Scientia Sinica

SCIENTIA SINICA Vol, V

Qo ars

is the result of a reversible process. This part 1s considered to be instantaneous since the suddenly applied pressure is transmitted almost instantaneously (by the molecular motion and intermolecular interactions) throughout the fluid element. The presence of the relaxational part s, makes the overall process of compression irreversible; upon sudden release of the applied pressure, the expansion will not retrace the original path of compression in the P—S diagram and, as is shown in a paper! of the author (equations (5)—(9) ), there will, in general, be a dissipation of mechanical energy turned into heat. Thus, the relaxational part constitutes a dilatational viscous flow. In any dilatational process, the rate of compression at any instant was written as

ds — da ds “at dt +(#) . _ @)

ds rier ds , where (~~ ) _ represents the contribution to [— from relaxational molecular

. d d oe processes. Since, when ae =0, we have ae = 0, and further in addition,

ds ds : 5 when s=s9, we have 7- = >) =0, we see that to a first approximation ‘ = ‘, vis

we may, in the case of a single relaxation time, T2, expect to have

ds Stas ic. vis — T > A3)

2

or, using(2), this may be written as

A(s—Se) _ $40 at a ®

The phenomenological theory formulated by the author leads to just such an equation, Viz., as) _ os i dt a, Bo 72 ° ©)

T2 = Bo 72, (6)

where B, is the static (total) compressibility under given thermodynamical condition and 7, a coefficient of volume viscosity (see § VI). : ds d; ; : ae Sues = a where 8, is the instantaneous compressibility,

equation (2) gives for the volume visco-elastic equation,

Ven

a . pe ae To (7)