Swimming bacteria are the paradigmatic example of biological self propelled particles. These systems show many interesting phenomena such as enhanced transport and rectification but it is hard to predict their behavior when they move in complex and disordered environments such as those encountered in real-life situations (e.g soil, biological tissues, etc.).
The present project aims to the systematic experimental investigation of swimming bacteria in disordered environments fabricated by soft lithography. The experiments will test a fundamental invariance theorem for random walks in bounded domains. The theorem predicts that the average length of the path in the domain, from entrance to exit, depends only on the ratio between the surface and the perimeter of the domain. This theorem was inspired by studies on ants, however its first experimental demonstration appeared only recently for photons in strongly scattering media (Savo et al., Science 2017). Our preliminary results show that the theorem is valid also for bacteria freely swimming on a surface. We want to exploit this universal property as a starting point to understand the behavior of bacteria swimming through a domain patterned with random obstacles. This will let us to expand the statistical mechanics of active matter tackling the problem of self-propelled particles in complex environments.
This research will tackle the open problem of self-propelled particles in presence of a complex environment combining an high-throughput experimental technique with a theoretical framework which has not been exploited so far. Understanding for which values of obstacle density and/or size the invariance theorem holds will be the milestone for the development of further theory. The project will give the possibility to study in detail the breakdown of the theorem in specific situations. For example if the obstacles are large and convex they can 'hydrodynamically trap' bacteria on their surface [5]. This will open many unexplored but relevant question such as how does the mean path length deviate from theory? Can be the theory be generalized including these specific trajectories bounded by an attractor?
Moreover this study could suggest important practical principles for medical applications, defining the optimal geometry of surfaces to reduce the efficiency of bacteria in exploring their environment and seek for nutrients and hinder the formation of colonies and biofilms.