Revisiting the Solid Flux Theory

Several variations of the basic activated sludge process and of the related design procedures for final clarifiers have been developed, which are frequently based on the well-known solid flux theory (SFT). In this paper, by using the Lambert W function and a “virtual” solid flux corresponding to the Vesilind parameters’ ratio, the SFT is reformulated, and dimensionless groups are detected, which highly reduce the number of parameters that are involved in the final clarifiers’ design procedure. The derived dimensionless relationships and the corresponding plots have general validity since they can be applied to all the possible design/verification parameter combinations. Moreover, it is shown that for any input dataset, the suitable domains of the SS concentration and of the solid flux can be simply expressed by the two branches of the Lambert W function. By using data retrieved from the literature, several numerical applications and validations of the dimensionless relationships are performed. Finally, it is shown that by introducing in the SFT a new reduction hydrodynamic factor, rhoR, to be applied to the modified return flow formula rather than to the limiting solid flux as in the past, a significant improvement in the comparison between the results by theory and by experiments can be obtained.