University of Chicago MRSEC: IRG 2

1. IRG 2: Shock-front Scars: A clue to fractal tree- like growth Blowing air into a fluid-soaked porous medium creates a multibranched tree-like bubble. Despite its chaotic randomness, the subbranches mimic the larger branches in a strict statistical relationship, also seen in the dendritic growth of mineral deposits. Physicists have struggled for decades to account for this quantitative mimicking. Experimentallists and theorists at the Materials Research Center at the University of Chicago have found a new way to understand these phenomena by devising novel variants of the process. The new theory ignores the surface tension of the bubble but allows the fluid to compress. As Paul Wiegmann and collaborators show[1], the result is a cusp that propagates into the fluid, as seen experimentally (right) [2]. The theory becomes tractable in an idealized limit. Then the cusps take the form of shock fronts (right) that repeatedly branch as they grow, thus capturing an important element of the puzzling mimicking phenomenon. Work made possible through NSF MRSEC DMR-0213745 and DMR-0820054. [1] “Shocks and finite-time singularities in Hele-Shaw flow,” S. Y. Lee, R. Teodorescu, P. Wiegmann, Physica-D, 238 1113-1128 (2009). [2] “Toward the zero surface tension limit in the granular fingering instability,” Xiang Cheng, Lei Xu, A. Patterson, H. M. Jaeger and S. R. Nagel, Nature Physics 4 234-237 (2008) University of Chicago MRSEC: IRG 2