Flow through a settling mesh

As a starting point to gain an understanding of settling porous objects with complex geometries, such as marine snow and biofouled microplastics, we study the settling of a thin porous mesh. Motivating the theoretical-numerical work presented here are laboratory experiments that show the meshes settle without tumbling and the settling speed is effectively independent of the mesh lateral extent. The numerical simulations model flow through the mesh using a time-relaxation method. This captures the qualitative features of the laboratory experiments and gives insight into the dynamics governing the steady state settling velocity. Specifically it shows that a steep pressure gradient develops across the thickness of the mesh equal in magnitude to the reduced gravity, which itself equals the difference of the fluid and mesh velocity divided by the relaxation time scale. In effect, fluid is sucked through the mesh which provides the balance between buoyancy forces and drag controlled primarily by the mesh thickness, not its lateral extent. This insight justifies a dimensional analysis approach which successfully collapses measurements of the steady state flow across the mesh and mesh settling speeds thus giving semi-empirical predictions for these speeds as they depend upon the reduced gravity, mesh thickness and relaxation time scale.