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.