# An Experimental Study of the Leakage Mechanism in Static Seals
## 1 Introduction  
A surface-to-surface contact static seal is widely applied in various industries (such as deep space exploration and nuclear power generation [1; 2; 3]) and has always been a research topic of great concern. Although simple in structure, the leakage of contact static seals can directly affect the operation safety of the device and lead to environmental pollution and waste of resources. As machine-processed sealing end faces (even highly polished) are rough, leakage is inevitable [4; 5; 6; 7; 8]; however, it is only possible to control the leak rate of the seals to within a certain range to meet the requirements for normal operation of mechanical devices. Therefore, theoretical studies on the leak rate prediction of sealing interfaces (the sealing interfaces formed by surface-to-surface contact) and experimental studies on leak rate measurements are of great significance for the design of seals. In terms of theoretical research, as early as the middle of the 20 th century, [PERSON] [9], [PERSON] [10], [PERSON] [11; 12] et al. carried out research on the prediction model for the leak rate of sealing interfaces. However, they all simplified the characterizations of the sealing surface topography and the leakage channels to various degrees, which consequently caused a large error between the calculated and the actual leak rates. In recent years, with the development of the fractal theory, there has been new theoretical support for the characterization of multiscale contact states and leakage channel complex structures in contact interfaces. [PERSON] [13; 14] proposed a contact pressure theory that considered the multiscale effect by mathematical methods such as fractal theory and frequency domain transformation, as well as a prediction model for the leak rate of rubber gaskets. Subsequently, many researchersimproved this model [15; 16]. Compared with rubber gaskets, metal gaskets are more sensitive to the microstructure of leakage channels. In 1991, [PERSON] et al. [17] used the Weierstrass-Mandelbrot fractal function (i.e., W-M function) to characterize the surface topography, and proposed a contact pressure model (i.e., M-B model) based on different observation scales. The M-B model eliminated the effect of sampling length and instrument resolution on the characterization of rough surfaces. However, it described the initial surface profile of rough surfaces through the asperity contact area \(A\), resulting in the initial profile varying with the contact area \(A\), and consequently concluded that \"full plastic deformation happens to asperities before elasto-plastic deformation and elastic deformation\", which is contrary to real-world observations. In our previous work [18] (the article \"Fractal Modeling of Fluidic Leakage through Metal Sealing Surfaces\"), we improved the M-B model (by setting up a reference surface on the fractal surface), as the original M-B model was violating real-world observations when applied to calculating the contact load; moreover, using the improved contact model, the leakage channel under the contact surface is mathematically modeled based on the fractal theory and proposed the fractal surface leak rate prediction model. When it comes to experimental research, few experimental studies have been conducted on the leakage mechanism at sealing interfaces. [PERSON] et al. [19] used the \"water bubble\" method to measure the gas leak rate and studied the deformation of the sealing surfaces under load but did not conduct corresponding theoretical research on the leak rate. In the follow-up study by the same authors in 1991, the effect of lead coating on the sealing performance in a low-temperature environment (70 K) was verified through experimental studies [20]. [PERSON] and [PERSON] [21; 22] studied the effect of sealing surface materials (copper, stainless steel, or other alloyed steel) and machining processes (polishing, grinding, etc.) on the gas leak rate.