Abstract
A semi-empirical approach using Darcy's law for flow in a porous medium is applied to the problem of a sedimenting column of particles. Application of the mass continuity equations for the moisture ratio, ϑ, leads to a non-linear Fokker-Planck equation with non-linear boundary conditions in the material coordinate system. The governing equations and boundary conditions are suitably linearised to predict volume outflows (or volume of clear liquid at the top), and concentration and equilibrium profiles. Experiments were carried out on two columns of different length to record both the volume concentration profiles of particles and volume outflow. The particle concentrations were obtained by a γ-ray attenuation method. Theoretical and experimental determinations of volume outflows agree well, and for early times the profiles for the volume concentration as a function of height are similar. However, near equilibrium the two profiles do not compare so favourably, this being attributed to the limitations of the linear analysis at this stage of the sedimentation process.
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