Wave model for longitudinal dispersion: development of the model

A new 1-D model for longitudinal dispersion is proposed as an alternative to the Fickian-type dispersed plug-flow model. Accounting for significant features of longitudinal mixing gives rise to a quasilinear hyperbolic system of two first-order equations for the average concentration. The model equations are obtained based on minor extensions of the heuristic equilibrium analysis of Taylor. A qualitative, more general derivation of the equations is given on the basis of the simple generalization of Fick's law, taking into account the finite velocity of fluid elements. For linear problems the mean concentration and the dispersion flux obey a hyperbolic equation of the second order. The proposed hyperbolic model contains three parameters that depend only on the flow conditinos, the physical properties of the fluid, and the gemetry of the system. It effectively resolves the well-known problem of boundary conditions that, for unidirectional flow, are formulated now only at the reactor inlet. The new model eliminates the conceptual shortcomings inherent to the Fickian dispersed plug-flow model: it predicts a finite velocity of signal propagation and does not involve backmixing in the case of unidirectional flow.