ICON₁₀: Constitutive Breakdown Validation Suite

1. The Continuum Paradox in NanoconfinementThe Navier-Stokes equations rely on the local constitutive assumption, where shear stress is linearly proportional to the local velocity gradient via a constant viscosity. While valid for macroscopic bulk flows, this assumption breaks down in nanoconfined fluids (channel heights below 20 nm). In these regimes, the discrete molecular granularity becomes comparable to the system size, violating the separation of scales required for continuum hydrodynamics. 2. Rigorous Methodological FrameworkThis suite implements a first-principles validation pipeline using Molecular Dynamics (MD) simulations of Lennard-Jones fluids.- Irving-Kirkwood Formalism: We compute the exact microscopic stress tensor, decomposing it into kinetic and configurational contributions. The critical configurational term is calculated via the bond-line integral method, ensuring precise local momentum conservation across arbitrary control volumes.- Hydrodynamic Limit Verification: The methodology is first benchmarked in the bulk limit, confirming the recovery of the analytical Poiseuille flow profile and the matching of the extracted effective viscosity with Green-Kubo bulk predictions. 3. Systematic Breakdown Analysis (Three Regimes)We probe the failure of the local constitutive law across three distinct confinement levels: A. Strong Confinement (7.5 nm): Slip-Dominated RegimeIn the narrowest channels, transport uses a plug-like flow mechanism. The breakdown is driven by massive boundary slip, where the slip length reaches approximately 22% of the channel height. The concept of local viscosity becomes ill-defined as surface effects dominate bulk rheology. B. Moderate Confinement (12 nm): Transition RegimeA mixed transport mode emerges. The fluid exhibits both significant boundary slip (10% of channel height) and the onset of viscosity stratification. The effective viscosity begins to deviate spatially, creating a non-uniform rheological profile. C. Weak Confinement (20 nm): Stratification-Dominated RegimeIn wider nanochannels, slip becomes negligible (1%). However, the local law still fails due to strong molecular layering near the walls. This structural ordering creates sharp viscosity gradients, with wall viscosity exceeding bulk viscosity by nearly an order of magnitude. 4. Theoretical ImplicationsThe universal failure of the local stress-strain relationship across all tested regimes implies that viscosity is not a material constant under confinement. The results demonstrate that momentum transport becomes fundamentally non-local: the stress at a given point depends on the velocity gradients throughout the entire channel history. This necessitates replacing the differential Navier-Stokes operator with a non-local integral operator, governed by a spatial kernel that encodes boundary correlations and memory effects.