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₃6 STATISTICAL ORIENT A TION

nevertheless true that thixotropic materials, which will be considered later, would under certain con-ditions show the phenomenon. Mathematically it is impossibłe to distinguish between the two effects, unless the length variation test is introduced.

Staudinger and fellow-workers find that there are length effects in the case of p>olymerised polystyrols; bnt these are very complex, the length effects coming out in the opposite sense from the <r-effect.

Any long narrow particie, suspended in a liąuid j that is being sheared through a capillary tubę, is I subjected to a viscous couple. When it is lying with its long axis across the tubę, the end nearer the centre is being driven forward, relative to the end nearer the wali, so that the particie tends to rotate. This rotation is fastest when the particles lie at right I angles to the direction of flow, and slowest when I they are parallel to this direction ; so that, at any I given moment, morę particles are aligned along the I streamlines than across them. This alignment may I be described as “ statistical orientation.'’ Near the I wali the rotation is inhibited, and there is morę I alignment. Surprisingly enough, there is no evidence I that needle-shaped particles show the o-phenomenon I morę than those which are sphere-shaped. The I effects of concentration, however, favour, this I orientation hypothesis, sińce cr₀ passes a maximum I with increased concentrations of clay. Movement I in a very thick pastę is extensively inhibited in any I case.

There is no evidence that the concentration near I the wali differs from that in the bulk of the materiał. I An attempt has been madę to calculate the thicknessof I the “ modified ” layer, but it was not very successful. I Scott Blair worked on the assumption that the thick- I ness of the " modified " layer could be considered as ■

definite, and independent oi the capillary radius; but his treatment was incomplete, and a morę e£Eective method was later worked out by Schofield and Scott Blair. Tłiese workers have also derived a generał equation, of which the Buckingham-Reiner eąnation is a special case,¹ and they show that, even if flow curves are not linear, and even where neither the Newton nor the Reiner assumption holds, the PB.

—— curves must be uniąue, so long as 2L

(1)    each particie of the materiał moves in a

straight linę, at a constant velocity, parallel to the axis of the tubę;

(2)    there is no slip at the wali;

(3)    the velocity gradient, at any point, is some

function of the shearing stress at that point, and depends on nothing else.

At almost exactly the same datę that the work of Schofield and Scott Blair was published, Reiner quite independently showed that " if ftuidity, as usually calculated, is plotted against the stress at the.wali, the curve is independent of the dimensions of the apparatus, irrespective of the law of flow of the liquid under test.” He went on to show that any slippage at the wali of the tubę would introduce a spreading of the curves, and that such slippage occurs for a solntion of nitrocotton in di-butył phthalate. The theoretical treatment is very similar to that of Schofield and Scott Blair, but the phenomenon to which it is applied is a simple pług flow. Several other investigators were working along very similar lines at this time (1931), and the question of priority is not easy to determine.

¹ Something of the same sort was also done independently by Rabinowitsch and by Mooney.