The dynamics of even modest sand particles still hold many surprises. When air is intermittently blown over sand, meso- and macroscopic structures appear, most magnificently witnessed in the structure of dunes and regularly spaced, striped patterns. Blow air through sand in a column, and a chaotic bubble stream appears above the minimum fluidization velocity of the sand particles. Yet, this same bubble stream becomes remarkably regular when the airflow is pulsed within a range of amplitudes and frequencies. A thin layer of sand on a vertically vibrated plate also forms regular patterns, and similar patterns form when the plate is not vibrated but porous and fluidized under the influence of an oscillating gas flow, again within a continuous range of frequencies.
Our most recent experiments and simulations are revealing new insights in these phenomena. Generally speaking, the patterns are a result of dynamic perturbation of a system out of equilibrium; they represent nonlinear resonance in a dissipative system. However, this generalized description does not tell us when which pattern forms, how stable it is, and how it is influenced by boundary conditions, gas-solid and solid-solid interactions. Conventional two-fluid models do not reproduce the experimentally observed patterns, likely because the long force-chains between particles are not properly accounted for in the two-phase closures of the (Eulerian-Eulerian) two-fluid model. Multiscale models that include discrete particles (a Lagrangian-Eulerian description) are required.
Interestingly, at much smaller length scales (about seven orders of magnitude smaller!), similar patterns are observed in the ordered pore structure of sub-micron sized nanoporous silica particles made by a process involving soft templating in an aerosol reactor. The particles form within seconds when a solution including tri-block copolymer micelles and silica precursors is sprayed through a tubular oven. Ordered polymer-silica composite particles form by evaporation induced self-assembly (EISA). After calcination of the polymeric phase, a regular array of pores emerges instead of the ordered polymeric phase. When a single, spherical particle of mesoporous silica produced in this way is observed by electron tomography, it reveals patterns that compromise between hexagonal order and the spherical surroundings, very similar to the self-assembled structures generated in the fluidized sand, but “frozen” in time. The details of the underlying system are no doubt different, but energy minimisation under constraints leads to very similar structures.
One can really see a world in a grain of sand.
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