Longitudinal Dispersion, Mixing and Diffusion

As the wash ratio increases the mechanism being used to remove the solute changes from displacement and other effects such as dispersion, mixiag and diffiision become significant. A great deal of theoretical work has been done to describe these effects in capillary tubes and many workers have applied the same arguments to the problem as it occurs in porous media. Brenner [1962], for example, discusses the behaviour of an initially sharp interfece between two miscible liquids, having identical dynamical and kinematical properties, in terms of the concentration Cj of solute at a distance x fi om the point of introduction of the wash hquid at time /. The process is described by the equation  

Lapidus and Amundson [1952] provided a modification to Equation (9.10) vtiiidi takes, adsorption effects into account  

Taking tke case of a step input gives a solution of the fonn [Michaels et al, 1967]  

For the case of perfect mbdng when the wash liquor is introduced to the cake i.e. when 

The proper application of the dispersion model is bedevilled by difficulties with the initial boundary condition and in obtaining accurate values for the axial disperaon coefficient D. Sherman [1964] realised that e q res g the initial condition by the step function, although convenient for the mathematical analysis, was not easy to do in practice especially with thin cakes and he contrived to measure the solute concentration at the inflow face of Ms beds. The initial boundary condition was th represaited by a power-eTqtonential function with six e erimental constants  

---