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THE SIGMA PHENOMENON

34

and Scott Blair to test the effect of using ^ differences in radius and length. The length eft^ was not found to be significant ; but changes i_n radius make a very big difference for clays, and Jebens has found the same thing for water paints, The smaller the tubę, the greater the mobility appearś to be.

There are, therefore, four possibilities, as shown in Fig. 8 :—

23lair)

Kio. 8. (After Schofiold and Scott

''fij

Ali these have been realised e.Kperime¹¹ , '^v'^fl I clays at suitable concentration, except is a curve for a true fluid, such as glycef

No. i shows “ spread,” but there is y * I the materiał behaves as a true fluid, f°^l capillary. over a wide pressure rangę.

No. ^:2 shows “ spread and intercep

No. 3 shows neither spread nor intercept (a true fluid).

No. 4 shows intercept, but no spread {a simple Buckingham-Reiner materiał).

This means that the viscosities of certain industrial materials, even when reproduced at a senes of stresses, may be in error by as much as 50 per cent., which is serious. It is not yet fully known how one is to correct for this effect, or to what it is due ; but the following treatment is suggested. Suppose that V/ttR² is plotted against PR/2L, where V/ttR² is the mean velocity, we get a series of curves of slope d(V/ttR²)jd(PR/2L). This slope will be called a. In the case of a true fluid, if 1 is plotted against R, a straight linę is obtained, passing through the origin and having a slope of \<f>. For these clays, the curve is fairly linear over a reasonable rangę, but it makes an intercept on the a axis, which will be called _Oo. The slope of this curve gives a value of mobility which would be the limiting value for an infinite radius.

This work has been done chiefly on clays, but it is eąually applicable to quite a number of rheologically similar materials, such as some paints, tooth-pastes, talc-suspensions, suspensions of insoluble precipi-tates, and of course, such things as soils and drilling muds. Othor treatments have been suggested, but the one deseribed seems reully to be the most, satisfactory, although the physical basis tur it is meagre, t he suggestion of Aiubrose and Loomis that the effect is due to thisotropy ¹ (i.*., a lower cunsistoney iu the uurrowor tubes, where the sheur >s greuter) is invuUdated Iły the lad that an ineteused length ot tubo iucreases the amouut of shear, without affaoting the eonsisteney. It is

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