Jens Eggers - How to make small things

To make a small object, ordinarily one needs a tool with features of corresponding size. Instead, we propose to harness the nonlinear character of free surface dynamics to focus a fluid into very small features. For example, a fluid drop can be forced into a self-similar object by an electric field, producing the so-called “Taylor cone”. But even flow alone is enough to produce very small scales. Stirring a viscous fluid below a free surface produces a linelike singularity whose width is exponentially small in the strength of stirring. A bubble in a viscous flow is even more efficient at generating small features, by focusing onto a single point. Scale invariance of self-similar shapes is broken in that case, so that the observed profile depends on the degree of magnification under which it is observed.