Kinetics of aggregate formation in rapid mix

Abstract

The growth of porous aggregates during initial mixing is investigated in a series of numerical simulations. Hydrodynamic radii of aggregates composed of i primary particles are used to calculate collision rate constants as a function of fractal dimension, D, and aggregation number, i. D is assumed to be independent of aggregate size. The rate of floc volume formation increases by several orders of magnitude as the fractal dimension decreases from 3 to 2. Neglecting aggregate porosity is estimated to introduce an error of < 10% in calculating the collision efficiency factor from particle number measurements and a coalescing-sphere model for particle aggregation. For conditions approximating those in which ferric sulfate is added to a rapid mix basin, simulations with D = 2.5 produce a volume fraction of flocs larger than 1 μm that approximates the volume fraction greater than 1 μm measured using an electronic particle counter. A fractal dimension of 2.35 produces an aggregate volume distribution that most nearly approximates the volume distribution observed in jar tests with ferric sulfate. These values of D are within the range of values reported in the literature for larger ferric hydroxide flocs. Mixing conditions in most full scale installations are likely to favor the formation of aggregates of precipitated coagulant particles that are sufficiently large for breakup and aggregate restructuring to control the size distribution of materials leaving the rapid mix basin.