The viscosity of suspensions of spherical particles. (The fundamental η‐c and φ relations)

Abstract Einstein's theory forms the sole basis for a theoretical consideration of the factors governing the viscosity of a suspension. The practical significance of this theory is however only very relative, since Einstein's theory is only valid for very dilute suspensions (to concentrations of a few percents by volume), while in practice suspensions of medium to fairly high concentration are usually dealt with. It was found possible to obtain theoretically a φ—c relation for a suspension of spherical particles which is in good agreement with the experimental results recently obtained by Eilers with asphalt emulsions. The relation derived by us is found to be valid up to high concentrations. The fluidity relation is as follows: magnified image The physical concept upon which the φ—c relation obtained is based may be summarized as follows: Due to the fall in velocity in the liquid a suspended particle takes on a rotating motion. To this rotating motion corresponds an extra motion of the liquid. The latter may now be considered as the cause of an energy dissipation (Einstein) or as the cause of a flow of liquid at the walls enclosing the flowing suspension, in a direction opposite to that of the main flow, and thus observable at a relatively great distance from the suspended particle (Burgers). Occurrence of the term −2.5 c. The other particles will also cause a motion of the liquid at the spot where the particle first considered is situated. The intensity of the extra motion of the liquid caused by the particle in question will hereby be changed. Occurrence of the term +1.552 c 2 . From the fundamental fluidity relation the following simple formula may be derived for the voluminosity See footnote 9 ). V R : magnified image c = the concentration of the suspension in g/cm 3 d = the density of the suspended substance in the dry state. There are indications that the same fundamental φ—c relation can be used as a basis for polydisperse colloidal systems, even when these systems are built up of long‐chain molecules.