Stability Ratio

Synonyms

Colloid stability

Definition

The stability ratio W is the ratio of the fast flocculation rate k_o to the slow flocculation rate k. In the absence of an energy barrier, the rate of flocculation (Smoluchowski rate) is diffusion controlled and the process is represented by second-order kinetics. The number of particles n at any time t may be related to the initial number (at t = 0) n_o by ${\rm n} = \frac{{{\rm n}_{\rm o} }}{{1 + {{\rm k}_{\rm o}} {\rm n}_{\rm o} {\rm t}}}$, where k is the rate constant for fast flocculation that is related to the diffusion coefficient of the particles D: ${\rm k} = {8{ \pi} {\rm DR}}$. D is given by

$$ {\rm D} = \frac{{\rm kT}}{{6{\pi} {\eta} {\rm R}}}\;\;\;\;\;{\rm k} = \frac{4}{3}\frac{{\rm kT}}{\eta } = 5.5 \times {{10}^{{ - 18}}}{{\rm m}^3}{{\rm s}^{{ - 1}}}\;{\rm for\;water\;at}\;25^\circ {\rm C}. $$

The slow flocculation kinetics was treated by Fuchs who related the rate constant k to the Smoluchowski rate by the stability constant \(...