Mathematical Model of an Inductive Measuring Cell for Contactless Conductometry

TL;DR

This paper presents a mathematical model of an inductive conductometric cell that accounts for sample-coil capacity and eddy currents, enabling impedance calculation for low conductive samples without complex PDE solving.

Contribution

It introduces a new mathematical model for inductive conductometric cells that simplifies impedance calculation and aids in device design and plasma studies.

Findings

Model accurately predicts impedance for various sample properties.

Experimental verification confirms model validity.

Design considerations for inductive conductometers are discussed.

Abstract

A research of inductive conductometric cell is presented. An equivalent circuit and a mathematical model of inductive cell are given in the article. The model takes into account sample-coil capacity (i.e. capacity formed by the coil and the sample under study) and eddy currents. It is sample-coil capacity that makes inductive cell applicable for measurement of electrical conductivity of low conductive samples (specific conductance is less than 1S/m). The model can be used to calculate impedance of inductive cell for different characteristics of sample, materials and dimensions of cell without numerical solving of partial differential equations. Results of numerical simulation were verified by experiment for several devices with inductive cell. Some features that an engineer has to hold in mind while designing a conductometer based on inductive cell are discussed. Presented model can be useful for those who study inductively coupled plasma.