Viscoelastic Droplet Impact on Surfaces with Sharp Wettability Contrast: Coupled Influence of Relaxation Time and Surface Tension

Abstract

The impact dynamics of viscoelastic droplets on solid surfaces play a critical role in numerous applications, including inkjet printing, spray coating, and microfluidics, where precise control of spreading, retraction, and rebound is essential. This numerical study investigates the coupled influence of fluid viscoelasticity, modeled via the Oldroyd-B constitutive equation, and gravitational-capillary balance on droplet behavior upon impact onto surfaces featuring sharp hybrid wettability. Employing a high-fidelity three-dimensional OpenFOAM-based solver that integrates the volume-of-fluid method, log-conformation formulation for improved numerical stability, and a velocity-dependent dynamic contact angle model, we simulated a 2 cm-diameter droplet impacting at 4 m/s across a range of relaxation times and surface tensions. Results demonstrate that increasing the relaxation time from 0.02 s to 0.12 s enhances elastic energy storage, leading to up to 12.9% larger maximum spreading diameters (from 24.97 mm to 28.09-28.17 mm) and a 16.6% reduction in minimum droplet height across uniform and hybrid surfaces. In contrast, increasing surface tension from 0.05 N/m to 0.15 N/m suppresses maximum spreading by about 1.1% (from 27.21 mm to 26.90 mm) while increasing minimum height by 3.3% (from 2.12 mm to 2.20 mm). On hybrid surfaces with static contact angles of 0{\deg} and 160{\deg}, the sharp wettability contrast induces pronounced asymmetric spreading and directional fluid migration toward the hydrophilic region, ultimately producing distinctive dustpan- and shoe-like equilibrium morphologies. Variations in surface tension, which simultaneously modulate the Weber and E\"otv\"os numbers, reveal that stronger capillary forces suppress radial expansion while enhancing curvature-driven recoil and redistributing viscoelastic stresses.