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CHAPTER VIII

Plastlcs, Pseudo-plastlcs andapibn-Newtonlan pi Wllllamson’s Eauatlon. Inverse Plastldty, Dilat ^^s* and Passlye Dllatancy. Thlxotroplc and R4_eo.?^ Materials. Applications to Honey, Drllllne M^Ct.'^c Starches, etc.    ^B

Williamson uses the Word " psenio^plastic ” describe Systems which do not show any kind oj yield-value, and which cannot be tnoulded. As be shown, he implies that at high stresses, the fl₀\v curves become sufiiciently linear for a reliablelinear asymptote to be drawn to them. Many materials apparently increase in mobility as the stress rises, right op to the condition where turbulence sets in. Such systems, when they show smooth fiow curves with no yield-value, are sometimes referred to aą " non-Newtonian ” hcpiids (Reiner).

Although plasticity cannot be defined in^imple terms of mobility and yield-value, yet there is no donbt that any substance, to be plastic,- must have some sort of yield-value (i.e., a sharp lipward inflection in the flow curve) so that the body will hołd its shape against gravity and yet not ^equire dangeronsly high stresses, such as _;would cause rupture, to deform it. Williamson realises tthat Bingham’s treatment can be applied only to plastics (in this sense), or if applied to pseudo-plastics, all the data on the curvilinear part of the flow curve have to be neglected; also he does not wish to use the log/log method. He has therefore developed a further method of his own, the importance of which

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wILIJAMSON'S TREATMENT 83

. rtunatdy been overlooked. He prefers to - jMg? tenns of the power used in shearing the S|¹ in shearing a pseudo-plastic, part of the reąuired for ordinary viscous flow, and c°^^e*fot tbe deformation and/or disintegration of Lri Ltes. As the ratę of shear rises, the extent of f^act°^r gradually becomes less. The linę

HilHHi    b

OGCB, in Fig. 16, shows a flow curve for a capillary tubę, for a typical pseudo-plastic.

The slope of the asymptote is Bingham’s mobility or fluidity at infinite ratę of shear, and Williamson calls this “ apparent fluidity": the stiffness, or reciprocal of this, he calls " apparent viscosity." He then proceeds to express graphically the power reąuired for viscous deformation by the rectangle BR/K, and R/OT represents the power needed to overcome the "plastic" resistance for a ratę of