An LBM-PNM framework for immiscible flow: With applications to droplet spreading on porous surfaces

The behaviour of droplets on porous media, combining the spreading above and imbibition into the medium, is of foundational interests for a series of applications. In this work, we combine the lattice Boltzmann method (LBM) and pore-network method (PNM) to develop an efficient and robust numerical framework in which the coarse-scale multiphase transport in porous media are modelled by the PNM while the fluid dynamics containing multiple components are resolved by the LBM. An effective transport mechanism has been implemented to ensure mass conservation and pressure continuity across the interface. This method is ideally adapted to flow domains, with two distinguishable characteristic length-scales. The numerical framework is validated by comparison with experimental observations of droplets on flat porous surfaces. Moreover, the behaviour of droplets on non-flat porous surfaces has been also investigated, demonstrating the influence of surface curvature on the competing mechanisms of droplet spreading and imbibition. (C) 2020 Elsevier Ltd. All rights reserved.