I am confusing in calculating permittivity of the fluid. Permittivity differs from one fluid to another.
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 permittivity factor of a dielectric medium can be expressed as a ration of capacity, $C_x$ of capacitor, which space between and around the electrodes is completely filled with the medium, to capacity $C_0$ of the same electrodes in vacuum.
I know and measured $C_0$ value. I am facing problems with calculating $C_x$ 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 AC signal (125 KHz) to the capacitive sensor which is filled with some fluid, in response I am getting AC 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 $C_x$ value from above known values ($V_g$ (input), $V_r$ (output), $\phi$ (phase difference)).