We have simulated the dynamics of suspensions of fibres sedimenting in the limit of zero Reynolds number. In these simulations, the dominant inter-particle force arises from hydrodynamic interactions between the rigid, non-Brownian fibres. The simulation algorithm uses slender-body theory to model the linear and rotational velocities of each fibre. To include far-field interactions between the fibres, the line distribution of force on each fibre is approximated by making a Legendre polynomial expansion of the disturbance velocity on the fibre, where only the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution can be specified completely by a centre-of-mass force, a couple, and a stresslet. Short-range interactions between particles are included using a lubrication approximation, and an infinite suspension is simulated by using periodic boundary conditions. Our numerical results confirm that the sedimentation of these non-spherical, orientable particles differs qualitatively from the sedimentation of spherical particles. The simulations demonstrate that an initially homogeneous, settling suspension develops clusters, or streamers, which are particle rich surrounded by clarified fluid. The instability which causes the heterogeneous structure arises solely from hydrodynamic interactions which couple the particle orientation and the sedimentation rate in particle clusters. Depending upon the concentration and aspect ratio, the formation of clusters of particles can enhance the sedimentation rate of the suspension to a value in excess of the maximum settling speed of an isolated particle. The suspension of fibres tends to orient with gravity during the sedimentation process. The average velocities and orientations, as well as their distributions, compare favourably with previous experimental measurements.

We investigate the lateral migration of a confined polymer under pressure driven and uniform shear flows. We employ a hybrid algorithm which couples point particles to a fluctuating lattice-Boltzmann fluid. We observe migration in both uniform shear and pressure driven flows, supporting the idea that migration is driven by a combination of shear and hydrodynamic interactions with the wall, rather than by the shear gradient. Recent numerical and theoretical investigations have suggested that polymers migrate toward the centerline when hydrodynamic interactions are included, but our simulations show that in sufficiently narrow channels there is a reversal of direction and the polymers move toward the wall.

International audienceThe large-amplitude oscillatory flow of a suspension of spherical particles in a pipe is studied at low Reynolds number. Particle volume fraction and velocity are examined through refractive index matching techniques. The particles migrate toward the centre of the pipe, i.e. toward regions of lower shear rate, for bulk volume fractions larger than 10 %. Steady results are in agreement with available experimental results and discrete-particle simulations for similar geometries. The dynamics of the shear-induced migration process are analysed and compared against the predictions of the suspension balance model using realistic rheological laws

We demonstrate that a polymer confined to a narrow channel migrates towards the center when driven by an external force parallel to the channel walls. This migration results from asymmetric hydrodynamic interactions between polymer segments and the confining walls. A weak pressure-driven flow, applied in the same direction as the external force, enhances the migration. However, when the pressure gradient and the external force act in opposite directions the polymer can migrate towards the boundaries. Nevertheless, for sufficiently strong forces the polymer always migrates towards the center. A dumbbell kinetic theory explains these results qualitatively. A comparison of our results with experimental measurements on DNA suggests that hydrodynamic interactions in polyelectrolytes are only partially screened. We propose new experiments and analysis to investigate the extent of the screening in polyelectrolyte solutions.