Incorporating the Molecular-scale into a Hydrodynamic Description of Confined Aqueous Systems

Hydrodynamics provides a continuum-level description of fluid motion, but its applicability at the nanoscale is uncertain due to emerging molecular-level effects such as spatial heterogeneity. Hydrodynamic boundary conditions incorporating molecular details partition the system into a near-wall region with distinct local properties and a bulk fluid region. We identify a hydrodynamic wall inside the fluid that marks where slip begins. Extending this wall by the slip length establishes the position of the extrapolated wall, offering a unified description of slip and stagnant flow, with wall hydrophobicity characterized by its relative location to the physical wall. Analyses of equilibrium and non-equilibrium molecular dynamics (MD) simulations of Couette and Poiseuille flows show consistency across flow types and confinement levels, demonstrating the robustness of linear response theory. We then examine the effects of fluid-wall and bulk fluid interactions on hydrodynamic properties and extend the analysis to beidellite clay systems with varying surface charges. These findings improve molecular simulations of complex confined systems in nanofluidics, biology, and colloidal science, providing a complementary molecular-scale perspective to continuum approaches.