63481 str (72)

124 SMOLUCHOWSKI-S EQUATi_0x

increases the rdscosity. Kfetoluchowski , modińed eąuation to allow for fłn«= effect °^duces a. j

where A — the specificEeemductivity per . centimetre ot liquid; Lg == the radius of ^ particies ; £ — the double layer^felectrokinettó potential; and D = the dielectric constant of the liąuid.    '' -

This formula has been tested, with fair success, by Kruyt and his pupils. The eąuation suggested by Taylor has been applied, with cónsiderable success, by Leviton and Leighton to creams. The dis-crepancies from the modified Einstein eąuation arę actually used as an index of the degree of^elump-ing " of the fat particies.

Arrhenius proposes an empirical formula, in which log r/ is linear with concentration, which Works well for protein sols (Chick’s data). Scott Blair, Watts and Denham successfully apply the same type of eąuation to ńout suspensions. Shaip and Gdtfner, however, use a log 17/log (concentratiom ||jnation. No adequate theoretical foundation has been found for these eąuations. They fail for such sj^stems as highly concentrated cellulose nitrate or |eetate sols. Carver and Folts get surprisingly good straight linę flowcurves for cellulose incuprammonium hmrpxide. Bungenberg de Jong and his fehow-workersUaaye done some interesting experiments inj§|||nection with coaceryation.¹ If a sol (A) &pproximatęly obeys PoiseuiIle's law, and the jSnfc|M|iówski eąuation, and a sol (B) does the same, then, pn mixing the sols, if there is no |p&pervation the 1ńscosities are additive. If there is eoacervation tle

¹ Derived from the Latin, acervus = heap.

_cy between the measured and the calculated A'$cf^e?^es passes through a maximum when the sols BęSPm in about equal proportions. Coacervation ||j|pl two oppositely charged sols is known as 0SSM coacervation.”

“ ^c°f_C]i_ek suggests the following formula for the lĘjmiĘś the velocity gradient is so high that the cas^goid particies are fully deformed elastically, su^^gj-e the concentration is high, so that <f>> 0*5.

v,

1 — Ą/<f>K

jjgj-e K is a constant. This formula works well for ^_ta obtained by Trevan on suspensions of red blood corpuscles, which are suitably elastic. Sibree, y/orking on emulsions of paraflin in sodium oleate, found that the Hatschek formula only works when the correction (K) is applied to (f>. <f> must be multi-plied by a " volume factor g of about 1-3. It should be noted that his experiments confirm Hatschek’s assumptions that viscosity is very largely independent both of particie size and of size distńbution, as well as of the viscosity of the disperse phase. He also shows that the viscosity becomes independent of the velocity gradient at high velocity gradients.

Very little seems to be known about the “ volume factorIt is not really constant, even for a single senes of emulsions: presumably it has something to do with soivation.

The ice-cream mix is an interesting system. Leighton and his co-workers very surpńsingly find straight linę flow curves for these systems. This is independently conńrmed by Bateman and Sharp.

It is most surpńsing to find this type of fiow curve -for such hydrophylic mateńals, and it is possibly

¹ Kwasaotintroducedin this eąuation when it hrst appeared.