The use of hindered settling data to evaluate particle size or floc size, and the effect of particle-liquid association on such sizes

Interpretation of the hindered settling of calcium carbonate suspensions in terms of permeability

Many pharmaceutical formulations are produced in the form of concentrated suspensions. Calcium carbonate suspensions are used in this study and interpreted as the "model" for the behavior of such suspensions. The behavior of concentrated suspensions of powders in a liquid medium cannot be treated by the simple application of the normal principles of free fall and the use of Stokes Law pertaining to the viscous resistance offered by the surrounding fluid to fall. A single particle operating by the Stokes principle obeys this relationship. This law applies to the behavior of particles at low concentration in a liquid medium and is the basis for particle size distribution methods. At higher concentrations, however, the particles do not enjoy the freedom of unhindered fall. The system subsides "en bloc," and it is common practice to offer a modification to the Stokes equation which takes into consideration some function of the porosity of the system. There have been a considerable number of equations developed and modified based on this principle. However, an alternative method is to approach the problem by dealing with the permeability of a bed of powders in a liquid in which the bed is slowly altering with time. This is best achieved by the use of the permeability equation developed and presented by Kozeny-Carmen. This equation, as well as the Richardson-Zaki expression, are related to show that the Kozeny parameter K varies with the suspension porosity under sedimentation conditions. The values of K are often larger than the value normally reported (i.e., approximately 5). The data and treatment outlined here are extended to include not only the calcium carbonate suspensions, but other systems previously mentioned in the literature.