how to calculate the electric relative permittivity of fluid or medium.

[veerubiji]

Hi,
I am confusing in calculating permitivity of the fluid. Permittivity differs from one fluid to another.
Ɛ=ƐrƐ0.
Since it is an electrical property combined with an electrical capacity, it is possible to measure it indirectly in a capacitive sensor. I have used capacitive sensor to measure electric relative permitivity factor of a dielectric medium can be expressed as a ration of capacity, Cx of capacitor, which space between and around the electrodes is completely filled with the medium, to capacity C0 of the same electrodes in vacuum.
Ɛr= Cx/C0.
I know and measured C0 value. I am facing problems with calculating Cx of capacitor, which space between and around the electrodes is completely filled with the medium.
I am using method as described below.
I am applying an A.C signal (125 KHz) to the capacitive sensor which is filled with some fluid, in response I am getting A.C signal with some phase difference. I am able to measure the amplitudes of sensor input, sensor output signals and their phase difference also. I am trying to make equation that will give Cx value from above known values (Vg (input), Vr (output), ᶲ (phase difference)).
Any help appreciated. Please help me.

[Hero999]

I would have thought it would be easier to measure the RC time constant, rather than phase difference. It's as simple as building a relaxation oscillator with Cx + the parasitics as the capacitor being tested and measuring the frequency which will be inversely proportional to the capacitance.