Clustering and self-organization in small-scale natural and artificial systems

Abstract

Physical properties of clusters, i.e. systems composed of a 'small' number of particles, are qualitatively different from those of infinite systems. The general approach to the problem of clustering is suggested. Clusters, as they are seen in the graphs theory, are discussed. Various physical mechanisms of clustering are reviewed. Dimensional properties of clusters are addressed. The dimensionality of clusters governs to a great extent their properties. Weakly and strongly coupled clusters are discussed. Hydrodynamic and capillary interactions giving rise to clusters formation are surveyed. Levitating droplet clusters, turbulent clusters and droplet clusters responsible for the breath-figures self-assembly are considered. Entropy factors influencing clustering are considered. Clustering in biological systems results in non-equilibrium multi-scale assembly, where at each scale, self-driven components come together by consuming energy in order to form the hierarchical structure. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 3)'.

Keywords: biological clusters; capillary interactions; cluster; dimension; hydrodynamic interactions; self-organization.

Figure 1.

Classification of clusters and clustering processes. (Online version in colour.)

Figure 2.

Cluster built of interacting particles seen as the network. Particles shown as circles correspond to vertices; edges, shown as lines, correspond to physical interactions between the particles. (Online version in colour.)

Figure 3.

Cluster built from floating polyethylene particles is shown. The scale bar is 3 mm. (Online version in colour.)

Figure 4.

Lateral capillary forces acting between solid particles. φ₁ and φ₂ are the interfacial angles (the meniscus slope angle) at the contact lines separating particles and liquid. (a,c,e) flotation forces; (b,d,f) immersion forces.

Figure 5.

The configurations of levitating droplet clusters are depicted: (a) the hexagonal 2D lattice of the typical ‘large’ clusters is shown; (b) clusters built of 8–14 droplets are depicted [17]; (c) the cluster comprising chain structures is presented [19].

Figure 6.

Typical micro-porous polymer (polystyrene) pattern arising from the breath-figures self-assembly process. Clusters of water droplets condensed on the rapidly evaporated surface of polymer solution give rise to the ordered micro-porous topography. The scale bar is 20 µm.