# Research Progress and Engineering Applications of Viscous Fluid Mechanics
## 2 Advances in the Study of the State of Motion of Viscous Fluids
### Experimentation and Research
#### 2.1.2 Experiments and Studies on Droplet Impacts in Viscous Fluids  
The study of viscous fluid droplet impact is an important branch in the field of fluid mechanics and surface phenomena, which involves the dynamic behaviors and physical processes of droplets in contact with solid or liquid surfaces under different conditions. These studies not only have far-reaching impacts on basic science but also have important implications in engineering applications. The dynamic process of droplet impact involves the deformation, expansion, and sputtering of droplets [35; 36]. As a droplet approaches a surface, its shape is affected by surface tension, viscous, and inertial forces, which in turn affect the post-impact response. For example, higher surface tension and viscosity cause droplets to be more difficult to expand, which may cause droplet buckling or sputtering, while lower surface tension may contribute to droplets expanding more easily and forming a thin film. The phenomena of energy transfer and dissipation during droplet impact are also crucial [37]. Upon impact, energy is transferred between the droplet and the contacting surface, and some of this energy is either dissipated as heat or converted into the kinetic energy of the droplet, affecting the subsequent behavior and morphological evolution of the droplet. The understanding of these processes is particularly critical for engineering applications such as inkjet printing, coating technologies, and microfluidic system design [38; 39]. The study of viscous fluid droplet impingement is also of direct practical relevance for solving problems in a variety of real-life and industrial applications. For example, in medical devices, understanding the expansion and adhesion behavior of droplets on various surfaces can help design more efficient fluid dispensing systems; in coating technology, controlling droplet impingement and expansion can improve the uniformity and quality of coatings [40]. Overall, the study of viscous fluid droplet impingement not only deepens our understanding of fluid dynamics and surface phenomena but also provides an important foundation and guidance for modern engineering technologies and applications. The droplet impact velocity, angle, and impact energy have important effects on the experimental results. Too high or too low impact energy may lead to the atypical behavior of droplets or unrepeatable experimental results [41]. If the droplet cannot be fully wetted on contact with a solid surface or if there is a large contact angle, this will affect the deformation and rebound behavior of the droplet, making it difficult for the experimental results to accurately reflect the theoretical model [42]. Also, the Weber number of the liquid can greatly affect the collision results of viscous droplets [43]. With the development of technology and the increase in the demand for precise control, high-frame-rate high-speed video cameras for viscous droplet collision experiments to detect the experimental collision process, simulation software to simulate the collision process, and other methods of scientific research and investigation have been gradually and widely used [44; 45; 46]. For example, in the study of the impact of the Weber number on droplet collision, experimental controllable variables such as substrate elasticity, impact velocity, liquid viscosity, and liquid material can be systematically changed, and then, high-speed cameras can be used to clearly observe the phenomena of the diffusion, rebound, retraction, and wetting of droplets with different viscosities after impacting different substrates. By observing the experimental images, we can further study the influence of liquid viscosity on the critical rebound Weber number, maximum spreading, and contact time and speculate the mathematical model of the change in the Weber number before and after the collision [47; 48; 49]. In this line of thinking, [PERSON] et al.