Abstract. 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 alternatingoperator-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. The lack of adequate mathematical schemes to solve the expressions used to describe the particle transport and aggregation phenomena remains an important problem that limits our ability to predict the behavior of particulate material in suspension. Usually the set of equations used to describe particle transport and aggregation do not have general analytical solutions and must be solved numerically. However, the domain discretization required for these numerical schemes can In this study, we start by analyzing some artifacts introduced by the use of first-order finite difference numerical schemes in the modeling of particle settling and show the effect of these artifacts when particle aggregation is considered. A new numerical scheme is presented, the residence-time scheme (RTS), to adequately model particle settling. Then, we apply the alternating-operator-splitting technique (AOST), a methodology widely used for solving transport-reaction aqueous systems [Valocchi and Maimstead, 1992; Kaluarachchi and Motshed, 1995a, b], for solving the equations governing particle transport and aggregation. We discuss why AOST is a computationally efficient and flexible methodology compared with more traditional numerical frameworks used to model the fate of microscopic particles in aqueous systems. 2249
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