# 2D Example: Electro Static application tutorial

## Foreword

This paragraph is a summary of cases studied in detail in the 2D example: "Electro Static application tutorial".

The files relating to the studied cases, are accessible via the Supervisor "Open Example" context.

## Study carried out

The study proposed in the 2D tutorial "Electro Static application tutorial" is the study of a cylindrical cell for the measurement of resistivity and permittivity of liquids.

## Studied device

The device to be analyzed, presented in the figure below, consists of:

• two circular upper and lower electrodes
• a guard ring
• two glass spacers
• one is situated between the upper electrode and the guard ring
• another is situated between the guard ring and the lower electrode

## Operating principle

The analyzed cell is used to measure the resistivity and permittivity of liquids. The testing liquid is placed between two plate electrodes to form a capacitor. The measured capacitance is then used to calculate permittivity. When simply measuring the dielectric material between two electrodes, stray capacitance or edge capacitance is formed on the edges of the electrodes and consequently the measured capacitance is larger than the capacitance of the dielectric material. A solution to the measurement error caused by edge capacitance is to use the guard electrode. The guard electrode absorbs the electric field at the edge and the capacitance that is measured between the electrodes is only composed of the current that flows through the dielectric material.

## Studied cases

Three cases are carried out with the Electro Static application:

• case 1: static study (mono value), a testing liquid is pure water
• case 2: multi-parametric static study (multi values)
• case 3: static study (mono value), a testing liquid is mineral oil

## Case 1

The first case is a static study (mono value)

The testing liquid is pure water.

## Case 2

The second case is a multi-parametric static study (multi values)

In this case, the influence of a physical parameter and two geometric parameters is studied.

The physical parameter is the relative permittivity of the testing liquid (pure water) varying between 10 and 120.

The first geometric parameter is the curvature radius of the rounded corners of the electrodes varying between 0.6 mm and 0.8 mm.

The second geometric parameter is the height of the upper glass spacer. The height of the upper spacer decreases when the value of the curvature radius increases.

## Case 3

The third case is a static study (mono value)

This study differs from case 1 only by the nature of the testing material.

The testing liquid is mineral oil.