Numerical simulations of a sphere settling through a suspension of neutrally buoyant fibres

The sedimentation of a small dense sphere through a suspension of neutrally buoyant fibres is investigated via a numerical simulation technique that i ncludes both fibre-fibre contact forces and long-range hydrodynamic interac tions. In situations where the diameter of the sphere is smaller than the l ength of the fibres, calculations that exclude the effect of contacts betwe en fibres severely underestimate the drag force on the sphere measured in e xperiments. By including fibre-fibre contacts in our simulations we are to able to account for this discrepancy, and also the strong dependence of the drag on the initial orientation of the fibres. At low and moderate values of nL(3), where n is the number of fibres per unit volume and L the fibre l ength, hydrodynamic interactions are found to be important in moderating th e effect of contacts between fibres. An asymptotic solution is presented for the limit when the sphere diameter is much smaller than both the fibre length and inter-fibre spacing, but lar ge compared to the fibre thickness. This is found to be in good agreement w ith the simulations. Results of calculations on sedimentation through a monolayer of fibres are also presented, as a model of a semi-concentrated suspension. Collisions be tween fibres are much more frequent, due to the geometric confinement.