A nanoscale flow characterization model based on the apparent boundary layer

The incompatibility between macroscopic continuum assumptions and microscopic molecular mechanisms remains a key challenge in nanoscale flow modeling. To address this issue, this work introduces the concept of an apparent boundary layer, with its thickness denoted as happ. The model is constructed by combining a short-range interaction viscosity model with a fixed-partition viscosity model under flow conservation constraints. The parameter happ is determined through numerical solution of the resulting implicit equation. After model validation, the flow behavior within a single nanopore is systematically analyzed. The results demonstrate that happ is jointly governed by the geometric scale R, contact angle θ, Hamaker constant AH, and the solid–liquid Lennard-Jones size parameter σLS. The absolute thickness happ increases with R, whereas the dimensionless thickness happ/R exhibits a more intricate dependence: at low AH or high σLS, happ/R increases with R (a larger radius yields a larger dimensionless thickness); conversely, at high AH or low σLS, happ/R decreases with R (a smaller radius yields a larger dimensionless thickness). In contrast, θ primarily modulates happ through boundary viscosity and slip contribution; within the effective mapping range, θ regulates happ nonlinearly but exhibits no pronounced saturation over the studied range. AH and σLS display monotonic variations accompanied by significant saturation: both markedly affect the thickness within their respective effective ranges, yet their regulatory effects diminish rapidly beyond a certain threshold. The synergistic interplay among these three parameters ultimately governs the evolution of happ. The maximum effective mapping range of happ occurs in the parameter regime characterized by high θ, high AH, and low σLS. This model bridges the gap between macroscopic description and microscopic mechanisms in nanofluid flow, offering a theoretical reference for understanding transport phenomena in shale matrix nanopores.