Effect of convective stretching and folding on aerosol mixing deep in the lung, assessed by approximate entropy

There is a surprisingly substantial amount of aerosol mixing and deposition deep in the lung, which cannot be explained by classic transport mechanisms such as streamline crossing, inertial impaction, or gravitational sedimentation with reversible acinar flow. Mixing associated with "stretch and fold" convective flow patterns can, however, be a potent source of transport. We show such patterns in experimental preparations using rat lungs and in the theoretical Baker Transform. In both cases, mixing is associated with the temporal evolution of two length scales. The first is the slowly increasing diffusive length scale. The second is the rapidly decreasing lateral length scale, due to "stretching and folding," over which diffusion must take place. This interaction leads to aerosol mixing in much shorter times than previously appreciated. Finally, we propose a new method by which to quantify the state of mixing, using an approximation to the entropy of the aerosol concentration distribution. The results of the analysis suggest that stretching and folding may be a key feature underlying peripheral aerosol transport.