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

A numerical technique for the dynamical simulation of three-dimensional rig id 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 tech nique is used to model the sedimentation of prolate spheroids of aspect rat io b/a=5 at Reynolds number 0.3. For a periodic lattice of single spheroids , the ideas of Hasimoto are extended to obtain an estimate for the finite-s ize correction to the sedimentation velocity. For a system of several spher oids in periodic arrangement, a maximum of the settling speed is found at t he effective volume fraction phi (b/a)(2)approximate to0.4, where phi is th e solid-volume fraction. The occurence of a maximum of the settling speed i s partially explained by the competition of two effects: (i) a change in th e orientation distribution of the prolate spheroids whose major axes shift from a mostly horizontal orientation (corresponding to small sedimentation speeds) at small phi to a more uniform orientation at larger phi, and (ii) a monotonic decrease of the the settling speed with increasing solid-volume fraction similar to that predicted by the Richardson-Zaki law proportional to (1-phi)(5.5) for suspensions of spheres.