The forces that burst bubbles

Biological organisms use capsules to contain and transport liquid: Red blood cells, fish eggs, and various mammal organs all fit the model of a liquid enclosed in a thin elastic shell. Those examples, along with human-designed capsules used for drug delivery and emulsifying agents, need to withstand trauma. Despite capsules’ importance and ubiquity, how they burst on impact has rarely been examined in the physics literature. Now, using air cannons and high-speed photography, Pierre-Thomas Brun and his colleagues at Princeton University have established the physical rules that govern capsule impact. They find that they can predict the extent to which a capsule shell deforms before bursting and that the value depends on liquid viscosity and shell elasticity.

Brun and his colleagues started with the simple example of a water balloon. Besides buying commercial balloons, the researchers fabricated elastic shells with different shear moduli and used a syringe to fill them with liquids of different viscosities, ranging from water to honey. Then they dropped the capsules from various heights or launched them upward toward a flat surface and recorded the impact with a video camera operating at up to 20 000 frames per second. After impact, the part of the capsule in contact with the surface flattened and spread outward like a pancake, while the rest retained its round shape and continued toward the surface until it joined the outward flow. The capsule then elongated vertically and bounced back, as shown in the figure. In a series of experimental runs, the researchers measured the radial deformation for different elasticities, viscosities, and impact velocities. From those measurements, they derived a model based on the balance between capsule kinetic energy, shell elastic energy, and liquid viscous dissipation. The model predicted both the deformation of the elastic capsules and the bursting point for the water balloons.

The researchers observed that the behavior of a capsule mimics that of an unenclosed liquid droplet, with the capsule shell playing the role of droplet surface tension. However, unlike a droplet, the capsule shell bends and stretches to contain the liquid. The quantitative model could help to refine safety guidelines that minimize the risk of an internal organ bursting during car crashes, to design passive firefighting equipment that delivers flame retardant upon rupturing, and to determine flow behavior in microfluidic devices. (E. Jambon-Puillet, T. J. Jones, P.-T. Brun, Nat. Phys., 2020, doi:10.1038/s41567-020-0832-x .)