The chief purpose of this paper is to formulate and partly analyze a new mathematical model for continuous sedimentation-consolidation processes of flocculated suspensions in clarifier-thickener units. This model appears in two variants for cylindrical and variable cross-sectional area units, respectively (Models 1 and 2). In both cases, the governing… (More)
We show how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments (" sedimentation with compression " or " sedimentation-consolidation… (More)
We consider scalar conservation laws with the spatially varying flux H(x)f (u)+(1−H(x))g(u), where H(x) is the Heaviside function and f and g are smooth nonlinear functions. Adimurthi, Mishra, and Veerappa Gowda [J. Hyperbolic Differ. Equ. 2:783–837, 2005] pointed out that such a conservation law admits many L 1 contraction semigroups, one for each… (More)
The well-known Lighthill-Whitham-Richards kinematic traffic flow model for uni-directional flow on a single-lane highway is extended to include both abruptly changing road surface conditions and drivers' reaction time and anticipation length. The result is a strongly degenerate convection-diffusion equation, where the diffusion term, accounting for the… (More)
Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of first-order, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill–Whitham–Richards traffic model and a model for the… (More)
We study a zero-flux type initial-boundary value problem for scalar conservation laws with a genuinely nonlinear flux. We suggest a notion of entropy solution for this problem and prove its well-posedness. The asymptotic behavior of entropy solutions is also discussed.
This paper reviews some recent advances in mathematical models for the sed-imentation of polydisperse suspensions. Several early models relate the settling velocity to the solids concentration for a monodisperse suspension. Batchelor's theory for dilute suspensions predicts the settling velocity in the presence of other spheres that differ in size or… (More)