electro-quasi static with high frequency implementing for RC circuit

Hi,

Let say if I have an insulator pipe with the conductive liquid inside it.
Then,I plan to attach one pair of rectangular metal electrodes on the periphery of the insulator pipe wall.
By doing this, I can assuming that the system will have two coupling capacitors of C1 and C2.
It is due to the coupling between the metal electrode and conductive liquid for each side of the cross section of the insulator pipe.
The detail schematic figure is illustrated here:
https://obrazki.elektroda.pl/7078315900_1454776844.png

Thus, from that figure, I can assume the total impedance, Z = Rliq + Xct, where Xct is the total reactance of C1 and C2

The purpose of the system is to obtain the conductivity information of the conductive liquid inside the pipe.

From my point of view, if I give the high enough frequency to the system to make the reactance part small; then I can ignore the reactance part and can get the information of the internal resistance of the liquid and relate it with conductivity information.

Also,if I want to get the value of Z or R in my case, based on ohm's law; I should give the voltage source instead of the current source to one part of the metal electrode. If not the current cannot flow or penetrate through to the insulator pipe. Then, the current can be measured at another metal electrode. Lastly, the value of R can be determined.

However, I believed that there will have the electromagnetic theorem behind this.
From my reading, I think the suitable electric field that can be used is the electro-quasi static field.
The reason is due to the current that flow from the source through the insulator pipe and conductive liquid is depending on the time.

But, if referring to the electro-quasi static field;
https://obrazki.elektroda.pl/2907048300_1454776886.png
the implementation of the high frequency is look likes will made the system has the capacitive (based on the permittivity value) behavior and mask the resistive (based on the conductivity value) behaviour.


Hence, I am doubt whether by implementing high frequency, does the conductivity of the conductive liquid can be measured?or does my understanding on the electro-quasi static field is the correct electric field that can be used to describe the electic field distribution inside the system?

An important problem not considered in your post is that that impedance of the liquid will be generally frequency dependent. So you don't measure a "conductivity" corresponding to the DC resistance but a complex impedance varying over frequency. Details depend on the chemical nature of the liquid, e.g. if the conductance is produced by ions, if it's polar or non-polar, etc.

From your diagram it appears that the capacitors C1 and C2 are formed by the end caps of the pipe. The electrodes are on the outside of the disk (end caps).

1. You can consider that there is only one capacitor with a composite dielectric; the solution is going to act as a dielectric.
2. You can also assume that there are two capacitors in series with a conducting liquid in between.

The conductivity of liquids is measured in the same way. Although metal electrodes are dipped in the solution, no faradic current flows if the applied potential is small.

If the applied potential is small, there is an electic double layer at and near the electrode that acts as a capacitor (electrolytic capacitors are made in a very similar fashion).

If we apply AC potential, still small (say less than 200 mV) enough not to cause electrolysis, current will flow (displacement current) that will give you the conductivity of the solution.

This conductivity is independent of the applied frequency (till several MHz) and is useful in various electrochemical studies (fuel cells etc)

In solution the current is carried by ions that are several thousand times heavier than electron and hence they move slowly. At high frequency, dispersion effects take place and conductance becomes frequency dependent (Onsager theory).

Conductivities are generally measured at 1000Hz or at 10kHz.

For organic liquids (non-ionic) there is little interest to measure conductivity. We simply measure their dielectric properties. The dielectric properties too will show dispersion at high frequencies.

Hi

Ok.thank you for replying.

Does it is possible if i want to concern only on the conductivity of the complex impedance ?
Also, it is possible to assume the system as the RC series circuit?

This question could be similar to exploring strategies for fluid level measurement. Besides using capacitive effect, you can try inductive effect. Since you specify the liquid is conductive, then eddy currents might play a part. Perhaps a long aircoil inductor mounted next to the pipe? You send different frequencies through it?

Besides advice given in the other posts, you may be able to find internet articles about fluid level measurement, with concepts that might be adapted to your project.