Dynamic contact angles and spreading on a flat plate at moderately low velocities

When a liquid displaces another immiscible fluid along a solid surface, the intersection of the three phases defines a dynamic contact line. Classical hydrodynamic analysis of this region leads to a non-integrable stress singularity and velocity-dependent contact angles, motivating extensive theoretical and experimental investigation. In this work, the flow field in the vicinity of the contact-line corner is analysed for small substrate velocities, U, with an asymptotic expansion carried out to O(U2) for the first time for a liquid-liquid system, focusing on regimes of large dynamic contact angles. The singularity is regularized using the molecular-scale cutoff proposed by de Gennes. Predictions from this formulation are systematically compared with experimental data across multiple configurations, as well as with alternative regularization approaches. The cutoff-based model is shown to provide a robust and versatile framework for describing dynamic wetting behavior. In parallel, comparisons with other singularity-removal models enable estimation of the small parameter ε, which characterizes microscopic physics introduced into continuum descriptions. Notably, a framework that bridges continuum hydrodynamics with equilibrium, yields ε by matching, that is, using singular perturbation theory, in excellent agreement with those inferred from experiments once kinetic theory is also invoked. These results, reported here for the first time in a unified manner, offer new insight into the interplay between macroscopic flow and microscopic physics at moving contact lines, with direct implications for predicting wetting rates, interfacial forces, and evolving interface profiles.