## 2 Experimental and Computational Numerical Methods
### CFD Digital Twin of Experimental Setup
In this study, we assumed that we could simulate the flow of liquid water droplets and the gas phase (primarily air) in a transparent square tube using the Eulerian-Lagrangian (E-L) framework. This framework involved solving the continuity and Navier-Stokes equations (Equations (8) and (9)) for the continuous gas phase and Newton's second law of motion for the individual liquid droplets. The advantages of this approach compared to Eulerian-Eulerian modeling techniques are substantial, as it provides a more detailed understanding of the behavior of discrete particles rather than focusing solely on continuous dynamics. Lagrangian tracking simplifies and reduces the cost of modeling a distribution of particle sizes or other properties of the dispersed phase, which would require separate treatment in the Eulerian technique. Despite its advantages, Eulerian-Lagrangian modeling has limitations. It can be computationally expensive because of the necessity to track a large number of individual particles or parcels, and its computational demands increase with the number of particles being tracked. We represented the entire population of dispersed phases, specifically liquid droplets, with a reduced number of computational parcels. Each parcel consisted of particles assumed to be spherical, sharing identical properties such as diameter, velocity, density, and temperature. This approach facilitated the modeling of turbulent dispersion. Each parcel was treated as a source term integrated into the governing equations of mass, momentum, and energy at its specific location. Furthermore, we conducted a computational study to determine the optimal number of droplets within each parcel, which enabled us to assess its impact on droplet distribution. The movement of water droplets was tracked using the Lagrangian multiphase model (LMP). Additionally, we assumed a spherical shape for the droplets, a valid assumption for droplets with a diameter less than 2 mm, as previously mentioned [36]. The NTC (no time counter) collision model was used to simulate the interaction between droplets that occurred during collisions and coalescence, in which colliding droplets stuck together to generate bigger diameter droplets. STAR-CCM+ used the NTC [37] and O'Rourke [38] collision models to identify and forecast the results of interactions between droplets. In the uncoupled CFD solvers, each velocity component and the pressure field are computed independently based on the flow equations, without considering their mutual interactions. Subsequently, the calculated fields are adjusted to satisfy the continuity equation, and the updated fields are predicted using the SIMPLE algorithm [39]. This approach, known as the segregated approach, was consistently employed in all four simulation cases presented in this study. Boundary conditions provide information on how the flow within the region interacts with its surroundings to STAR-CCM+ solvers. For this study, two boundary conditions were covered: the wall boundary condition and the bottom pressure outlet. Pre-processing, simulation, and post-processing were performed using Simcenter STAR-CCM+ (version 2020.1, Siemens Product Lifecycle Management Software Inc., Plano, TX, USA). The numerical simulations were carried out on the computer of the Max Planck Research Institute in Magdeburg using an 11 th Gen Intel Core I i7-11700 @ 2.50 GHz x64-based processors equipped with 64 GB of RAM.