Coexistence curves in mixtures of limited miscibility with the lower critical consolute temperature (LCT), of 3-picoline with deuterium oxide (D2O), and D2O/H2O have been determined. They were tested with respect to the order parameter, the diameter of the binodal, and coordinates of the critical consolute point (critical temperature $${T}_{\mathrm{C}}$$
T
C
and critical concentration $${\phi }_{\mathrm{C}}$$
ϕ
C
). Studies were carried out using the innovative method based on the analysis of relative volumes occupied by coexisting phases, yielding high-resolution data. The clear violation of the Cailletet-Mathew law of rectilinear diameter for the LCT mixtures of limited miscibility is evidenced. For the order parameter, the new distortion-sensitive analysis method yielded the evidence for the model-value of the order parameter critical exponent $$\beta =0.326\pm 0.003$$
β
=
0.326
±
0.003
, up to ca. 1 K from $${T}_{\mathrm{C}}$$
T
C
. Finally, the simple & easy method for determining the critical concentration by testing relative volumes of coexisting phases (or alternatively fractional meniscus heights, h) is presented. The significance of the invariant value $${h}_{\mathrm{C}}=h\left({T}_{\mathrm{C}},{\phi }_{\mathrm{C}}\right)=1/2$$
h
C
=
h
T
C
,
ϕ
C
=
1
/
2
is highlighted. The appearance of the milky & bluish critical opalescence is also shown.
Graphical abstract