Filament dynamics in vertical confined chemical gardens

Pattern selection by material aging: Modeling chemical gardens in two and three dimensions

Chemical gardens are complex, often macroscopic, structures formed by precipitation reactions. Their thin walls compartmentalize the system and adjust in size and shape if the volume of the interior reactant solution is increased by osmosis or active injection. Spatial confinement to a thin layer is known to result in various patterns including self-extending filaments and flower-like patterns organized around a continuous, expanding front. Here, we describe a cellular automaton model for this type of self-organization, in which each lattice site is occupied by one of the two reactants or the precipitate. Reactant injection causes the random replacement of precipitate and generates an expanding near-circular precipitate front. If this process includes an age bias favoring the replacement of fresh precipitate, thin-walled filaments arise and grow-like in the experiments-at the leading tip. In addition, the inclusion of a buoyancy effect allows the model to capture various branched and unbranched chemical garden shapes in two and three dimensions. Our results provide a model of chemical garden structures and highlight the importance of temporal changes in the self-healing membrane material.

Downward fingering accompanies upward tube growth in a chemical garden grown in a vertical confined geometry

Chemical gardens are self-assembled structures of mineral precipitates enabled by semi-permeable membranes. To explore the effects of gravity on the formation of chemical gardens, we have studied chemical gardens grown from cobalt chloride pellets and aqueous sodium silicate solution in a vertical Hele-Shaw cell. Through photography, we have observed and quantitatively analysed upward growing tubes and downward growing fingers. The latter were not seen in previous experimental studies involving similar physicochemical systems in 3-dimensional or horizontal confined geometry. To better understand the results, further studies of flow patterns, buoyancy forces, and growth dynamics under schlieren optics have been carried out, together with characterisation of the precipitates with scanning electron microscopy and X-ray diffractometry. In addition to an ascending flow and the resulting precipitation of tubular filaments, a previously not reported descending flow has been observed which, under some conditions, is accompanied by precipitation of solid fingering structures. We conclude that the physics of both the ascending and descending flows are shaped by buoyancy, together with osmosis and chemical reaction. The existence of the descending flow might highlight a limitation in current experimental methods for growing chemical gardens under gravity, where seeds are typically not suspended in the middle of the solution and are confined by the bottom of the vessel.

Archimedean Spirals Form at Low Flow Rates in Confined Chemical Gardens

We describe and study the formation of confined chemical garden patterns. At low flow rates of injection of cobalt chloride solution into a Hele-Shaw cell filled with sodium silicate, the precipitate forms with a thin filament wrapping around an expanding "candy floss" structure. The result is the formation of an Archimedean spiral structure. We model the growth of the structure mathematically. We estimate the effective density of the precipitate and calculate the membrane permeability. We set the results within the context of recent experimental and modeling work on confined chemical garden filaments.