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 fate have an important role in the regulation of contaminants and nutrients in natural settings. The mechanisms that control the transport and size of particulate material in solution also play a fundamental role in the successful operation of engineered systems, such as sedimentation ponds and flocculation 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 systems, as well as for designing efficient physicochemical processes to deal with suspended solids. In this paper we illustrate how numerical diffusion produced by the use of first-order finite difference schemes can introduce significant errors in the modeling of particle settling in quiescent systems and how this error is compounded when aggregation is considered. To model settling without introducing numerical diffusion, while preserving numerical efficiency, we propose the residence-time scheme, a simple numerical scheme based on the residence time of each size fraction in the elements of the spatial discretization. For the solution of the settling-aggregation equation the alternating operator-splitting technique (AOST) is used. The inherent modularity and simplicity of AOST allows smooth incorporation of additional particle transport mechanisms such as mixing, advection, etc.