Non-Equilibrium Diffusion in Complex Environments

2026-07-22

Diffusion is at the root of a huge number of microscopic structural and transport processes. During the last century, Einstein and Boltzmann's theories were successful in describing equilibrated systems, but they are not applicable to numerous strongly non-equilibrium conditions in nano-technological and macromolecular-scale biological contexts. Notably, many systems involve energy injection at an interface, either under dissipative shear flows or chemical reactivity. These common non-equilibrium situations are difficult to observe with precision and describe with statistical theory. NoDiCE’s purpose is thus to design model experiments placing functional colloidal particles in complex, non-equilibrium environments with quantitative assessment based on delicate and simultaneous observations of the particles’ advective and diffusive motions, along with their precise spatial organization. Our observations exploit evanescent- wave microscopy to observe fluorescent nanoparticles driven out-of-equilibrium in microfluidic devices, providing 3D nanometric precision at kHz temporal scales. Fluorescence correlation and atomic force spectroscopies complement these measurements, providing DC to MHz bandwidth and similar spatial precision. We will demonstrate how non-trivial interactions of hydrodynamic origin with a boundary reveal novel nanoscale self-organization strategies, and learn how to integrate a hydrodynamic component into the statistical theory. We then enter the recent scientific debate about the extent to which Brownian motion can be impacted by reactive environments with catalysis. Lastly, we combine these elements with particles that present specific surface binding and are driven out of equilibrium by an external flow. The insights provided by our model experiments open a path for the developments of breakthrough self-assembly strategies, reaction- pathway analysis based on particle dynamics, and possible next-generation diagnostic tools.

France

2025-10-01