Two principal methods have been used to simulate the evolution of two-phase immiscible flows of liquid and gas separated by an interface. These are the Level-Set (LS) method and the Volume of Fluid (VoF) method. Both methods attempt to represent the very sharp interface between the phases and to deal with the large jumps in physical properties associated with it. Both methods have their own strengths and weaknesses. For example, the VoF method is known to be prone to excessive numerical diffusion, while the basic LS method has some difficulty in conserving mass. Major progress has been made in remedying these deficiencies, and both methods have now reached a high level of physical accuracy. Nevertheless, there remains an issue, in that each of these methods has been developed by different research groups, using different codes and most importantly the implementations have been fine tuned to tackle different applications. Thus, it remains unclear what are the remaining advantages and drawbacks of each method relative to the other, and what might be the optimal way to unify them. In this paper, we address this gap by performing a direct comparison of two current state-of-the-art variations of these methods (LS: RCLSFoam and VoF: interPore) and implemented in the same code (OpenFoam). We subject both methods to a pair of benchmark test cases while using the same numerical meshes to examine a) the accuracy of curvature representation, b) the effect of tuning parameters, c) the ability to minimise spurious velocities and d) the ability to tackle fluids with very different densities. For each method, one of the test cases is chosen to be fairly benign while the other test case is expected to present a greater challenge. The results indicate that both methods can be made to work well on both test cases, while displaying different sensitivity to the relevant parameters.

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Droplet impact on porous media has a broad range of applications such as material processing, drug delivery and ink injection etc. The simulation studies of such processes are rather limited. To represent the spreading and absorption process of the droplet on porous materials, robust numerical schemes capable of accurately representing wettability as well as capillary effects need to be established. The current work, presents one of the first studies of droplet impact on a real porous media geometry model extracted from a micro-CT scan. The process involves processing of CT image and subsequent threshold based on the structures segmentation. The porous geometry is extracted in the form of a STL (STereoLithography) model, which, with the aid of dedicated software like ANSA and SnappyHexMesh, is converted to an unstructured mesh for successful discretization of the flow domain. The solution algorithm is developed within the open source CFD toolbox OpenFOAM. The numerical framework to track the droplet interface during the impact and the absorption phases is based on previous work [1,2]. The volume-of-fluid (VOF) method is used to capture the location of the interface, combined with additional sharpening and smoothing algorithms to minimise spurious velocities developed at the capillary dominated part of the phenomenon (droplet recession and penetration). A systematic variation of the main factors that affect this process are considered, i.e. wettability, porous size, impact velocity. To investigate the influence of porous structures on droplet spreading, the average porosity of the media is varied between 18.5% and 23.3% . From these numerical experiments, we can conclude that the droplet imbibition mainly depends on the porous wettability and secondly that the recoiling phase can be observed in the hydrophobic case but not in the hydrophilic case. Keywords; Droplet Spreading, Droplet Absorption, Porous media, 3D micro-Topography, VOF Introduction Micro-scale fluid phenomena are involved in various applications and research areas [3]. Understanding the behaviour of droplet spreading on porous media is important for a variety of industrial applications, such as ink jet printing, raindrops on textile, spray paint on wood, 3D-printing, penetration of rain drops into building walls, needle less injection, coating of porous materials, irrigation, cooling of electronic devices etc. Droplet spreading on solid flat surfaces has been the subject of numerous experimental and numerical studies over the last few decades [5,6]. However, droplet impact on porous media is still far from being understood. Studies of such micro-scale fluid phenomena need careful and combined consideration of droplet dynamics and porous media characteristics. Generally, this phenomenon is controlled by two main counter-acting processes: droplet spreading on porous surfaces and imbibition inside the porous media [8]. As the droplet spreads on the surface it also fills the voids of the porous material due to capillary action. The spreading be...