str (102)
76 HERSCHEL-BULKLEY EQUatioh
Lowe and Neale show that for certain starch <f> varies with variations in the stress. morę than one type of instrument, they covered an enormous rangę of stress, and find to over fairly wide ranges <f> is constant, but that ov the whole rangę it varies considerably. Schofiefo has examined their data to see if any <7-phenoraena occur; but he concludes that they are not signi-ficant.
Gallay finds the Ostwald treatment adeąuate for practical purposes for starch, while Herschel and Berąuist find ąuite good Bingham flow curves for some starches, and Porst and Moskowitz claim that some starches give good straight lines with Bingham, and others with Ostwald treatments. Porter and Rao use the Ostwald treatment. The results depend a good deal on whether the starch granules are intact or broken. j ■ ’
Scott uses a combination of the Bingham and Ostwald principles in work on masticated rubber, his eąuation being that proposed by; Herschel and Bulkley
5 = -(S-/)”.
which is rather like de Waele's eąuation. jilouwink even suggests that the extent of the milhng reąuired for any sample of rubber could be judged by nt the milling being continued until n — i, and j$the materiał conseąuently obeys Bingham's law. Ali this shows how very complex the subject has become.
The simple idea of shearing strength :(yield-value) and mobility only holds for comparatively simple systems. Scott Blair, in discussing the naturę of yield-value, concludes that it is simply a" Sharp mflection in a flow cuive. There are manMferials
show i slow-yield,” below the ordinary yield-as an example of which Bingham ąuotes va^e' jynds of marble. If a materiał consists of 06 ents, alł of which yield at the same stress, it e^gIears to have a sharp yield-vałue. If a number of r neham systems coułd be mixed in such a way that III indiridual components retained their own yield operties* the result would be an Ostwald system, sińce the resultant of such a series of straight lines js a curye. The yield-value observed is that of the lowest yielding element in the system. Very often expenments done slowly will reveal flow at stresses at which experiments done quickly show no flow. A yield-value may thus be described as a " kink in a flow curve.” In metal work Houwink States that a test piece is considered to have yielded when a permanent strain of 0'002 has been produced, a strain which is, of course, quite arbitrarily chosen.
The Ostwald-de Waele treatment has been applied to a great many industrial materials: starches, gelatine, dyestuffs, cellulose derivatives, amalgams, fats, etc. The structural viscosity of cellulose esters (especially cellulose acetate in acetone) has also been measured in a burette type of viscometer (the Ostwald-Auerbach viscometer) by Glikman, and by Glikman and Gooseva. These authors us© the ©Xpression " thixotropic viscosity "; but the sense appears to be the same as that in which " structural viscosity ” has been used in this book.
The Poiseuille equation was derived by integrating from the Newton assumption that the velocity gradient is proportional to the stress. Let us see the result of assuming that the velocity gradient is proportional to some power of the stress. The question of priority for such a treatment is a little involved. 11 seems that Herschel and Bulkley, in
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