Scientia Sinica
bo WI
No. | LU: VOLUME VISCO-ELASTIC THEORY OF FLUIDS
or
ds” ap SoS : (8)
dt Be at Bo 72
Since so = Bo(p—po), equation (7) may Also be written in the form
ds d s+ 125— = Bol? — Po) + Be age (9)
Since the values of the compressibilities By and 6. depend on the thermodynamical condition under which the compression takes place, we may talk about, for instance, isothermal or adiabatic visco-elastic equations when . isothermal or adiabatic compressibilities are used respectively. However, since, strictly speaking, a process can be isothermal only when it is carried out quasistatically or infinitely slowly, the visco-elastic equation becomes trivial (reduces to s=B)(p—po)) unless t, is much larger than the time required to establish thermal equilibium, as is the case considered in § V).
Il. On tHe EourvALENcE oF DIFFERENT MoLEcuLAR
MECHANISMS OF VOLUME RELAXATION
Volume relaxation may arise from different molecular processes, including: (1) Thermal relaxation (Herzfeld and Rice’, Bourgin™!, Kneser'’”), arising from the finite rate of conversion of external energy of translation and rotation into internal energy of vibrations of molecules, or, vice versa. :
(2) Structural relaxation (Frenkel"™!, Hall"!), arising from the finite rate of molecular rearrangement from a relatively loose structure into a more compact structure, or, vice versa.
(3) Chemical relaxation (Einstein', Luck", Liebermann" '), arising from the finite rate of reaction of the chemical components.
When any of these processes exists, the compressibility will depend upon the rate of compression. Our phenomenological theory makes no discrimination of these processes; they all give rise to a relaxational compressibility, B,=By—B..-
In the case of thermal relaxation, the relaxational compressibility arises from the relatively slow transfer of thermal energy from external degrees of freedom into internal ones, either from translational into rotational or from translational and rotational into vibrational, as the case may be. In this case, when thermodynamic equilibrium is not attained, it has nevertheless been found fruitful to assume separately states of partial equilibrium of the external