## 1 Introduction  
The development of the machining industry has led to the massive use of metalworking fluids (MWFs). When machine parts collide strongly, MWFs atomize or evaporate, generating numerous solid particles and oil mist droplets. Then, these pollutants spread to the entire workshop environment along with the airflow in the machining workshop [1, 2, 3]. Particles with a diameter of fewer than 10 \(\upmu\)m can stay in the air for a long time and thus are regarded as suspended particles; these pollutants easily enter the respiratory system and seriously endanger human health [4, 5]. Studies have shown that suspended oil droplets can pass through the respiratory tract to reach and be deposited in the lungs [6, 7]. Long-term exposure to suspended particles can cause respiratory diseases, such as sinusitis, asthma, and hoaseness of the throat [8, 9], and it may even lead to kidney cancer [10]. Meanwhile, anatomized MWFs are thrown off the inner wall of machines along with the rotation of turning tools to form surface-adhering oil contamination. Large-size droplets in the air also settle on surfaces in the workshop to form sedimentary contamination [7]. This kind of surface oil contamination presents challenges to the normal operation of machines [11, 12]. A study has shown that 60% to 80% of the hydraulic system's failure events of computer numerical control turning tools are caused by oil contamination on surfaces [13]. Most of the existing research focuses on suspended particles in workshops, particularly the emission mechanism of oil mist droplets during cutting and their transfer process in the air. The three generally recognized emission mechanisms are evaporation-condensation, impact-induced splashing, and fall-off [14; 15]. MWFs are emitted into the air through the abovementioned three ways to form suspended particles. Thus, the concentration of suspended particles in the air should be measured, and the movement of suspended particles based on indoor airflows should be predicted. [PERSON] et al. [16] developed an online monitoring system to monitor the dynamic concentration of oil mist in the air in a workshop in real-time. Their results showed that the oil mist concentration seriously exceeded the limit of the machining workshop. [PERSON] et al. [17; 18] studied the movement of indoor oil mist droplets in two forms; namely, upper-receiving and push-pull ventilation, through computational fluid dynamics (CFD) simulation. They also studied the oil mist diffusion between two adjacent workshops. The abovementioned findings demonstrated the spread of oil mist droplets in workshop environments and their distribution characteristics. Numerical simulation is a commonly used research method because it can effectively reproduce the dynamic movement of oil mist. However, few studies focused on the spread of liquid oil contamination on workshop surfaces. As the oil mist itself undergoes sedimentation, it forms deposited liquid oil contamination on surfaces. In addition, MWFs adhere to workpieces during machining. Similarly, oil contamination on workbenches cannot be ignored. Figure 1 shows the distribution of oil contamination on different workbenches in a workshop in Shanghai GKN HUAYU Driveline Systems Co., Ltd. (SDS). Given the contact behavior of workers, the oil contamination on the surface is transferred through workers' hands (active media) and workpieces (passive media), and it alters the quality of various surfaces in the workshop, including the production and assembly areas. Furthermore, as the contact behaviors between people and surfaces are extremely random, the Markov chain is introduced in this study to describe the process. The Markov chain is a commonly used mathematical model for describing random processes, and it can represent the transition process of discrete random states in the state space. In particular, for any moment, the state transition probabilities before and after this moment are independent of each other.