# A Machine Learning Approach to Predict Fluid Viscosity Based on Droplet Dynamics Features
## 2 Materials and Methods  
The dataset for this paper comes from a self-designed experiment. The experimental setup is shown in Figure 1. A precision flow pump (ELITE PICO SINGLE, Harvard Apparatus,Los Angeles, CA, USA) was used for fluid administration, and the flow rate Q was set to Q = 0.2 mL/min. The needle was fixed to the acrylic plate through a luer connector, the acrylic plate was fixed to a stand through a threaded peg, and the needle was adjusted to level by adjusting the threaded pegs with a level. Droplet images were captured using a high-speed video camera (FASTCAM MINI UX100 TYPE 200K-M, Photron, Tokyo, Japan) with a 100 mm fixed-focus lens (AT-X 24-70 F2.8 PRO FX, TOKINA, Tokyo, Japan). The camera was set to a shooting speed of 4000 fps, a shutter speed of 1/10,000 s, a resolution of 1280 \(\times\) 1024, and a pixel ratio of 13.7 \(\upmu\)m/pixel. A strobe-less LED light source (CDXINT XT120W, CDXINT, Chengdu, China) was used to fill in the light during shooting. To obtain smaller-scale changes in the filament, a homogeneous PMMA plate was used to shade the LED light source, reducing the amount of incoming light while maintaining the shutter speed, and reducing the diffraction of light so that the fine fluid details of the filament breakage could be shown. The needle material used was 304 steel, and the outer radius of the needle was R = 0.8 mm. A self-programmed ImageJ v.1.53t script program was used to capture the characteristic dimensions of the neck thickness during the dropping process. This study focuses on the kinetic characteristics of the viscosity of aqueous glycerol solutions during the dropping process, capturing the drop neck contraction data that have the strongest correlation with viscosity for use in training a machine learning model to establish a direct relationship between neck contraction and viscosity. Glycerol-water solutions can be prepared at varying percentages by adjusting the concentration of glycerol, allowing for the easy acquisition of fluid samples with different concentrations. Additionally, the influence of glycerol's viscosity on surface tension and density is minimal, which is advantageous for comparing experimental results related to viscosity differences. The commonality of glycerol-water solutions as standard samples enables convenient comparison and validation with other experimental outcomes, thereby promoting the reliability and accuracy of experimental results. We then enabled the input of drop video data of unknown viscosity to predict the viscosity of that fluid. In this work, first, eleven aqueous solutions of glycerol with different percentages were formulated; the concentrations of the glycerol aqueous solutions were distributed from 50% to 99% at 5% intervals and the physical parameters of different percentages of glycerol aqueous solutions are shown in Table 1. Due to the existence of humidity, temperature, and other error factors, even if the same glycerol aqueous solution is used in the experiments conducted at different times, there will be some errors. For the accuracy of the liquid neck shrinkage-viscosity dataset, the viscosity of the solution was measured once before each experiment, and the first drop video data of each viscosity counterpart was measured for that solution. Finally, eighteen liquid neck shrinkage-viscosity datasets were collected. The Greek letters \(\rho\), \(\mu\), and \(\sigma\) denote density, surface tension, and viscosity, respectively. [PERSON] et al. (2019) proposed that the free surface shape and the internal flow of a droplet depend only on the proportionality of the observed scale to the viscous scale. The viscous scale \(l_{\mu}=\mu^{2}/(\sigma\rho)\) indicates that the viscous effect increases significantly when the flow scale of the fluid reaches this scale.