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34 H1NGHAM-MURRAY METHOD

The length of the liquid column varies from zero at the start to L when the tubę is fuli. Let it be / uf ter time (ł) seconds. From the Poiseuille equa-tion

dł 8171

TTl PR⁵’ or

or

^ł ~    ¹² + constaut.

Since l — o when t = o, the integration constant is o. Hence

(8)

t PR^a

For a true fluid, curves plotting t/l* are linear, and the slope gives the viscosity. The least deviation from Poiseuille’s law is at once madę apparent by a curvilinearity of these curves.

This method was first described by Bingham and Murray, and is used by various workers for all kinds of materials in industry. Gregory, Rasweiler and Lampert describe a suitable modification for indus-trial use. Moness and Giesy use a similar technique for tooth-paste, a materiał which can be treated on the Bingham principle. St. John applies the method to egg white, flour suspensions and skini milk ; Wiggam to nitrocellulose dispersions; and Williamson to zinc oxido pigments. McMillen has used the method for paints. Scott Blair points out that for materials whicli break down under shear, and also show a fuli in viscosity with rising stress (and such materials are fairly common), the two

SCOTT BLAIR’S MODIFICATION 55

PR²

effects appear to cancel each other in the Bingham-Murray instrument, sińce, as flow proceeds, the stress falls owing to the increasing length of the coltimn, and the viscosity therefore rises. This rise in yiscosity is offset against the fali produced by the shearing. He suggests starting with a fuli tubę, and emptying it by means of air at a constant pressure. In this case Eąuation (8) has to be raodified, sińce when t Ig o, 1 = L, hence the

and the other term is

integration constant is

negative, sińce l decreases with increasing i. This gives

t ^PRa    M

⁷¹ (L^a — g| ’ 4    ’ * * ‘ ^

This method has been successfully used for honey, and is being applied to oils, greases and muds. If the Z/(L^a — P) curves are not linear, an empirical estimate of the degree of deviation from PoiseuiUe’s law can be obtained from the slopes of the log/log curves, which are generally linear over a considerable rangę. This means that although for these systems | is not linearly related to L^a — /^a, it is so related to some power of L^a — Z². This exponent differs from unity to an extent which is a measure of the dis-crepancy from truły fluid behaviour. There is no theoretical basis for this treatment, but it proves very effective in practice in many cases.

Numerous problems arise when the column of materiał is short; for example, surface tension corrections have to be madę. This can generally be done by subtracting an empirical constant from P, a constant which may be obtained either by calcu-lation from the static surface tension or, in the case only of a true fluid, by determining flow curves for a