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In an incompressible flow, fluid density remains invariant along fluidelement trajectories. This implies that the spatial distribution ofnon-interacting noninertial particles in such flows cannot develop densityinhomogeneities beyond those that are already introduced in the initialcondition. However, in certain practical situations, density is measured oraccumulated on (hyper-) surfaces of dimensionality lower than the fulldimensionality of the flow in which the particles move. An example is theobservation of particle distributions sedimented on the floor of the ocean. Insuch cases, even if the initial distribution of noninertial particles isuniform within a finite support in an incompressible flow, advection in theflow will give rise to inhomogeneities in the observed density. In this paperwe analytically derive, in the framework of an initially homogeneous particlesheet sedimenting towards a bottom surface, the relationship between thegeometry of the flow and the emerging distribution. From a physical point ofview, we identify the two processes that generate inhomogeneities to be thestretching within the sheet, and the projection of the deformed sheet onto thetarget surface. We point out that an extreme form of inhomogeneity, caustics,can develop for sheets. We exemplify our geometrical results with simulationsof particle advection in a simple kinematic flow, study the dependence onvarious parameters involved, and illustrate that the basic mechanisms worksimilarly if the initial (homogeneous) distribution occupies a more generalregion of finite extension rather than a sheet.

Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows