(205e) Measurements of Partial Derivative Properties -- Diffusion Coefficients and Spinodal

 At critical points, partial
derivatives  (:chemical potential
of i, :mole
fraction of i ) are well known to be equal to zero for mixtures. It drives
a curious conclusion that the values of diffusion coefficients will be zero at
critical points because the phenomenological  Fick's law is written as . Experimentally,
we found that acetone or benzene in supercritical CO₂ around 40 ºC
shows a minimum near the critical point and a maximum at a little higher
pressure. Equations of state also draw similar curves.

   At critical points of  pure
substances, instead of  Gibbs energy,  the relation of  is usually used. The region
between binodal and spinodal curves is called metastable. Metastable state
measurements follow probability. However, spinodal which is limit of stability should
be deterministic, because it is defined as a point of . When both temperature and
pressure was decreasing in a continuous flow of water, we found transmitted
light became darken because of light scattering. We believe that it is a point
of spinodal, i.e. as same as the critical point. At a
fixed temperature for water, spinodal pressures were higher than the saturation
pressures, i.e. binodal curve. Calculated curves with the Peng-Robinson
equation of state seem consistent.