Growth and form of a self-constructing tube network.

When a small amount of liquid is quickly injected into another liquid with similar density, the fluid jet usually does not propagate very far. However, when the two solutions chemically react to form a flexible membrane at their interface, then structures that are long and branching can form. Here, we describe the tube networks produced when a small amount of AlCl3 solution is quickly injected into a NaOH solution. Single straight tubes do not occur, but straight tubular "stems" with 2-5 "branches" are observed. The branches emerge relatively symmetrically from the stem at a common branching junction. These structures can have a ratio of propagation distance to stem width as large as 50. The stem and branches grow by the stretching of the membrane sheathing the closed tube system. These tube networks occasionally exhibit the spontaneous creation of new branches at a junction and also the splitting of a branching junction. A model explains why the branches occur, why they are symmetric around the central stem, and why the initial growth speed is insensitive to the flow rate.

The dynamics of open precipitation tubes.

When a flowing fluid is channeled by chemical or physical precipitation, then tubular structures form. These patterns are common in nature, however, there have been few quantitative studies of their formation. Here, we report measurements of the radius, length, and internal pressure, as functions of time and flow rate, for precipitation tubes growing in chemical gardens. Using these measurements we develop models for how single tubes grow and also for how multiple tubes interact with each other. In particular, when multiple tubes grow from the same source they compete for resources; short/wide tubes have less resistance to flow, and so consume more of the resources, "killing" the growth of long/narrow tubes. These tube interactions are described by an equation similar to an unstable logistic equation.

Emergence of complex behavior in chemical cells: the system AlCl3-NaOH.

Chemical cells that spontaneously form in simple inorganic systems are presented. The cells are surrounded by semipermeable membranes that allow water and some ions to diffuse through. These cells exhibit dynamical behaviors that are typically associated with biological entities. These behaviors may be used to perform tasks such as rotation or linear translation in the vertical and horizontal directions. Yet another system builds "curtains". Behaviors are controlled by a complex network of physical and chemical processes that are organized in space and time. The type of dynamical behavior is determined by the chemical composition of the cell and the environment. By studying these systems we may learn general rules for the growth of living entities, or at least about the spontaneous growth of complex chemical structures. Understanding and mastering the synthesis of these systems may lead to new technologies where complex structures are grown rather than assembled.

Chemical precipitation structures formed by drops impacting on a deep pool.

The experiments described here are at the intersection of two dynamical systems with long pedigrees for forming interesting patterns: liquid droplet impacts and precipitation membranes. Drops of calcium chloride solution have been allowed to impact on a deep pool of sodium silicate solution. The precipitation structures produced by this method, and how these structures subsequently evolve, have been observed. Many interesting patterns can be formed from this process. It is observed that the precipitation patterns produced are sensitive to the shape of the drop when it impacts the pool's surface. Also, at large drop heights, we determine two critical Weber numbers: one for forming a skirt around the structures and the other for breakup of the structures. On longer time scales, open tubes grow from the closed precipitation shell produced at lower drop heights. These tubes can appear in large numbers with nearly identical sizes and diameters as small as 50 µm.

Precipitation pattern formation in the copper(II) oxalate system with gravity flow and axial symmetry.

Chemical systems that are far from thermodynamic equilibrium may form complex temporal and spatiotemporal structures. In our paper, we present unusual precipitation patterns that have been observed in the system of Cu(II)-oxalate. Starting with a pellet of copper sulfate immersed in or by pumping copper sulfate solution into a horizontal layer of sodium oxalate solution, we have observed the formation of a precipitate ring and an array of radially oriented thin fingers. The development of these patterns is related to the internal structure of the different crystals, the gravity flow, and the circular symmetry of the experimental arrangement.

Pressure oscillations in a chemical garden.

When soluble metal salts are placed in a silicate solution, chemical gardens grow. These gardens are treelike structures formed of long thin hollow tubes. The growth is driven by the increase in internal pressure from osmosis. One particular case is examined here, calcium chloride in a solution of sodium trisilicate. We directly measure the internal pressure of a silicate garden as it grows via a series of relaxation oscillations. From these observations we deduce the stresses in the membrane and discuss how they influence the growth of tubes. Also we estimate the critical stress and the average Young's modulus for the silicate garden's membrane.

Oscillations of a chemical garden.

When soluble metal salts are placed in a silicate solution, chemical gardens grow. These gardens are treelike structures formed of long, thin, hollow tubes. Here we study one particular case: a calcium nitrate pellet in a solution of sodium trisilicate. We observe that tube growth results from a relaxation oscillation. The average period and the average growth rate are approximately constant for most of the structures growth. The period does fluctuate from cycle to cycle, with the oscillation amplitude proportional to the period. Based on our observations, we develop a model of the relaxation oscillations which calculates the average oscillation period and the average tube radius in terms of fundamental membrane parameters. We also propose a model for the average tube growth rate. Predictions are made for future experiments.