The special surface appearance of complex surfaces restricts the coating film quality of spraying. The study of the atomization and film formation characteristics of typical complex surfaces, as well as the spraying mechanism, is essential for planning the spraying robotic trajectory and improving the spraying efficiency. In this paper, modeling and characteristics of the atomization and film formation process, based on CFD numerical simulations in previous studies, are systematically reviewed, focusing especially on airless spraying. In addition, the advantages and disadvantages of the existing research from the perspective of numerical models and methods are discussed. Finally, a further research direction for spraying on complex surface is prospected. Overall, a comprehensive and up-to-date review of spray atomization and film formation characteristics is considered valuable to practitioners and researchers in these fields, and will facilitate the further application of robotic spraying in the mechanical, automotive, marine, aerospace, petrochemical and other industries.

Near-nozzle atomization characteristics in air-assisted spraying were investigated through a novel 3D transient model integrating Volume-of-Fluid and Large Eddy Simulation (VOF-DPM) methods, with experimental validation of droplet distributions (Malvern analyzer) and coating thickness profiles. Key findings reveal that (1) the spray field stabilizes within 30 mm downstream, achieving 80% atomization efficiency (droplets ≤ 100 μm) at 27.5 mm axial distance; (2) radial momentum originates dually from fan-shaped airflow (max 595 m/s) and transverse motion induced by central atomizing air entrainment—a previously unreported mechanism; (3) paint loading delays flow stabilization to 2.5 ms (vs. 0.7 ms for gas-only flow) while reducing peak axial velocity by 18%–22% due to gas–liquid momentum exchange; (4) auxiliary and fan airflows synergistically constrain dispersion, forming elliptical sprays with characteristic cone angles of 61.7° (short axis) and 99.1° (long axis). Significantly, surface tension plays a dual role in inhibiting droplet atomization while promoting ligament pinch-off at 8.1 mm breakup length. These results provide the first quantitative characterization of gas–liquid interactions in near-nozzle regions, enabling precise parameter control for enhanced coating uniformity on complex surfaces.

A model of wax deposition based on molecular diffusion mechanism, for oil-gas two-phase stratified pipe flow is developed. In the model, unidirectional fully developed flow analyses of momentum, heat and mass transfer are presented. And, a cube cage model is used to describe the wax deposit structure considering the effect of oil flow shear on the deposit. Calculation of wax deposit is compared well with a flow loop experiment. In particular, the model could give the wax deposit forming a crescent shape at the cross section of pipe, which is observed in different experiments. Furthermore, the cause of forming a crescent shape is revealed, which is indicated by the non-uniform circumferential distribution of mass flux for wax deposition along the pipe wall wetted by the oil. The mass flux from oil bulk flow to the oil-deposit interface is closely related to three parameters, diffusivity at oil-deposit interface, the temperature gradient at the oil-deposit interface at different time, and the slope of the wax solubility curve at oil-deposit interface temperature.

Gas–liquid flow in a pipeline is a very common. Slug two-phase flow is dominated in the case of slightly upward flow (+0.25°) and considered to be the comprehensive flow configuration, and can be in close contact with all the other flow patterns. The models of different flow patterns can be unified. Precise prediction of the slug flow is crucial for proper design and operation. In this paper, we develop hydrodynamics unified modeling for gas–liquid two-phase slug flow, and the bubble and droplet entrainment is optimized. For the important parameters (wall and interfacial friction factors, slug translational velocity and average slug length), the correlations of these parameters are optimized. Furthermore, the related parameters for liquid droplet and gas bubble entrainment are given. Accounting for the gas–liquid interface shape, hydrodynamics models, i.e., the flat interface model (FIM) and the double interface model (DIM), of liquid film in the slug body are applied and compared with the experimental data. The calculated results show that the predictions for the liquid holdup and pressure gradient of the DIM agree with experimental data better than those of the FIM. A comparison between the available experimental results and Zhang’s model calculations shows that the DIM model correctly describes the slug dynamics in gas–liquid pipe flow.