Abstract:
The invasion of one fluid into another of higher viscosity is unstable in a quasi-two dimensional geometry. This viscous-fingering instability typically produces complexpatterns that are characterized by repeated branching of the evolving structure, which leads to the common morphologies of fractal or dense-branching growth. However, for two miscible fluids with a high viscosity ratio between the inner and the outer fluid, an entirely different type of pattern formation occurs. Here, structures form that, most remarkably, all expand at nearly the same rate in all directions. This leads to patterns that do not change shape as they develop. This type of growth is called proportionate growth and it has not previously been identified in a physical system despite its common occurrence in the biological world. Such growth relies on a high degree of regulation of the growth rate of widely separated features. We discuss the characteristics of this growth and its relation to the common morphologies of fractal, dense-branching and dendritic growth.