The motion of spherical micro- and nano- particles in a solvent under gravity, known as sedimentation, is common in nature and technology. While the flow of an individual sphere obeys the classical Stokes’ law, at finite particle concentrations the physics is much more complex, with the sedimentation rates depending nonlinearly on time and position along the sample, as also on tiny temperature gradients which invariably exist in most experimental systems. In some cases, an initially-homogeneous suspension, subject to an effective gravity in a centrifuge, spontaneously forms well-defined layers of constant particle density, so that the density changes in a staircase-like manner along the axis of gravity. This spectacular phenomenon is well-known for longer than a century; yet, it has never been quantitatively studied under reproducible conditions so that its physical mechanism remained controversial.

We follow the full dynamics of layer formation in sedimenting suspensions of several different types of nanoparticles in various organic solvents, subjected to an effective gravity in a centrifuge, employing light transmission through the samples. We demonstrate that, with the nanoparticles being used, the layering phenomena are much more robust than in the previous studies, enabling for the first time quantitative and reproducible studies of the effect. Furthermore, we vary the effective gravity g in the centrifuge to study the critical onset of layering, demonstrating that the number of layers N in a sample exhibits a unique power-law scaling as a function of g and the sample height. We reproduce most of our observations by numerical calculations, employing a hydrodynamical model, which attributes the layering to a convective instability, allowing the physical mechanism of the effect to be fully elucidated.