We report distinct growth regimes of hollow silica fibers formed by hydrodynamic injection of cupric sulfate into silicate solution. The tubes grow either steadily along a continuous jet of buoyant solution or through relaxation oscillations that are governed by chemo-mechanical processes. The dependence of the oscillation period on flow rate and copper concentration is explained in the framework of a simple model. Tailored flow patterns allow the directional control of the tubes and their use as miniature connectors. Our findings are applicable to the understanding of chemical gardens, promise a wealth of nonlinear phenomena, and offer possible applications in microfluidics.

Abstract. -Chemical gardens consist of hollow silica fibers that form from silicate solution upon seeding with salt crystals or injection of salt solution. We investigate the outer radius of these tubes for steady and oscillatory growth dynamics. The radius increases with increasing injection rates and concentrations of cupric sulfate seed solution. For steady growth, we find that the tube radii are described quantitatively by the Poiseuille-flow characteristics of the buoyant jet of injected solution. The oscillatory regime gives rise to wider tubes and involves the cyclic expansion and detachment of a membrane-bound droplet at the growth point. The droplets' expansion rate equals the applied injection rate indicating that, in this growth regime, the fluid flow is constrained to the interior of the silica structures.A variety of seemingly unrelated reaction-precipitation systems can give rise to the growth of mesoscopic tubular structures. Examples include hollow rust fibers [1,2] formed in corrosion processes and microscopic, needle-like tubes created during the setting of cement [3]. The latter example is closely related to the formation of silica tubes in chemical gardens which are a well-known demonstration experiment in physics and chemistry [4]. Chemical gardens involve the growth of colorful, plant-like fibers from aqueous solutions containing anions such as aluminate, borate, carbonate, or silicate [5][6][7]. These structures have diameters in the micro-and millimeter range and reach lengths of several decimeters. Tube growth can be induced by seeding the latter solutions with crystals of various soluble salts (e.g., CuSO 4 , MnCl 2 , FeCl 3 ) excluding group (I) compounds [7].Early references to chemical gardens can be traced back to the 17th century [8,9]. In the 20th century, these structures attracted considerable interest because they were mistaken to be prototype models of simple life forms [10]. Recently, the study of chemical gardens has been experiencing a renaissance as tubular structures in the aluminosilicate system have been shown to be promising catalytic materials with an intriguing hierarchical nanostructure [11,12]. For

Silica gardens consist of hollow tubular structures that form from salt crystals seeded into silicate solution. We investigate the structure and elemental composition of these tubes in the context of a recently developed experimental model that allows quantitative analyses based on predetermined reactant concentrations and flow rates. In these experiments, cupric sulfate solution is injected into large volumes of waterglass. The walls of the resulting tubular structures have a typical width of 10 microm and are gradient materials. Micro-Raman spectroscopy along with energy dispersive X-ray fluorescence data identify amorphous silica and copper(ii) hydroxide as the main compounds within the inner and outer tube surfaces, respectively. Upon heating the blueish precipitates to approximately 150 degrees C, the material turns black as copper(ii) hydroxide decomposes to copper(ii) oxide. Moreover, we present high resolution transmission electron micrographs that reveal polycrystalline morphologies.

Numerous types of reaction-precipitation systems involve the growth of tubular structures similar to those formed in "silica gardens". As a model case for this phenomenon, we investigate the rapid growth of hollow tubes in the reaction between sodium silicate and cupric sulfate. The latter solution is injected hydrodynamically at constant flow rates of 1-20 mL h(-1) into a large reservoir of waterglass. In this study, the growth is templated and guided by single, buoyant gas bubbles. The resulting tubes can be several decimetres long and have constant radii in the range of 100-600 microm. Systematic measurements show that bubble size governs the tube radius. According to this radius, the system selects its growth velocity following volume conservation of the injected solution. Moreover, scanning electron microscopy reveals intricate ring patterns on the tube walls. We also show evidence for the existence of a minimal and a maximal tube radius. Finally, we report an intriguing collapse of tubes created at high silicate concentrations, which yields twisted ribbon-like structures. Critical radii and tube collapse are discussed in terms of simple competing forces.

Two reaction systems that are at first sight very different produce similar macroscopic filamentary product trails. The systems are chemical gardens confined to a Hele-Shaw cell and corroding metal plates that undergo filiform corrosion. We show that the two systems are in fact very much alike. Our experiments and analysis show that filament dynamics obey similar scaling laws in both instances: filament motion is nearly ballistic and fully self-avoiding, which creates self-trapping events.