Sedimentation of supsensions: implications of theories of hindered settling

Abstract

Expressions are derived for the parameters A in Steinour's theory and n Richardson and Zaki's expression dealing with the hindered settling of powdered materials. It is shown that n is simply related to ϵ 1, the initial liquid volume fraction of a uniformly mixed suspension for which [ Q(1 — ϵ)] was maximum value, Q being the linear settling rate of the suspension/supernatant interface and ϵ the initial liquid volume fraction of the suspension. For systems obeying the Richardson-Zaki expression, the settling rate at ϵ 1 approaches the limit V s exp −1, where V s is the estimated Stokes' law limiting velocity for the system, when ϵ 1 approaches unity ( i.e. infinite dilution). Highly hindered systems have large values for n, and ϵ 1 values approaching unity; for such systems Q ϵ 1 ⋍ V s exp −1. It is suggested that such behaviour implies the existence of relatively long-range forces within suspensions, hindering settling, and that particle-liquid (including particle-liquid-particle) forces are of importance in addition to particle-particle interactions. Evidence is presented that hindrance to settling is directly proportional to the polarity of the solid/liquid system and that the density of charge on the superficial particle surface is the dominant factor in determining hindrance. Maximum reduction of surface polarity without causing flocculation is suggested as the most efficient condition for separation by settling under gravity and pumping off supernatant liquor. n and ϵ 1 can be considered as useful indices of hindrance to sedimentation. ϵ 1 has particular significance as the initial liquid volume fraction at which solids flux has maximum value (for any suspension which obeys the Richardson-Zaki equation).