  Dynamic wetting processes inherently manifest as multiscale phenomena. While
the capillary length is typically millimeters, solid-liquid interactions occur
at the nanometer scale. These short-range interactions significantly affect
macroscopic behaviors like droplet spreading and menisci dynamics. The Navier
slip length, determined by liquid viscosity and solid-liquid friction, plays a
crucial role in three-phase contact line dynamics. It varies from nanometers
(hydrophilic) to microns (hydrophobic). However, resolving it in computational
fluid dynamics (CFD) simulations can be computationally expensive. In this
study, we propose simplified ordinary differential equation (ODE) models,
leveraging local dissipation rates from Stokes flow solutions near the moving
contact line, to bridge the nanoscale physics and macroscopic dynamics. Our ODE
model accurately predicts the impact of the slip parameter in fully resolved
CFD simulations, focusing on capillary rise dynamics.
