Scientia Sinica

No. 1 LU: VOLUME VISCO:ELASTIC THEORY OF FLUIDS ; 47

viscous flow being then absent. Therefore, the absence of relaxation should mean the absence of volume viscosity, or, in other words, 7, should concern

3 : : ds : dS ww : be itself only with the viscous part of =F and not with —7*. With our definition

of 7 the visco-elastic equation (8) or (9) may be written in the form

. ds p—to=kos + m(S) (46)

P= Po + P= 72 —— — Ros se Varia (47)

. a which, when relaxation is absent, i.c., when t,=0 and hence 7,=0, reduces to the correct limiting form

pe oe 7 oe (48)

where now R= ko=k, and s=s=s..

Recently, Litovitz, Lyon and Peselnick’*! have criticized our definition of volume viscosity. For sinusoidal change alone, they have, instead, introduced a frequency dependent volume viscosity

7(w) = tee (49) where T, = Be 72 = T2 Bx/Bo (50)

. : ds is the relaxation time” for pressure change at constant volume (= =)

as readily shown from (47). In our choice of expression, this may be written as

In terms of this 7, the visco-elastic equation (7) or (9) yields the following stress-strain relation for harmonic changes

= d p—to= (ho +e otrs,)5+ Veer (52):

Since, when relaxational process is absent, Ryp=k..=k, ™=0, and (49) makes 7, Vanish, we see that equation (52) also yields the correct limiting form

1) By setting T, equal to T, the relaxation time for the change of shearing stress, our equations for sound absorption phenomena reduce to those used by Litovitz, Lyon and Peselnick. In fact, these equations were derived by them in identically the same manner as already done previously by the author.