Numerical investigation of droplet impacting, spreading and penetration on porous substrates

The behavior of droplets impacting porous surfaces, including spreading and penetration, plays a critical role in various engineering applications, yet the underlying mechanisms governing the interaction between these processes remain unclear. In this study, the complex interplay between droplet spreading and penetration on porous media was comprehensively investigated using the Level Set method. The droplet evolutions outside and inside the porous substrate influenced by droplet size, impact velocity, porosity, particle diameter, surface tension, and dynamic viscosity were explored. The results indicate that increases in droplet size and velocity lead to a simultaneous increase in both spreading factor and penetration depth. Higher values of porosity, particle diameter, and surface tension facilitated droplet penetration, despite at the expense of impeding droplet spreading on porous surfaces. Droplet size and surface tension exhibited less pronounced effects on penetration depth, particularly during the early stages. The spreading factor exhibited a non-monotonic trend with viscosity, initially increasing and subsequently decreasing, while the penetration depth decreased accordingly. Moreover, a larger spreading diameter corresponds to an expanded penetration width. A correlation was proposed to predict the maximum spreading factor based on Weber number, Reynolds number, and Darcy number, which can predict 83 % data in literature with deviations within ±20 %. This study provides new insights into the droplet dynamics on porous media and offers practical guidance for optimizing relevant engineering applications.