Experimental observations of fractal landscape dynamics in a dense emulsion

TL;DR

This study demonstrates that the complex, random motion of droplets in a dense emulsion can be explained by their movement over a high-dimensional fractal energy landscape, linking empirical data with theoretical models.

Contribution

It provides a model-free method to analyze and quantify the fractal geometry of energy landscapes from empirical trajectory data in soft glassy materials.

Findings

Empirical trajectories reveal high-dimensional fractal landscape features.

The observed droplet dynamics match computational model predictions.

Experimental data can elucidate fractal landscape influences in soft materials.

Abstract

Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening foam, suggested that the random motions of its bubbles are due to the system configuration moving over a fractal energy landscape in high-dimensional space. Here we show that the salient geometrical features of such high-dimensional fractal landscapes can be explored and reliably quantified, using empirical trajectory data from many degrees of freedom, in a model-free manner. For a mayonnaise-like dense emulsion, analysis of the observed trajectories of oil droplets quantitatively reproduces the high-dimensional fractal geometry of the configuration path and its associated energy minima generated using a computational model. That geometry in turn drives the droplets' complex random motion observed in real space. Our results indicate that experimental studies can elucidate whether the similar dynamics in different soft and biological materials may also be due to fractal landscape dynamics.