Geometric Rectification of Surface Activity Induced Flow in Confined Channels

Abstract: Conventional pressure-driven flow obeys Poiseuille's law, with the mean velocity scaling as $u \propto r^2$ under confinement. Here we identify a distinct transport mode driven by spatially structured surface activity (e.g., mass exchange or boundary slip gradients), which is rectified by geometric asymmetry into a net axial flux. Using a minimal exchange model, we show that this mechanism exhibits four defining signatures that are inconsistent with classical lubrication theory: (i) an inverted confinement scaling $u \propto r^{-1}$ (``narrower-is-faster''); (ii) leading-order viscosity independence; (iii) macroscopic length amplification ($Q \propto L$); and (iv) linear superposition with pressure-driven flows. These results establish confined channels as active geometric rectifiers and provide a unified framework for surface-induced transport from microfluidic to biological settings.