# Study on Two-Phase Mixing Inside Flow Focusing/Blurring Nozzle by Gray Distribution Analysis Method
## 1 Introduction  
The flow focusing/blurring nozzle is a two-phase nozzle developed by [PERSON] [1, 2]. Although this nozzle is simple in structure, it is effective in producing droplets and atomizing. In recent years, this nozzle has been widely used in various industrial applications, including biological medicine, high viscosity liquid atomization, multiphase combustion and industrial painting [3].  
When the flow parameters or nozzle structure change, the nozzle will show two different modes: flow focusing and flow blurring. In the flow focusing mode, the nozzle is more likely to produce micro-nano droplets. [PERSON] conducted experimental and theoretical research on the flow focusing nozzle [4, 5, 6] and presented the relationship between nozzle inlet pressure, flow rate, jet diameter and droplet diameter. [PERSON] gave the influence relationship between the recirculation cell and the dripping regime by numerical simulation [7]. [PERSON] further divided the flow focusing into six modes and studied the characteristics and causes of each mode [8]. A large number of research results enable people to have a deep understanding of flow focusing so that it can be widely used in the biological medicine field.  
In the flow blurring mode, the nozzle is more widely used in the liquid atomization and combustion. Many researchers used experimental methods to study the atomization effect of the nozzle. The results show that the nozzle has a good atomization effect on the liquid, even if the viscosity of the liquid is high [9, 10, 11, 12]. However, due to the small size of the nozzle, it is difficult for experimental equipment to observe the two-phase flow insidethe flow blurring nozzle, so the research on the working principle of the flow blurring nozzle is not comprehensive, which limits the further application of this nozzle in the atomization and combustion field.  
In recent years, image processing and analysis technologies have developed rapidly, and they have been well applied in multiphase flow and mixing fields. [PERSON] studied two-phase mixing in a direct contact boiling heat transfer process, by using the gray distribution of the images [13; 14; 15]. The results show that the gray distribution of the experimental images are related to the degree of two-phase mixing. [PERSON] made a comparative study on the gray distribution of different cross sections of the two-phase mixing images in the mixer and believed that the gray distribution of experimental images could describe the two-phase mixing [16]. [PERSON]'s research results showed that the gas flow rate at the mixer inlet would change the bubble distribution and thus affect the gray distribution of the experimental images [17]. [PERSON] [18; 19] and [PERSON] [20] also studied the unstable mode of underexpanded jets and the generation mechanism of screech harmonics in supersonic jets by using shadowgraph imaging methods similar to the gray distribution analysis method. These research objects are similar to the gas-liquid flow in the mixing zone of the flow blurring nozzle. Therefore, it is feasible to use the gray distribution of the experimental images to study the gas-liquid flow in the mixing zone of the flow focusing/blurring nozzle.  
In this paper, the gas-liquid interaction in the mixing zone of the flow focusing/blurring nozzle was analyzed and studied by using the gray distribution of the experimental images. We compared the gray distribution of two-phase flow images in the mixing zone under different conditions and analyzed the feasibility of using this method to study the two-phase flow in the mixing zone of the flow focusing/blurring nozzle. Using the gray distribution of the experimental images, we analyzed the gas-liquid's mixing intensity and uniformity in the mixing zone and studied the flow characteristics of the local flow field.