Spreading dynamics of a droplet upon impact with a liquid film containing solid particles

This study examines how a deionized water droplet behaves when it centrally collides with a liquid film containing TiO₂ nanoparticles at low impact velocities, aiming to understand how nanoparticles affect droplet spreading, in particular its maximum spreading diameter. Typically, we found that both the spreading velocity and dynamic contact angle of the droplet would be similarly affected by increasing TiO₂ nanoparticle concentration. During retraction, the droplet's dimensionless spreading diameter oscillates, with more pronounced oscillations at higher nanoparticle concentrations. Moreover, both the droplet's maximum dimensionless rebound height and dynamic contact angle show similar trends with increasing TiO₂ nanoparticle concentration. Interestingly, we proved that the influence of the solid-liquid interaction (Stokes force) on the fluid during the spreading process accounts for less than 2% of the surface energy when the droplet reaches its maximum spreading diameter, indicating a negligible effect on droplet spreading. We hypothesize that the droplet's initial energy is fully converted into surface energy and viscous dissipation at maximum spreading diameter, which involves viscous dissipation both between the fluid and the solid wall surface and the fluid and solid particle surface. Based on this, we developed a model for predicting the droplet's maximum spreading diameter that includes parameters associated with the solid particles. Compared to models in the literature that do not consider the effect of solid particles, our model aligns more closely with experimental data. The results indicate that adding solid particles leads to increased viscous dissipation, which in turn reduces the droplet's maximum spreading diameter.