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Immersed boundary method for a permeable sedimenting circular particle between two parallel rigid walls

This paper demonstrates settling of an isolated permeable circular particle in 2D, which corresponds to an infinite cylinder in 3D, in a viscous, incompressible fluid contained within a two-dimensional channel. The fluid-structure interaction problem considered here is simulated numerically using the immersed boundary method wherein, the added mass is formulated using Boussinesq's approximation. This has been possible since the density of the particle is slightly greater than the density of the fluid. The paper has demonstrated both analytically and numerically that the settling velocity of a permeable cylinder is greater than that of an impermeable cylinder and it increases with increasing permeability. The effect of channel walls, the so called wall effect, on a permeable particle, located initially along the centreline, is investigated. It is found that the wall-effect on the settling velocity decreases as the permeability of a particle increases. Furthermore, for a given permeability the wall effect on terminal settling velocity was found to decrease with decreasing fluid viscosity. In addition to such, the settling dynamics of a particle initially located at an off-centre location has been studied for different viscosity and permeability values. It is shown that numerical results reproduce the expected behaviour qualitatively.