A scaling theory for number-flux distributions generated during steady-state coagulation and settling and application to particles in Lake Zurich, Switzerland.
In this study, we extend the established scaling theory for cluster size distributions generated during unsteady coagulation to number-flux distributions that arise during steady-state coagulation and settling in an unmixed water mass. The scaling theory predicts self-similar number-flux distributions and power-law decay of total number flux with depth. The shape of the number-flux distributions and the power-law exponent describing the decay of the total number flux are shown to depend on the homogeneity and small i/j limit of the coagulation kernel and the exponent kappa, which describes the variation in settling velocity with cluster volume. Particle field measurements from Lake Zurich, collected by U. Weilenmann and co-workers (Limnol. Oceanogr.34, 1 (1989)), are used to illustrate how the scaling predictions can be applied to a natural system. This effort indicates that within the mid-depth region of Lake Zurich, clusters of the same size preferentially interact and large clusters react with one another more quickly than small ones, indicative of clusters coagulating in a reaction-limited regime.
Boehm
Alexandria B
AB
Department of Civil and Environmental Engineering, Stanford University, Stanford, California, 94305-4020, USA. aboehm@uci.edu