Not Involved Reaching Zero

If the post "To Infinity But Slightly Less..." dated 28 Dec 2017 is correct, that the extent of the fluid in the thermometer is due to temperature charge particles extending in the temperature field by \(r\) to \(V=0\).  The temperature particles carry the fluid with them as they reach for \(V=0\).  Then,

all thermometers, no matter the fluid type, will have the same extend at steady state, given the same temperature charge \(q_s\), provided that all fluids are free to move in the bores of the thermometers.

Essentially no material properties of the fluid are involve here.  Not drag, not viscosity and not thermal expansion.

The fluid acts like a dye to mark the measurement, the imbued temperature particles gauge the temperature field and carry the dye along.