Critical thresholds in molecular transport through nanogrooves.

Liquid transport through nanometre-scale grooves departs from classical continuum behaviour as confinement approaches only a few molecular diameters. In this regime, the central challenge is to determine where linear, continuum-like response breaks down and molecular occupancy begins to control the effective flow domain. Here we use non-equilibrium molecular dynamics simulations of simple liquid argon confined in rectangular grooves between copper walls (width 1-4 nm; depth 0.5-2.5 nm) to isolate geometry-driven effects. We show that confinement induces strong layering and exclusion zones that reduce the hydraulically active region, and we introduce an accessible flow depth defined from time-averaged molecular occupancy relative to an ideal continuum filling. This metric reveals a clear breakdown threshold: for wide grooves, continuum-like behaviour holds down to a depth of ∼1.5 nm, below which flow rate and occupancy deviate sharply from macroscopic predictions; in narrower grooves the deviations are stronger and persist across the studied depths. These results provide a compact, physics-based baseline for groove-confined liquid transport and offer practical guidance for designing etched-like features with predictable delivery, relevant to advanced semiconductor fabrication where groove dimensions are now in the single-digit-nanometre range.