How to calculate permittivity of a fluid
One approach is to compare it with a known capacitor C1 in a bridge. If you will excuse very crude ASCII circuits...

Either of the following combinations would be suitable

AC --- C1 --- V1 --- CX --- Gnd
|----- R1 --- V2 --- RX --- Gnd


or

AC --- RX --- V1 --- CX --- Gnd
|----- R1 --- V2 --- C1 --- Gnd


C1 should be about the centre of the expected permittivity range times C0.

In either case, adjust RX until V1=V2 (the output of a differential amplifier calculating V2-V1 is 0) at which point RX/R1 = CX/C1 giving you an easy reading of permittivity.

It will also tell you if the medium is lossy (e.g. if the fluid is conductive to some extent). In that case, there is no zero on V2-V1, but just a minimum, where V2-V1 is 90 degrees out of phase with Vin. The magnitude of the out-of-phase component gives some estimate of the loss.