Pattern formation in thin film suspensions

Whenever suspensions or granular mixtures flow as a thin film down a substrate, they form patterns on the surface. We identify two classes of pattern that occur universally. The spontaneous formation of these patterns is relevant to the coatings industries and to geophysical applications, and their morphologies are familiar in residues from household fluids, drinks, and accreted dirt on windows among other manifestations. In some well-characterised experimental systems, we show that varying the distribution of particle sizes in a suspension leads to profound changes in the type of pattern that emerges from the flow. A transition is observed, from a pattern of vertical channels, for systems with small particles and a gel-like behaviour of the suspension, to horizontal bands, for systems with large particles in which the granular nature of the suspension plays a dominant role. The ubiquity of these patterns throughout nature is a consequence of the small number of basic features required for their formation. They are intrinsically non-equilibrium phenomena, generated by frictional forces in flowing films. The presence of friction between the suspended particles and a substrate, together with viscous and excluded-volume couplings between the particles and fluid, are sufficient to generate spatial structures on a scale much larger than the particles themselves. The frictional forces are generally mediated by the confinement of the flow to a thin film geometry, where the film thickness decays with time, forcing particles into close proximity with the substrate. While many non-trivial structures have previously been documented in both gel-forming and granular systems, our results demonstrate a striking transition, at the cross-over from the former to the latter, between two pattern types that are immediately recognizable due to their ubiquity and large scale.