Role of coagulation in the kinetics of sedimentation

The combined results of analytical, numerical, and laboratory studies are used in examining the kinetic be- havior of sedimentation in well-mixed systems. The rate of mass removal of solids, dC/dt, as a function of mass concentration C, can be described as the sum of three power laws, dC/dt = -BdsC2.3 - B,hC1.g - BbC1.3, each term of which corresponds to a particular coagulation mecha- nism: differential settling, shear, and Brownian motion. Empirical relationships for the coefficients Bds, Bsh, and Bb as a function of system parameters are provided. Introduction Understanding sedimentation kinetics is important for determining the performance of treatment processes and assessing the impact of waste disposal in natural waters. Sedimentation rates are now typically described by a fixed distribution of settling velocities, corresponding to the discrete settling of individual particles. Experimental results (1-7) however have shown the importance of par- ticle-particle interactions, most notably coagulation, re- sulting in the aggregation of smaller particles into larger ones. According to Stokes law, large particles settle much faster than smaller ones, and overall sedimentation rates can thus be dramatically affected by coagulation. Basic coagulation theory, which is largely attributable to the work of Smoluchowski (8,9), is presented elsewhere (5-7,lO-12). Combining coagulation theory with Stokes law for gravity settling yields the dynamic equation of sedimentation kinetics. No general analytical solution exists for this equation. Investigators have thus relied on laboratory observations (3-6, 13), simplified analytical solutions (5, 6,14), and numerical simulations (12,15) to determine sedimentation behavior. A number of problems are associated with these individual approaches. First, extrapolating experimental settling rates to field Eonditions is difficult since dispersion is not represented in laboratory studies and the appropriate scaling of the laboratory results is unknown. Second, simplified analytical solutions, namely those developed by Hunt (5, 6) and Morel and Schiff (14), describe the mass removal of solids by a sec- ond-order dependency on mass concentration. Although this second-order rate law appears to be an adequate de- scription of laboratory data, it has only been tested over a limited range, encompassing less than an order of mag- nitude change in suspended mass. Further testing of this rate law is clearly needed. Finally, numerical simulations based on the dynamic equation for sedimentation have so far been performed for case-specific applications-providing little insight into the general behavior of sedimentation. Since no systematic comparison of numerical results with laboratory or field data has been performed, the applica- bility of the numerical simulations remains questionable. The goal of this study is to combine results of laboratory, analytical, and numerical studies for predicting the rate of solids removal from water. Simplified descriptions of sedimentation behavior previously hypothesized by Hunt (5,6), Morel and Schiff (14), and Farley (16) are used as a starting point and tested in a series of numerical simu-