Quantitative measurement of fluid inertial effects in confined Brownian motion

The hydrodynamic response of Brownian particles in liquids is fundamentally altered by inertial forces arising from unsteady momentum transport in the surrounding fluid. These forces are of two distinct types\,: the added mass and the history effect. While both are well understood in bulk and weakly-confined geometries, under deterministic driving, their respective behaviours under strong confinement and thermal fluctuations remain scarcely addressed, unclear and often entangled together. The goal of the present study is thus to fill this fundamental gap. The behaviours of the two distinct inertial contributions are quantitatively investigated in the vicinity of a flat, rigid wall, using a combination of broadrange thermal colloidal-probe atomic-force-microscopy experiments, advanced numerical simulations and theory. The separation of the added-mass and history-force contributions is achieved through their different frequency-scaling signatures within the measured high-resolution thermal spectra. Our results establish a complete picture of Brownian motion at interfaces, in the lubrication regime, with direct relevance to nanofluidics and interfacial biophysics.