A critical look at the kinematic-wave theory for sedimentation-consolidation processes in closed vessels

The two-phase flow of a flocculated suspension in a closed settling vessel with inclined walls is investigated within a consistent extension of the ki nematic wave theory to sedimentation processes with compression. Wall bound ary conditions are used to spatially derive one-dimensional field equations for planar flows and flows which are symmetric with respect to the vertica l axis. We analyse the special cases of a conical vessel and a roof-shaped vessel. The case of a small initial time and a large time for the final con solidation state leads to explicit expressions for the flow fields, which c onstitute an important test of the theory. The resulting initial-boundary v alue problems are well posed and can be solved numerically by a simple adap tation of one of the newly developed numerical schemes for strongly degener ate convection-diffusion problems. However. from a physical point of view, both the analytical and numerical results reveal a deficiency of the genera l field equations. In particular, the strongly reduced form of the linear m omentum balance turns out to be an oversimplification. Included in our disc ussion as a special case are the Kynch theory and the well-known analyses o f sedimentation in vessels with inclined walls within the framework of kine matic waves, which exhibit the same shortcomings. In order to formulate con sistent boundary conditions for both phases in a closed vessel and in order to predict boundary layers in the presence of inclined walls, viscosity te rms should be taken into account. Copyright (C) 2001 John Wiley & Sons, Ltd .