So you're doing... what? A one-port and measuring its impedance relative to a baseline? A two-port and measuring its transmittance and reflectance?
I was thinking 2 port, the concept at the most basic level is the more conductive the fluid, the stronger the signal amplitude at the receive coil, its acting like a single turn between 2 separate toroid transformer cores, when its poor at conducting it cannot carry as much power and the RX coils load sees a smaller signal.
This was where i thought using a current mode output amplifer for the TX coil would help, as it would remove the resistance of the coil, and just be amp-turns,
I was planning to measure both the output signal amplitude and the received with AD8307 power detectors, as they can work down to 10KHz with capacitor sizes that are still easy to get in COG capacitors. and as a feature creep option using an AD8302 for phase recovery if it was needed to compensate the amplitude. this however is far from being set in stone.
For the antennas as I only cared about magnetic induction and not electrostatic, I am thinking the coils would need electrostatic screening, to reduce the measurement to just magnetic coupling of the induced current. however I am not sure this is required,
As for design, what kinds of liquids? Electrolytic solutions? Liquid metals? What temperature range? (If temp is different from the reference coil -- a reference based method is going to be useless!) What do you estimate the signal strength to be? Can you design a coil that delivers a stronger signal (greater sensitivity of \$\Delta Z\$ to liquid conductivity)? Why do you suspect it should be toroidal? Should it have any other features, like low/minimal external field? (Toroidal windings have the upside of being more-or-less self-shielded.)
The liquid would be Ionic solutions so essentially electrolytic in both water and solvents, temperature range from -70C to +180C, and pH over most of the spectrum, and both coils would be present in the fluid with at least 25cm immersed on all sides, so they will be at the same temperature. in my head this should also remove the issue with the cores changing over temperature, but i suspect i am wrong.
The signal strength is whatever it needs to be at this point, so far testing has been using a +-10mA AC source with a compliance up to 70V. but resonances and dips at various points are a problem.
The reason I am leaning towards toroidal is that it needs to induce a signal in the fluid, normal conductance is measured with a 4 wire setup with conductive probes immersed into the water. an AC current applied and the voltage measured, the toroidal approach generates that current but with no contact to the fluid required.
Also, what about chemical sensitivity? Is it okay to use boring old hookup wire, or enameled magnet wire? Does it need to be encased in Teflon, or glass? Exposed to vacuum and plasma?
It will be encased in teflon, between the 2 with a hollow center. like shown in the image attached.
Hope that helps.