Modeling bursting bubble dynamics

Bubbles of soap and other liquids have long been known to adopt the shape that minimizes their surface area. An isolated bubble is a sphere; bubbles in a foam or cluster meet so that their surfaces form 120° angles at junctions. But that equilibrium picture is far from a complete description of a foam, an inherently nonequilibrium system. Under pressure gradients and gravity, fluid drains from the liquid films that constitute the bubble walls. When one of the films gets too thin, it ruptures. The remaining bubbles are left to rearrange into a new configuration, and the cycle begins again. Each of the processes affects the others, but they occur on such different length and time scales that recreating them all in a single numerical simulation has been computationally prohibitive. Now mathematicians Robert Saye and James Sethian (University of California, Berkeley) have created a framework for capturing the essential physics from the various scales while efficiently using computer resources. For each of the three processes—drainage, rupture, and rearrangement—they developed a separate numerical model with its own equations, simplifying assumptions, and characteristic time step. By treating each process in turn with the appropriate model, they can transmit the critical information from one scale to another and produce realistic simulations of large bubble clusters. The researchers anticipate that by modifying their models to include additional physics—evaporation, liquid–solid phase transitions, and so forth—they'll be able to address a variety of "bubble problems" with industrial and scientific applications. (R. I. Saye, J. A. Sethian, Science 340, 720, 2013.)—Johanna Miller