Spreading and rebound dynamics of sub-millimetre urea-water-solution droplets impinging on substrates of varying wettability

Abstract The interaction of droplets consisting of urea-water solution (UWS) with a wall is of interest for automotive exhaust gas after-treatment of Diesel engines by selective catalytic reduction (SCR). Since the impingement of tiny UWS droplets on the solid substrate is difficult to examine experimentally, little is known about the detailed dynamics of this process. In the present study, the normal impact of single UWS droplets impinging on dry solid substrates of greatly differing wettability is investigated numerically under axisymmetric conditions. Simulations are performed by a diffuse interface phase-field solver developed by the authors where the coupled Cahn-Hilliard Navier-Stokes equations are solved using OpenFOAM. The code is thoroughly validated against a number of experiments from literature considering the rebound of millimetre-sized water droplets from hydrophobic substrates. The numerical simulations on the impact dynamics of UWS droplets cover wide ranges of sub-millimetre droplet sizes and impact velocities that are relevant in technical SCR systems. A strong influence of substrate wettability on droplet dynamics is identified. Reducing wettability from hydrophilic to superhydrophobic conditions reduces spreading and enables drop rebound with reduced drop-surface contact time. The effects of drop diameter, drop impact velocity and equilibrium contact angle on the maximum spreading ratio are quantified, and regime maps on rebound versus non-rebound (deposition) impact outcomes are provided. The results of the present interface-resolving numerical simulations may be useful for development of more advanced drop-wall interaction models as they are required in CFD codes relying on the Euler-Lagrange approach for large-scale computations of UWS sprays.