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Al A X W EL L’S LAW

proportional to the straifl, or

dS

Tt

oc S ¹

The reciprocal of the proportionality factor is calleci by Maxwell the relaxation time (t_r). There is much confusion about the meaning of this expression, and it is perhaps a pity that the name “ relaxation time ” was chosen, sińce it suggests to many people the time that a materiał which shows elastic after-effect takes to recover when all stress is removed. This is, of course, not at all the same thing.

Now viscosity is defined as shearing stress dirided by the ratę of non-recoverable deformation, so that

		d<r S At r\
and sińce		dS _ S dt
	S %	n . S r ^ _7) t) ^r n

(4)

(5)

The relaxation time is thus shown to be equal to the ratio of viscosity to shear modulus.

Maxwell himself realised however, that t_f might not be, for all materials, a constant independent of stress. The first experimental test of this was madę by Schwedoff, using gelatine sols. The apparatus consists of a cylinder (A) as before, of radius a, suspended in another larger, concentric cylinder (B), of radius b, containing the sol. A is suspended on a long wire, the upper end of which is twisted

RELAXATION

through an angle 9. If the liquid wero truły fluid, A would follow the win: through the wliole angle 0 , but if there is rigidity, it only foliowa through a smaller angle u> (<l0), and stays there SO Long as the elastic strain can be maintained. '1 he torque on t lic wire is jo(9 — co), where fi is the torsional moment per unit angle.

As with the previous treatment, it can be shown that

Ł/ł. ~ 1\ i ~ j

IWmM b²) co

where h is the effective height of the inner cylinder.

When the materiał is not perfectly elastic below its yield-value, the elastic strain is gradually dissipated. If the torąue is reduced, so as to keep the cylinder at constant deflection, the values of the torąues (6 — co values), should give a logarithmic curve, when plotted against the times, if Maxwell’s law holds.

Schwedoff for gelatine, and Hatschek and Jane for benzopurpurin sol, find that this does not hołd. Hatschek and Jane suggest that the abnormahty is caused by a diminution in the size of the water envelopes surrounding the colloidal particles as stress inereases. The water envelopes are labile, and at Iow stresses contribute largely to the vis-cosity.² Rice starch forms a rigid suspension in a mixture of toluene and carbon tetrachloride, and yet there is a fali in viscosity with rising stress, presumably produced by the desolvating process. There is a residual elastic deformation which persists for an indefinite time. Schwedoff proposes an eąuation to fit his data, but Hatschek’s materiał does not agree with either Maxwell’s or Schwedoff’s

1

Since the stress is falling, this eąuation is often written witli a negative sign. Since Eąuation h) would then also be written with a negative sign, Eąuation (5) remains unaffected.

2

See also Humphrey and Hatschek.