# Possible Limitations of the Particle Image Velocimetry Method in the Presence of Strong Electric Fields

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}), which acts as a larger grounded electrode, and of thin copper wire with a radius of 0.04 mm stretched between glass insulating rods parallel to the larger electrode in 30 mm distance; see Figure 1. This wire acts as a smaller electrode connected to high DC voltage.

#### 2.1. Analysis of Forces

_{P}is tracer particle density, R represents its radius, v is the flow velocity, η

_{G}is the dynamic viscosity of the flowing medium and a is the characteristic dimension of the obstacles. In our experiment, the Stokes number Stk was expected to be in the order of 10

^{−4}. This value is much lower than one, and therefore, the particles would follow the flow closely.

^{5}–10

^{6}m·s

^{−2}; therefore, we could consider an immediate response of the particle to the drag force. Thus, the Basset–Boussinesq–Oseen equation did not have to be used, because the problem could be described sufficiently by simple aerodynamic drag force.

#### 2.1.1. Aerodynamic Drag

_{D}affecting the particles is described by the following drag equation:

^{−3}. In preliminary test measurements with the constant temperature anemometric (CTA) probe TESTO 425, close to the grounded wire mesh (with a voltage of 14 kV), the results indicated an oriented airflow with the velocity ca. 1.4 ± 0.1 m·s

^{−1}. For these values, we obtained the following drag force: ${F}_{D}=4.7\xb7{10}^{-11}$ N.

_{D}can only be in the order of 10

^{−11}N or 10

^{−10}N.

#### 2.1.2. Coulomb Forces

#### 2.1.3. Dielectrophoretic Force

_{DEF}affecting a spherical electroneutral particle, with radius R and relative permittivity ε

_{p}, can be described by the following formula [12]:

_{m}is the relative permittivity of the medium surrounding the particle, ε

_{0}is the permittivity of vacuum, and $\overrightarrow{E}$ is the electric field strength. The force acts in the direction of the electric field gradient, which, in our case, was from the grounded wire mesh electrode towards the high voltage electrode. This, in essence, means that dielectrophoretic force acts against the airflow generated by the motion of ions.

^{8}. The area closer to the electrode was in our experiment insignificant because we examined the macroscopic character of the airflow between the electrodes. Therefore, the maximum value of dielectrophoretic force F

_{DEF}was considered in the order of 10

^{−19}N.

#### 2.1.4. Magnetic Forces

_{M}affecting a particle with charge Q in motion is described by the following formula:

_{0}is the permeability of the vacuum, d is the distance from the path, and I is the current caused by the charged particles travelling between the electrodes.

_{M}in our experiment in the order of 10

^{−22}N. Additionally, the direction of the magnetic force is perpendicular to the motion of the charged particles, and therefore, the only effect on the flow this force might have is a slight rotational effect.

## 3. Results

^{−1}. This corresponds with the value measured by the CTA probe (TESTO 425). It is also observed that there is no significant discontinuity in the velocity values above and below the grounded larger electrode.

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Graphic representation of $\nabla {|\overrightarrow{E}|}^{2}$ in relation to the distance from the grounded wire mesh electrode along the shortest path between the electrodes for the voltage 14 kV.

**Figure 4.**Scalar map of velocities obtained using PIV method examining the airflow between the electrodes for the voltage of 14 kV.

**Figure 5.**Vector map of velocities obtained using the PIV method to examine the airflow between the electrodes for the voltage of 14 kV.

**Figure 7.**The magnitude of velocity vector v (black) and their respective uncertainties U (red) and V (green) are 10 mm below the grounded wire mesh electrode (

**left**) and 10 mm above the grounded wire mesh electrode (

**right**).

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**MDPI and ACS Style**

Malík, M.; Primas, J.; Schovanec, P.; Novák, J.; Pokorný, P.; Sanetrník, F.
Possible Limitations of the Particle Image Velocimetry Method in the Presence of Strong Electric Fields. *Processes* **2021**, *9*, 1790.
https://doi.org/10.3390/pr9101790

**AMA Style**

Malík M, Primas J, Schovanec P, Novák J, Pokorný P, Sanetrník F.
Possible Limitations of the Particle Image Velocimetry Method in the Presence of Strong Electric Fields. *Processes*. 2021; 9(10):1790.
https://doi.org/10.3390/pr9101790

**Chicago/Turabian Style**

Malík, Michal, Jiří Primas, Petr Schovanec, Josef Novák, Pavel Pokorný, and Filip Sanetrník.
2021. "Possible Limitations of the Particle Image Velocimetry Method in the Presence of Strong Electric Fields" *Processes* 9, no. 10: 1790.
https://doi.org/10.3390/pr9101790