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DE WAELE’S EQUATION

and has the efiect of increasing the viscosity, as do the turbulence. The whole situation is very cónfuse?

De Waele extends the Ostwald theory consider" ably and applies the treatment with success to ma® materials: inks, oils, clays, etc. He describes the disaggregation of structure under stress and the re-assem bling on release as a type ot deflocculation and subsequent flocculation, the slope of the log/log curves giving a measure of the extent of the process. He modińes the Poiseuilie eqiiation to read

In this, <f>¹ is a measureof the- structural effect (being i-o for a true fluid), and f is a type of yield-value. This is an ńnprovement dn Ostwald’s treatment, which makes no allowance for the fact that, in so many systems, there Iś^e^eeedingly little flow below a certain critical- stress. '. Williamson has carried the idea further, and his work will be dis-cussed in the next chapter.

De Waele is especially interested in pigments. He classes his materials into three sets, dividing-them by the conditions existing within them f'

(i) those in which the particles are a|traeted by the solvent morę than by each other. These he calls unflocculated;

(ii) those in which the attractions of the particles for each other and for the solvent are equal;

(iii) those in which there is greater jćąttraction between particie and particie than between particie and medium. This he dęscribes as a flocculated condition.

Systems in the first condition should obey Póiseuille’s 1 ^Not to be confused with fluidity in Chapter I.

_DE WAELE’S TREATMENT 75

pR concentrations, at which those in the J^/i-oup would not do so.¹ pg| ^gfailure to find agreement between the caicu-Aand the experimental estimates of dispersion p ^ finely divided systems is due to bound and **?°tated molecules. In shearing these have to be °^fleed out of their natural orientation, and work to be done in the process. At high stresses a ^ndition of Iow viscosity is reacłjed, where very fttle further distorting of these molecules is needed, fcence    Waele concludes that " flocculated

systems . . . show the effect of the interference of the dispersoid particles, one with another, by the variabihty of the coefficient of fnction with the ratę ₀f shear in the first place, and the static ligidity of the system ąs a whole, when the packing is close.”

The author has found in his own work (unpub-lished 1938) that milk and some creams are almost true fluids at 37°C., even in the case of creams having very high viscosities. Other creams follow an Ostwald type of equation and deviate considerably from PoisenOle^ law. The same appears to be true of butter.^{2 3}

The reader will have noticed that tj, in de Waele's eąuation, has the wrong dimensions for a viscosity, a fact which has aroused much discussion. Perhaps it is a pity that de Waele uses tj asa symbol in this case, sińce he fully realises that his y is not truły a viscosity. Some people prefer to use “ or y*, in order to avoid confusion.

A much morę serious criticism of this treatment is that for certain materials the dimensions of y are not constant, but depend on the value of <f>. Farrow,

1

Those interested in the naturę of attractions between

2

colloidal particles are referred to the work of Hamaker.

3

* See Scott Blair, /. Dairy Res., *93⁸>    ^2oS