The Countoscope: measuring self and collective diffusion with fancy counting
Modern microscopy techniques can image complex, microscopic systems with an unprecedented resolution – but methods to analyze these images are much less robust. Available techniques rely on reconstructing and analyzing particle trajectories which can be difficult or impossible in dense, heterogeneous systems, or when particle frequently flux through the finite field of view. Inspired by the early work of Smoluchowski we introduce the `Countoscope’, a technique that near completely ameliorates the issues with trajectory-based techniques by simply dividing images into observation boxes and counting the number particles in each box. We show that by analyzing the statistical properties of particle number fluctuations in observation boxes of varying sizes, we can `zoom’ in or out to measure individual or collective particle kinetics. Using colloidal suspensions as a test case, we employ a combination of experiments, simulations, and analytical theory to support our findings. The `Countoscope’ is a potent tool to interrogate biological and soft matter systems, both in and out of equilibrium, and its development is ongoing.
Brennan Sprinkle is an Assistant Professor of Applied Mathematics at the Colorado School of Mines, in Golden, CO. Dr. Sprinkle received is B.S. and M.S. in Applied Mathematics from the Colorado School of Mines in 2011 and 2013, respectively. He received his Ph.D in applied mathematics from Northwestern University in 2018. From 2018 to 2022, he was a postdoctoral researcher and Courant instructor at the Courant Institute of Mathematical Sciences at New York University. His research interests include designing numerical simulation tools to study problems in soft matter physics and fluid dynamics.