# One-Dimensional Solid-Liquid Separation

## Summary

We describe an approach to separation of finely dispersed solid from liquid which has general application for many practically important suspensions. We propose that the separation of the liquid from the solid in particulate suspensions can usefully be described in terms of the liquid flow relative to the solid. The combination of this proposition with continuity equations for the liquid and the solid then gives rise to a flow equation that may be expressed in either spatial or material coordinates. For both filtration and sedimentation, the latter formulation is more convenient since it gives rise to a nonlinear Fokker-Planck equation for which solutions are known for many sets of initial and boundary conditions important in solid-liquid separation processes.

The theory is macroscopic in the sense that it deals with material properties that represent averages taken over a material volume (or cross-section) large enough to contain many particles of the solid. It applies to systems in which the energetics and hydrodynamics of the liquid phase are fully characterised by readily measurable functions that relate the chemical potential of the liquid and the permeability of the system to the liquid content. The theory is restricted to one-dimensional processes, although this is not seen as a serious restriction on its application because many separation processes approximate the one-dimensional condition. Finally, we describe a range of tests of the theory, present experimentally-derived material properties which might be used in illustrative calculation for a number of practically important situations, and identify initial and boundary conditions for many important separtion procedures.

### Keywords

Clay Permeability Filtration Sedimentation Compaction## Preview

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