Consolidation of Non-Colloidal Spherical Particles at Low Particle Reynolds Numbers

When a system of identical spheres settles under conditions of negligible surface and inertial forces an idealised form of sediment consolidation unfolds amenable to a universal description. We have described this complex process using a simple constitutive model expressed as an elementary scaling law in time, t, applied at the local particle level. The free-volume surrounding a particle consists of two volume contributions occupied by fluid, one portion fixed and the other portion variable, the latter of which declines with t−2. A comprehensive system of analytical equations was derived using this one idea, and associated boundary conditions, to describe all aspects of the batch settling process. An experimental system exhibiting negligible surface and inertial forces was used to validate the model and hence assess the merits of the scaling law. Excellent agreement was achieved. The precise physics responsible for this scaling law, and the applicable boundary conditions, remain unclear at this stage. Hence this work is likely to motivate further work in this area, concerned with the dynamics of random consolidation of settling spheres.

Abstract licence: CC BY

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