It is interesting to speculate whether under ideal conditions -- with an initially homogeneous membrane -- the tube spacing might be determined by a dynamical instability. The model put forward by Sørensen [43] attempted to address this question, but found no such characteristic wavelength of instability. Sørensen suggested that the addition of additional factors to his model might provide the answer, and Jones and Walter [33] speculated as to the physical mechanism that might lead to such an instability. In the initial stages of chemical-garden membrane formation and expansion, especially if buoyancy may be suppressed, as in microgravity, molecular transport is diffusive rather than convective. The chemical-garden system may be considered as a flexible self-renewing semipermeable membrane that hardens slowly and is subjected to osmotic pressure. A flat membrane, or one with constant curvature, may become unstable under internal pressure, as a slightly more flexible region will form a bulge, and in the process become thinner, be renewed by diffusion with fresh membranous material, and thence weaken further and develop into a finger. This describes the instability of Laplacian growth first noted by Mullins and Sekerka [44], and so chemical-garden tube formation would be related to viscous fingering, dendritic growth, and dielectric breakdown among many other systems describable with the Laplace equation. However, although it is appealing to consider, in the actual experiments the membrane is rather inhomogeneous, and ruptures at its weakest points, so there is no evidence of this. With other reagents a characteristic spacing of tubes may be more apparent; cf. Fig. 2 of Double and Hellawell [18], and Fig. 1 of Coatman et al. [13], both obtained with cobalt nitrate.
There are a couple of phenomena commonly noted in work on chemical gardens that we have not yet mentioned. Leduc [1], Hazlehurst [6], and others have observed segmentation and striation patterns on chemical-garden tubes. These appear to derive from a periodic growth mechanism for a tube that forms not by continuous accretion at its open end, but as a series of vesicles that accumulate in line by membrane formation and rupture. We have occasionally observed some such segmentation effects, but they are not present in the experiments shown here. Possibly they require weaker osmotic and convective processes that may be produced with different reagents. Hazlehurst [6] proposes that the main mechanism of tube growth involves a gas bubble trapped in the tube mouth. We have not observed such bubbles in our work. The reason for this may be that we performed our experiments in a closed growth cell, while his were open to the atmosphere. Although if they are present they may accelerate tube growth, our work shows that gas bubbles are not necessary components for chemical-garden formation.
Chemical-garden experiments have long been used to excite the interest of the non-scientific public in chemistry, and are included in most chemistry sets for children [45]. They have even entered literature, being mentioned in Thomas Mann's novel Doktor Faustus [46]. It is ironic, then, that this first introduction to chemistry is a complex phenomenon not fully understood after more than a century of study. Our aim in this work has been to carry a step forward the knowledge of the mechanisms involved in forming these fascinating patterns. From Leduc's synthetic biology [1], Herrera's plasmogeny [2], and others pursuing similar researches -- see Chapter 10 of Leduc's book for a review of the investigators then active in the field and their findings -- came studies of chemical-garden growths imitating many natural forms: stems, leaves, twigs, roots, shells, mushrooms, and other fungi, flowers, amoebae, and worms. These they produced by varying the composition and concentrations of the reacting solutions during the growth phase. They were searching for the origin of life, an end that as we now understand, could not be achieved without a knowledge of biochemistry. Their researches, although now nearly forgotten, were not however in vain. Their accurate descriptions of chemical-garden formation are as valid today as a century ago. Leduc argued that the formations were osmotic growths, while Herrera maintained that buoyancy forces were the critical component. We have shown here that, on Earth at least, chemical gardens result from a combination of these two mechanisms.