Colloidal random-walkers for probing anomalous diffusion in heterogeneous micro-environments

The natural habitat of many microorganisms is not a simple homogeneous environment. A ubiquitous observation is that diffusion becomes anomalous with nonlinear scaling between mean-squared displacement and time. A major challenge in biological sciences and condensed matter physics is to uncover these links to gain insight paramount for design of efficient filter membranes, medical diagnostics and drug delivery, and micro-robots operated in heterogeneous environments.
Building on our recently developed tunable colloidal random walker, we combine microfluidics experiments with theory to characterize and quantify the degree of anomalous diffusion. We define high-order measurable microstructural descriptors which carry information on connectivity and clustering of the designed obstacles that offer a convenient platform to test the theoretical predictions. Results reveal a complex nature of interactions between the colloidal random walker and obstacles which goes beyond a simple correlation between the diffusive behavior and obstacle volume fraction. Using scaling analysis, we provide new quantitative measures for predicting how anomalous diffusion emerges in a heterogeneous micro-environment with known morphological information.