Computation of particle settling speed and orientation distribution in suspensions of prolate spheroids

A numerical technique for the dynamical simulation of three-dimensional rigid particles in a Newtonian fluid is presented. The key idea is to satisfy the no-slip boundary condition on the particle surface by a localized force-density distribution in an otherwise force-free suspending fluid. The technique is used to model the sedimentation of prolate spheroids of aspect ratio b/a = 5 at Reynolds number 0.3. For a periodic lattice of single spheroids, the ideas of Hasimoto are extended to obtain an estimete forthe finite-size correction to the sedimentation velocity. For a system of several spheroids in periodic arrangement, a maximum of the settling speed is found at the effective volume fraction Φ(b/a)² ≈ 0.4, where Φ is the solid-volume fraction. The occurence of a maximum of the settling speed is partially explained by the competition of two effects: (i) A change in the orientation distribution of the prolate spheroids whose major axes shift from a mostly horizontal orientation (corresponding to small sedimentation speeds) at small Φ to a more uniform orientation at larger Φ, and (ii) a monotonic decrease of the settling speed with increasing solid-volume fraction similar to that predicted by the Richardson-Zaki law α (1 - Φ)⁵.⁵ for suspensions of spheres.