscattering of edge states by the constriction, was the simplest. We understand these oscillations within a Coulomb-dominated model where electrons tunnel between propagating ES through a single QHI created around a potential inhomogeneity [6]. Intuitively, this model states that a variation in the magnetic field creates an energy imbalance between the QHI and the propagating ES. This imbalance generates one CB-type oscillation per populated ES circling around the QHI per flux quantum φ 0 . In this case, the device resistance oscillates with a period [6]:

∆B = (φ 0 /A)/N * , (1)
where N * is the number of filled ES around the QHI and A is the QHI area. From equation (1), figure 1(d), and assuming that N * = N = 6, where N is the number of fully occupied ES in the bulk, we deduce that the QHI has a surface A equivalent to that of a disk with a radius r 200 nm. Equivalently to the effect of B described above, varying the tip-QHI distance also generates CB-type oscillations and isoresistance lines on figure 2(a) are indeed iso-φ lines. Variations of the visibility of the fringes are observed when the tip approaches the QHI, a typical feature of CB experiments [START_REF] Kouwenhoven | Applied Sciences[END_REF][START_REF] Beenakker | [END_REF]. Furthermore, the amplitude also varies along a single concentric fringe, most likely due to the variation of the tunneling strength through the QHI, which depends sharply on the potential landscape. In figure 2(a), we chose V tip = 2 V to make sure that N * = N = 6 during the entire scan. Otherwise, when approaching a negatively charged tip near the constrictions of the quantum ring, N * decreases and the resistance sharply increases [34], which hinders the observation of CB-type fringes. Noteworthy, the same fringes are present in both negative and positive V tip as long as N * = N , i.e. for both repulsive or attractive tip potential, respectively. Changing V tip , the fringes are simply shifted with respect to the position of the QHI. Finally, the ES model states that a complete reflection of K edge channels by a quantum point contact gives rise to a resistance shift of h e 2

1 N -K -1 N [2,34]. Using this argument [2] with N = 6 and taking into account that the amplitude of the oscillations is around 40Ω, we deduce K = 0.05, meaning that the peak conductance across the QHI is about 0.05 e 2 /h, also consistent with the tunneling regime required for CB. This also means that most of the current flows in the transmitted ES and only a small fraction is used to probe the QHI, in contrast with typical CB experiments where all the current flows through the quantum dot.

LOCAL SPECTROSCOPY OF THE QHI

A deeper understanding of the QHI's electronic structure can be reached using SGS:

positioning the tip at point α, both V tip and the current I through the device are swept.

The bias current can be converted to a voltage bias V bias across the QHI thanks to the quantized Hall resistance: V bias = h/(e 2 N )I. The plot of the differential resistance R in the (V tip , V bias ) plane is drawn in figure 3(a), where a set of narrow straight lines is superimposed Coulomb diamond, a characteristic signature of excited states [42]. The energy gap between these excited states is ∆E 380 µeV, much smaller than the Landau level spacing, ∆E LL 26.8 meV, and the Zeeman splitting, ∆E z 1.65 meV, in our system around B = 9.5 T.

These values are determined making use of ∆E LL = eB/m * , where e is the electron charge, m * = 0.041 m e is the electron effective mass in our two-dimensional electron system with respect to the free electron mass m e [43], and ∆E z = |g|µ β B, where µ β is the Bohr magneton and g 3 is the Landé g-factor in the heterostructure [44]. The QHI is thus in the quantum limit of CB defined by k B T << ∆E << e 2 /C Σ ∼ 1.6 meV obtained from figure 3(b) [START_REF] Kouwenhoven | Applied Sciences[END_REF],

which justifies the 1/T temperature dependence found previously in [35]. Assuming that the Coulomb excited states emerge as a consequence of circular confinement, we can determine an average of the derivative of the confining potential dU/dr using the relation [14,15,17]:

∆E = v/r = |dU/dr| /(e rB), (2)
where v is the ES velocity in the QHI. Taking into account that r 200 nm, we obtain |dU/dr| 1 meV/nm for the QHI formed around a potential inhomogeneity. In QHIs created around antidots etched in GaAs/AlGaAs heterostructures [14,16,17], which are known to generate soft-wall potentials, |dU/dr| was found to be around 20 µeV/nm [16], and data in [14,17] give |dU/dr| 50 µeV/nm. In the case of a GaAs quantum Hall Fabri-Pérot interferometer [7], in the high-magnetic-field limit, |dU/dr| was found to be 80 µeV/nm. 2), we extract v = 9.8 × 10 4 m/s, which is close to the lower limit of results in [7]. As v decreases with increasing B, this data copes with the larger values reported in [7] at lower B. The numerical values determined here for v and |dU/dr| constitute upper bounds as the shape of the QHI is assumed to be circular.

CONCLUSION

In conclusion, we have used SGM to locate an individual quantum Hall island and directly probed its excited states arising from confinement with SGS. We were able to confirm that Coulomb blockade governs transport and to characterize the confining potential of the QHI. Both the slope of the confining potential and the edge state velocity were estimated.

The combination of SGM and SGS techniques is therefore extremely useful to unveil the microscopic nature of charge transport inside complex nanodevices even in the quantum Hall regime, just like the combination of scanning tunneling microscopy and scanning tunneling spectroscopy was key to understand the electronic local density of states of surface nanostructures. Another advantage of the presence of the tip is the possibility to tune in situ the local electrostatic environment of the nano-device by depositing charges on its surface [46]. This way, one could envision to induce QHIs with controlled geometries.

FIG. 1 :

 1 FIG. 1: (Color online) (a) AFM topography of the quantum ring obtained at B = 9.5 T and T = 100 mK. The black bar represents 1 µm. (b) Schematic representation of our device showing a QHI connecting opposite edge channels through tunnel barriers (dotted lines). Current carrying contacts (1-2) and voltage probes (3-4) allow resistance measurements. (c) Magnetoresistance of the quantum ring (R) together with the longitudinal resistance R xx , in red, and the transverse resistance R xy , in green, of a Hall bar a next to ν = 6. In the inset we zoom a set periodic oscillations corresponding to the yellow region. (d) Close-up of the orange-shaded region in (c). (e) Fast Fourier transform of magnetoresistance (d).

  and T = 100 mK, just before SGM measurements.As sketched in figure1(b) the current is injected between ohmic contacts 1 and 2 and the voltage drop is measured between 3 and 4. Next to the ring, we patterned a Hall bar where we measure a low-T electron density and mobility of 1.3 × 10 16 m -2 and 4 m 2 /Vs, respectively. Additionally, two lateral gates visible in figure1(a) were grounded during the experiments shown here.

FIG. 2 :

 2 FIG. 2: (Color online) (a) SGM map obtained at B = 9.5 T, T = 100 mK, D tip = 50 nm and V tip = 2 V. Continuous lines indicate the position of the quantum ring whereas α marks the origin of concentric fringes. The black bar represents 1 µm. (b-c) B-dependence of 500 nm long resistance profiles over the left/right regions marked with white lines in (a), respectively, with V tip = -1 V.

  The effects of both B and tip-QHI distance along the white lines in the left and right sides of figure2(a) are illustrated in figures 2(b) and (c), respectively (note that figure2(a)was obtained with positive V tip while figure 2(b) and (c) with negative V tip ). Along the B-axis, clear oscillations are visible with a period around ∆B ∼ 6 mT in agreement with the magnetoresistance in figure1(d). For the case of a potential hill, resistance peaks should follow positive dV tip /dB slopes, i.e. decreasing B should be compensated by a tip voltage decrease in order to keep the same magnetic flux through the QHI[8,10,11]. In our case, approaching the negatively charged tip has the same effect as decreasing V tip as it corresponds to an increase of the QHI area. The slope of the fringes in figures 2(b-c) therefore supports the CB picture.

5 FIG. 3 :

 53 FIG. 3: (Color online) (a) SGS measured when placing the tip at α, in figure 2(a). (b) Numerical derivative dR/dV tip of (a) in the V tip -V bias plane. Note that each resonance in the differential resistance appears as a black and white double line. (c) High-pass-filter version of (a), where two yellow dashed lines indicate the transition between Coulomb-blockaded regions. Black dashed lines highlight Coulomb excited states.

  These results are summarized in table (I), from which we conclude that |dU/dr| scales with the carrier density of the two-dimensional electron system[45]: 1 × 10 15 m -2 [16], 2.6 × 10 15 m -2 [14, 17], 2.7 × 10 15 m -2 [7] and 1.4 × 10 16 m -2 in the present sample. In the same framework, using equation (

TABLE I :

 I Comparison between dU/dr calculated from data in the literature and extracted in this work as a function of the carrier density in the 2DES.

	[14, 17]	2.6 × 10 15	50
	[7]	2.7 × 10 15	80
	this work	1.4 × 10 16	1000

Acknowledgements F.M. and B.H. acknowledge support from Belgian FRS-FNRS. This work has been supported by FRFC grant no. 2.45003.12 and FNRS grant no. 1.5.044.07.F and by the Belgian Science Policy (Interuniversity Attraction Pole Program IAP-6/42). This work has also been supported by the PNANO 2007 program of the Agence Nationale de la Recherche (MI-CATEC project). V.B. acknowledges the award of a Chaire d'excellence by the Nanoscience Foundation in Grenoble.


P Atten
email: janusz@imp.gda.pl

Abstract

I. INTRODUCTION

HE fine dust particles emitted by industry and transportation means can contain substances harmful to human health, such as oxides of sulphur, nitric oxides, ammonia and heavy metals. The most dangerous for health are dusts with the diameter of grains below 2.5 µm (fraction called PM2.5), which can penetrate from lungs directly to blood. Therefore, in the last years in the European Union a special attention to the inspection of emission of fine dust particles of micron and submicron sizes increased. The European Parliament is preparing the new directive concerning the quality of air in the European Union [START_REF] Corbey | European Parliament resolution on the thematic strategy on air pollution[END_REF][START_REF] Krahmer | Report on the proposal for a directive of the European Parliament and of the Council on ambient air quality and cleaner air for Europe[END_REF].

The industry, in particular the heat and power industry based on coal fuel, is a major source of fine dust particle emission. For several decades the heat and power plants are equipped with filters to reduce dust emission. Most popular are electrostatic precipitators (ESPs) which are basic devices for the reduction of dust emission. The total mass collection efficiency of dust in modern ESPs is very high (above 99%), however the collection efficiency of micron and submicron dust particle is much lower (below 80%) and still unsatisfactory [START_REF] Mizuno | Electrostatic precipitation[END_REF]. It means that a large number of fine particles is emitted to the atmosphere, becoming dangerous to people and animals.

The precipitation of particles in the ESP duct depends on the dust-particle properties, electric field, electric space charge and gas flow field [START_REF] Atten | The electrohydrodynamic origin of turbulence in electrostatic precipitators[END_REF]. The primary gas flow (that entering the ESP) is disturbed by the electrohydrodynamic (EHD) secondary flow generated in the ESP. The EHD secondary flow causes considerable changes and turbulences in the primary flow structures. Influence of the EHD secondary flow on the ESP collection efficiency has been debated for decades. To elucidate this influence many experimental [START_REF] Yamamoto | Electrohydrodynamics in an electrostatic precipitator[END_REF][START_REF] Leonard | An experimental study of the electrohydrodynamic flow in electrostatic precipitators[END_REF][START_REF] Podliński | Electrohydro-dynamic gas flow in a positive polarity wire-plate electrostatic precipitator and the related dust particle collection efficiency[END_REF][START_REF] Podliński | EHD flow in a wide electrode spacing spike-plate electrostatic precipitator under positive polarity[END_REF][START_REF] Podliński | ESP performance for various dust densities[END_REF][START_REF] Podliński | EHD flow patterns in narrow and wide ESPs measured by 3D PIV method[END_REF][START_REF] Atten | Turbulence generation by charged fine particles in electrostatic precipitators[END_REF] and numerical [START_REF] Kogelschatz | Advanced computational tools for electrostatic precipitators[END_REF][START_REF] Brocilo | Numerical modelling of wire-pipe electrostatic precipitator for control of fine particulates[END_REF][START_REF] Fujishima | Numerical simulation of three-dimensional electrohydrodynamics of spikedelectrode electrostatic precipitators[END_REF] investigations were carried out. Some of the results showed that the EHD secondary flow and corresponding gas flow turbulences are important for collecting fine dust particles in ESPs [START_REF] Atten | Turbulence generation by charged fine particles in electrostatic precipitators[END_REF][START_REF] Kogelschatz | Advanced computational tools for electrostatic precipitators[END_REF].

In this paper, the results of 3-dimensional Particle Image Velocimetry (3D PIV) [START_REF] Raffel | Particle Image Velocimetry, A practical guide[END_REF] measurements of the flow velocity fields in a relatively wide wire-plate type ESP are presented. The measurements were carried out in the observation midplane along the ESP.

II. EXPERIMENT

The apparatus used in this experiment consisted of an ESP, DC high voltage supply and a standard 3D Particle Image Velocimetry (PIV) equipment for the flow velocity field measurement (Fig. 1). Instantaneous and time-averaged velocity fields in a wide electrostatic precipitator

T

The wide-type ESP used in this work was an acrylic parallelepiped 1000 mm long, 200 mm wide and 100 mm high (width:height = 2). The electrical electrode set consisted of a wire discharge electrode and two collecting plate electrodes. The wire electrode (diameter 1 mm, length 200 mm) was placed perpendicularly to the main flow, in the middle of the ESP between the plate electrodes, which were placed on the top and bottom of the ESP. The width of each plate electrodes was 200 mm, while the plate-to-plate electrode spacing was 100 mm. A flow homogenizer was placed before the ESP inlet.

Air flow seeded with a cigarette smoke (majority of smoke particles lower than 1 µm in dry air) was blown along the reactor duct with an average velocity (from 0 to 0.9 m/s). The negative DC voltage of up to 28 kV was applied to the wire electrode through a 10 MΩ resistor, while the plate electrodes were grounded. The averaged discharge current was up to 150 µA.

The standard 3D PIV equipment consisted of a twin second harmonic Nd-YAG laser system (λ = 532 nm), imaging optics (cylindrical telescope), two CCD cameras and a PC computer with Dantec FlowManager software.

The 3D PIV measurements were carried out in a plane placed perpendicularly to both electrodes, at the wire electrode midpoint. The observation area (the area of the laser sheet "seen" by both CCD cameras) covered a region between the plate electrodes, ranging from 20 mm towards the flow upstream direction to 205 mm towards the flow downstream direction, when measured from the wire electrode (Fig. 1).

The results obtained from 3D PIV measurements are presented in this paper among other things as vector maps and colour maps. The vector maps (called flow velocity fields) show velocity x-and y-component. The colour maps show velocity z-component.

III. RESULTS

Figs. 23456show the results of the 3D PIV measurements in the ESP when no voltage was applied. The Reynolds number was Re = V × L / ν = 5730 [START_REF]Recommended international standard for dimensionless parameters used in electrohydrodynamics[END_REF]. The parameters used to calculate Re were: the primary flow average velocity V = 0.9 m/s, the characteristic length (plate-plate distance) L = 0.1 m, and the air kinematic viscosity ν = 1.57 × 10 -5 m 2 /s). Fig. 2 shows a typical single image of the flow in the ESP taken by the CCD camera. The dust particles scattering the laser light are visible as bright points in the image. When no voltage was applied, the submicron dust particles followed the gas main flow and, in this case, the measured velocity field of the particles corresponds to the gas flow velocity field. Figs. 3 and4 show the particle flow velocity field resulted from averaging of 100 PIV images, which means that the velocity field is time-averaged. Based on the measured velocity fields, the velocity standard deviation for the x-component (Fig. 5) and the z-component (Fig. 6) was determined. It is clearly seen from the presented figures that the flow was laminar. The standard deviation of the velocity x-component was very low (lower than 0.035 m/s). Small disturbances of the flow were found in the wake behind the wire electrode. The average velocity z-component was very low (lower than 0.05 m/s in the + and -z direction). Its standard deviation was very low (Figs. 4 and6). It means that the flow was practically 2-dimensional in the observation area when no voltage was applied.

It is worth mentioning that the flow velocity patterns measured for the primary flow average velocity of 0.2 m/s and 0.6 m/s (not shown in this paper), when no voltage was applied, were very similar to that for the primary flow average velocity of 0.9 m/s.

When a high voltage was applied to the wire electrode, the electric forces exerted by the corona discharge and electric field induce a considerable EHD secondary flow of the gas which altered significantly the primary laminar flow. On another hand, the electric force exerted on each individual dust particle with charge q p induces a drift of the particle with respect to the suspending air. Therefore, the net motion of the charged dust particles has two components, one due to the gas flow and the other, due to the electric force q p E (the particle drift velocity), where E is the electric field. For submicron particles, except just around the wire electrode (where E is very high), the particle drift velocity is much lower than the gas velocity [START_REF] Atten | The electrohydrodynamic origin of turbulence in electrostatic precipitators[END_REF]. Therefore, we can assume that also the charged dust particles follow the gas flow. Hence, the measured by us particle flow velocity fields represent also the gas flow velocity fields in the ESP, except for the nearwire region.

Figs. 7-15 show the time-averaged results of the 3D PIV measurements in the ESP when negative voltage of 28 kV was applied. The average total discharge current was 150 µA. At this current, the EHD number, which is related to the electric forces, was 5 × 10 7 . The EHD number was calculated using a formula: Ehd = I × L 3 / (ν 2 × ρ × µ i × A) [START_REF]Recommended international standard for dimensionless parameters used in electrohydrodynamics[END_REF], with the parameters as follows: I = 150 µA (the average total discharge current), L = 0.1 m (the distance between the collecting electrodes), ν = 1.57 × 10 -5 m 2 /s (the air kinematic viscosity), ρ = 1.205 kg/m 3 (the air density), A = 0.04 m 2 (the discharge area) and µ i = 2.55 × 10 -4 m 2 /Vs (the ion mobility).

The particle flow velocity field and the corresponding flow streamlines in the ESP for 28 kV and 0.9 m/s are presented in Figs. 789. The Reynolds number was Re = 5730, the EHD number was 5 × 10 7 , and the ratio of the EHD number to the Reynolds number squared was 1.5 (Ehd/Re 2 describes the ratio of the electric forces to the inertial force). For this relatively low Ehd/Re 2 ratio the influence of the discharge on the dust particle trajectories is mostly seen in the discharge region, i.e. in a radius of about 50 mm from the wire electrode. As can be seen in Figs. 7 and8, the particle trajectories are bent towards the plate electrodes in this region. The average velocity z-component (Fig. 9) in almost whole observation Fig. 7. Averaged flow velocity field in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.9 m/s. Fig. 8. Flow streamlines in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.9 m/s. Fig. 9. Averaged flow velocity z-component in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.9 m/s. area was very low (lower than 0.05 m/s), increasing near the wire electrode and plate electrodes up to 0.15 m/s.

When the primary flow average velocity decreased to 0.6 m/s (Figs. [START_REF] Podliński | EHD flow patterns in narrow and wide ESPs measured by 3D PIV method[END_REF][START_REF] Atten | Turbulence generation by charged fine particles in electrostatic precipitators[END_REF][START_REF] Kogelschatz | Advanced computational tools for electrostatic precipitators[END_REF], the Reynolds number decreased to 3820 and the ratio Ehd/Re 2 increased to 3.4. Under these conditions the influence of the discharge on the dust particle motion is a stronger than that at 0.9 m/s (Figs. 789). The particle trajectories bent stronger towards the collecting electrodes. The velocity y-component increased in the discharge region. The average velocity z-component is still very low (lower than 0.05 m/s). For a still lower primary flow average velocity (0.2 m/s) (Figs. [START_REF] Brocilo | Numerical modelling of wire-pipe electrostatic precipitator for control of fine particulates[END_REF][START_REF] Fujishima | Numerical simulation of three-dimensional electrohydrodynamics of spikedelectrode electrostatic precipitators[END_REF][START_REF] Raffel | Particle Image Velocimetry, A practical guide[END_REF], the Reynolds number decreased to 1270 and the Ehd/Re 2 ratio increased to 30.6 (the electric forces clearly dominate over the inertial force). In consequence, the EHD secondary flow significantly changed the average velocity field in the majority of observation area. 100 mm downstream from the wire electrode a pair of vortices occurred. As a result the particle flowed in the opposite direction to the primary flow direction in the ESP duct centre. The average velocity z-component is still very low (lower than 0.05 m/s) and only near the electrodes it reaches the values up to 0.15 m/s. As it can be seen from Figs. 7-15, the increase in Ehd/Re 2 ratio caused strong disturbances of the average velocity field, whereas the average velocity z-component was not much disturbed by the discharge and maintained almost constant small value. It means that the time-averaged flow velocity field measured in the ESP midplane as shown in Fig. 1, is almost 2-dimensional. However, we can expect that the time-averaged velocity field in the observation planes near the ESP walls are 3-dimensional due to the end-walls effect. From the time-averaged results presented above one can conclude, that the flow in the ESP is 2-dimensional. However, our analysis of the instantaneous flow velocity fields measured by us and presented below show that the flow in the ESP is 3 dimensional when short time intervals are considered.

The instantaneous images of the particle flow and corresponding instantaneous flow velocity fields measured in the ESP for a negative voltage of 28 kV are presented in Figs. [START_REF]Recommended international standard for dimensionless parameters used in electrohydrodynamics[END_REF]-24.

As it can be seen from instantaneous images shown in Fig. 16, voltage 28 kV, primary flow average velocity 0.9 m/s (Ehd/Re 2 1.5), the Karman vortex structure occurred just behind the wire electrode. However, this structure is unstable and it is scattered by irregular flow disturbances starting at the latest 40 mm downstream from the wire electrode. The corresponding instantaneous flow velocity fields (Fig. 17) as well as velocity z-component (Fig. 18) also show this irregular disturbances. In the downstream from the wire electrode quite distinct instabilities occurs for the flow velocity x-and y-component. The velocity z-component reaches values up to 0.3 m/s and even more near the plate electrodes. This means that the instantaneous velocity z-component is higher than the time-averaged one. At a lower primary flow average velocity of 0.6 m/s (Ehd/Re 2 3.4) the particle flow disturbances, caused by the electric force, were stronger than those for the 0.9 m/s. The Karman vortex structure attempted to arise behind the wire electrode, but it was immediately scattered by irregular flow disturbances (see Figs. 19 a-c). At these conditions also the particle flow instabilities occurred near the plate electrodes. As it can be seen in corresponding instantaneous flow velocity fields (Figs. 20 a-c) irregular vortices arisen near the plate electrodes before the wire electrode. These vortices were scattered and floated by the primary flow. The velocity z-component fields (Fig. 21) are similar to those presented in Fig. 18 The instantaneous images of the particle flow and the corresponding instantaneous flow velocity fields measured in the ESP for the primary flow average velocity of 0.2 m/s (the Ehd/Re 2 ratio was 30.6) are presented in Figs. 222324. One can see that the particle flow was very turbulent in the whole observation area. Any regular structure cannot be seen in the instantaneous images presented in Figs. 22 a-c. Also the flow velocity fields (Figs. 23 and24) suggest that the particle flow in the ESP is turbulent and 3 dimensional when short time-interval are considered. However, some regularity in the particle flow patterns can be found from Figs. 23a-c. 50 mm downstream from the wire electrode and farther in the downstream, the velocity x-component near the plate electrodes reaches values up to 1 m/s (much higher than the primary flow average velocity). At the same time, the velocity x-component in the ESP duct centre reaches much lower values. At about 100 mm downstream from the wire electrode the velocity x-component becomes negative, i.e. the particles flow in the opposite direction to the primary flow direction. This counter-flow was already shown in the timeaveraged results presented in Figs. 13 and14. At the primary flow velocity of 0.2 m/s, the flow velocity z-component (Fig. 24) exhibit also very irregular structures, and with maximum velocity amplitude of about 0.45 m/s (i.e. higher than those at the primary flow velocity of 0.6 m/s and 0.9 m/s). The standard deviations (SDs) of velocity z-component for the primary flow average velocities of 0.9 m/s, 0.6 m/s and 0.2 m/s are presented in Figs. 25, 26 and 27, respectively. As it can be seen from these figures, the velocity z-component SDs of reaches highest values in the wake behind the wire electrode. The SDs are higher for the primary flow velocity of 0.9 m/s (up to 0.3 m/s) than for 0.2 m/s (up to 0.25 m/s). However, at 0.9 m/s the particle flow in the ESP seems to be more stable in the majority of the observation area, and corresponding SDs of the velocity z-component is lower than 0.1 m/s. In comparison, at the primary flow velocity of 0.6 m/s and 0.2 m/s, the SDs of the velocity z-component reaches values up to 0.15 m/s and 0.2 m/s, respectively.

IV. CONCLUSION

In this paper, the 3D PIV velocity field measurements in the midplane set along the ESP duct are presented. The obtained results showed that the time-averaged flow velocity in the z-direction (i.e. perpendicular to the primary flow direction) is low (lower than 0.05 m/s). This confirms the previous time-averaged results [START_REF] Podliński | EHD flow patterns in narrow and wide ESPs measured by 3D PIV method[END_REF] indicating that the mean flow in the wide ESP is almost two-dimensional in terms of time-averaged observations. However, the analysis of instantaneous EHD flow images and velocity fields showed that the EHD flow is very turbulent with a relatively high instantaneous velocity z-component (up to 0.45 m/s). The high level of the velocity z-component standard deviation, calculated from the instantaneous velocity z-component fields, confirmed this observation. We expect that the flow turbulences are higher near the end-walls of the ESP. These results show that even in wide ESPs the EHD flow cannot be assumed to be 2-dimensional when its short-time flow behaviour is considered.

-

  This work was aimed at clarifying whether the electrohydrodynamic (EHD) flow in a relatively wide electrostatic precipitator (ESP) (width:height = 2) is 2-or 3dimensional (3D). The previous our measurements of 3D timeaveraged flow velocity fields suggested that the flow in the ESP duct centre is almost 2-dimensional. In this paper we present both the 3D instantaneous and time-averaged flow velocity fields in a relatively wide ESP (width:height = 2). The ESP used in this work was an acrylic parallelepiped with a negatively polarized wire discharge electrode and two plate collecting electrodes. The velocity field was measured using Particle Image Velocimetry in the observation midplane along the ESP. Index Terms -electrohydrodynamic flow, EHD, electrostatic precipitator, ESP, Particle Image Velocimetry.

Fig. 1 .

 1 Fig. 1. Experimental set-up for 3D-PIV flow velocity field measurements in ESP.

Fig. 2 .

 2 Fig. 2. Instantaneous image of the flow in the ESP when no voltage was applied. The primary flow average velocity was 0.9 m/s. Exposure time: 6 ns.

Fig. 3 .

 3 Fig. 3. Averaged flow velocity field in the ESP when no voltage was applied. The primary flow average velocity was 0.9 m/s.

Fig. 4 .

 4 Fig. 4. Averaged flow velocity z-component in the ESP when no voltage was applied. The primary flow average velocity was 0.9 m/s.

Fig. 5 .

 5 Fig. 5. Standard deviation of velocity x-component in the ESP when no voltage was applied. The primary flow average velocity was 0.9 m/s.

Fig. 6 .

 6 Fig. 6. Standard deviation of velocity z-component in the ESP when no voltage was applied. The primary flow average velocity was 0.9 m/s.

Fig. 10 .

 10 Fig. 10. Averaged flow velocity field in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.6 m/s.

Fig. 11 .

 11 Fig. 11. Flow streamlines in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.6 m/s.

Fig. 12 .

 12 Fig. 12. Averaged flow velocity z-component in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.6 m/s.

Fig. 13 .

 13 Fig. 13. Averaged flow velocity field in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.2 m/s.

Fig. 14 .

 14 Fig. 14. Flow streamlines in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.2 m/s.

Fig. 16 .

 16 Fig. 16. Three instantaneous images (a, b and c) of the particle flow in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.9 m/s. Exposure time: 6 ns.

Fig. 17 .

 17 Fig. 17. Three instantaneous flow velocity fields (a, b and c) in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.9 m/s.

Fig. 18 .

 18 Fig. 18. Three instantaneous flow velocity z-component fields (a, b, c) in the ESP. Applied voltage: -28 kV. Primary flow average velocity: 0.9 m/s.

  . The flow velocity z-component structures are irregular. The velocity z-component reached values up to 0.35 m/s and more near the plate electrodes.

Fig. 19 .

 19 Fig. 19. Three instantaneous images (a, b and c) of the particle flow in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.6 m/s. Exposure time: 6 ns.

Fig. 20 .

 20 Fig. 20. Three instantaneous flow velocity fields (a, b and c) in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.6 m/s.

Fig. 21 .

 21 Fig. 21. Three instantaneous flow velocity z-component fields (a, b, c) in the ESP. Applied voltage: -28 kV. Primary flow average velocity: 0.6 m/s.

Fig. 22 .

 22 Fig. 22. Three instantaneous images (a, b and c) of the particle flow in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.2 m/s. Exposure time: 6 ns.

Fig. 23 .

 23 Fig. 23. Three instantaneous flow velocity fields (a, b and c) in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.2 m/s.

Fig. 24 .

 24 Fig. 24. Three instantaneous flow velocity z-component fields (a, b, c) in the ESP. Applied voltage: -28 kV. Primary flow average velocity: 0.2 m/s.

Fig. 25 .

 25 Fig. 25. Standard deviation of velocity z-component in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.9 m/s.

Fig. 26 .

 26 Fig. 26. Standard deviation of velocity z-component in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.6 m/s.

Fig. 27 .

 27 Fig. 27. Standard deviation of velocity z-component in the ESP. The applied voltage was -28 kV. The primary flow average velocity was 0.2 m/s.

6 ème Conférence de la Société Française d'Electrostatique, Paris & Gif-sur-Yvette, 8-9 juillet 2008, ISBN : 978-2-9505432-6-4, pp. 142-149 (2008)

	Janusz Podliński, Pierre Atten, Jerzy Mizeraczyk

This work was supported in part by the Polish Ministry of Science under Grant 1857/B/T02/2007/33. J. Podliński is with the Centre for Plasma and Laser Engineering, The ), Fiszera 14, 80-952