Bravais lattice structures settling in viscous media: scaling of terminal velocity with porosity

The settling velocity of porous objects in Stokes flow depends on their geometry. Complex geometries of such objects occur in nature and technology, such as marine snow, particles in pulmonary drug delivery, chemical catalysts and pollen grains. To model the fundamental building blocks of porous geometries, we conduct experiments on sedimentation of various Bravais lattice unit-cell structures at low Reynolds numbers (∼ 10⁻⁴), where each structure consists of equally sized spheres connected by thin rods. For each of these structures, porosity becomes a function of the lattice parameter. We show that the sedimentation behaviour of all Bravais lattices can be collapsed when the settling velocity is scaled using the number of particles in the lattice. A ball-and-stick model using Stokesian hydrodynamic kernel for spheres and slender-body theory for connecting rods, captures the settling behaviour accurately. We perform PIV measurements of flow inside these structures to understand the dependence of permeability on porosity and also the validity of our theoretical model. Our experiments and calculations pave the way for understanding sedimentation of systems closer to reality by introducing disorder in the lattice.