Stretching and breakup of droplets in chaotic flows

We investigate the stretching and breakup of a drop freely suspended in a viscous fluid undergoing chaotic advection. Droplets stretch into filaments acted on by a complex flow history leading to exponential length increase, folding, and eventual breakup; following breakup, chaotic stirring disperses the fragments throughout the flow. These events are studied by experiments conducted in a time-periodic two-dimensional low-Reynolds-number chaotic flow. Studies are restricted to viscosity ratios p such that 0.01 1, on the other hand, stretch substantially, O (10 2 –10 4 ), before they break, producing very small fragments that rarely break again. This results in a more non-uniform equilibrium drop size distribution than in the case of low-viscosity-ratio systems where there is a succession of breakup events. We find as well that the mean drop size decreases as the viscosity ratio increases. The experimental results are interpreted in terms of a simple model assuming that moderately extended filaments behave passively; this is an excellent approximation especially for low-viscosity-ratio drops. The repetitive nature of stretching and folding, as well as of the breakup process itself, suggests self-similarity. We find that, indeed, upon scaling, the drop size distributions corresponding to different viscosity ratios can be collapsed into a master curve.