# Investigation of the Partial Permittivity of Rigid Polyurethane Foams by a Circular One-Side-Access Capacitive Sensor

## TL;DR

This paper presents a novel experimental study on the partial permittivity of rigid polyurethane foams using a circular one-side-access capacitive sensor with three electrodes.

## Contribution

The study introduces an original method to determine model functions for partial permittivity data and identifies the highest rate of change in permittivity.

## Key findings

- The highest rate of change in partial permittivity occurs at the inter-electrode zone.
- The rate of change depends nonlinearly on density and true permittivity, approximated by second-order polynomials.
- The overall permittivity change pattern matches the theoretical surface charge density distribution curve for a two-electrode sensor.

## Abstract

The determination of the surface charge density distribution and the transcapacitance of capacitive one-side-access circular sensors with three electrodes on the active surface remains problematic both theoretically and experimentally. To provide an input, a novel experimental study was carried out on the partial permittivity of rigid PU foams by means of a capacitive circular OSA sensor with three electrodes on the active surface. An original and effective method was elaborated in order to determine the model functions of the obtained experimental data of the partial permittivity. A numerical estimation for the rate of change in the partial permittivity was made and the highest rate of change was determined. It was identified that the highest rate of change takes place at the inter-electrode zone and depends on the density and the true permittivity in a nonlinear mode, approximated with second-order polynomials. The overall character of the rate of change in the partial permittivity in the dependence of the radius of the covered area was found to be comparable to that of the surface charge density distribution curve, estimated theoretically for a circular two-electrode OSA sensor. The experimental results on the partial permittivity can be useful in the performance evaluation and design of the optimal proportions of capacitive circular OSA sensors, as well as in the verification of the corresponding mathematical models.