Modeling particle transport and aggregation in a quiescent aqueous environment using the residence-time scheme

Suspended particles are a ubiquitous component of aqueous environments and are found over broad ranges of size and density. Particle transport and fat e have an important role in the regulation of contaminants and nutrients in natural settings. The mechanisms that control the transport and size of pa rticulate material in solution also play a fundamental role in the successf ul operation of engineered systems, such as sedimentation ponds and floccul ation tanks, as well as flotation and filtering reactors. Adequate modeling of particle transport and aggregation is required for better understanding and prediction of the effects of particulate material in natural aqueous s ystems, as well as for designing efficient physicochemical processes to dea l with suspended solids. In this paper we illustrate how numerical diffusio n produced by the use of first-order finite difference schemes can introduc e significant errors in the modeling of particle settling in quiescent syst ems and how this error is compounded when aggregation is considered. To mod el settling without introducing numerical diffusion, while preserving numer ical efficiency, we propose the residence-time scheme, a simple numerical s cheme based on the residence time of each size fraction in the elements of the spatial discretization. For the solution of the settling-aggregation eq uation the alternating operator-splitting technique (AOST) is used. The inh erent modularity and simplicity of AOST allows smooth incorporation of addi tional particle transport mechanisms such as mixing, advection, etc.