## 2 Methods and Data
### Generalized Variable System to Diverse Geometry Configurations  
The various configurations in the microchannel had been listed with the different geometry parameters (Table 1). It was necessary to establish a generalized variable system to describe the different geometry configurations uniformly. The rectangular and circular cross-sections were the common shapes featured by \(W\) and \(h\), and \(d\), respectively. They were the equivalent physical quantities obeying the following equation. \[\mathrm{d}\ =\ \frac{2W\times h}{W+h} \tag{1}\]  
Where \(d\) is the diameter of circular, \(W\) is the width of rectangular, and \(h\) is the height of rectangular. Figure 1: Flow chart of machine learning algorithms. Compared with other publication, our team proposed a novel normalized model to the microchannel based on the convergent coaxial (or tapered co-flow) structure [27; 28]. In Table 1, for the generalized variable system, it was the rectangular microchannel possessed the 8 independent geometry parameters (\(W_{c}\), \(h_{c}\), \(W_{d}\), \(h_{d}\), \(W_{out}\), \(h_{out}\), \(X\), \(\alpha\)) more than the circular microchannel with the 5 independent geometry parameters (\(d_{c}\), \(d_{d}\), \(d_{out}\), \(X\), \(\alpha\)). The circle microchannel degenerated from the rectangular microchannel and decreased the number of geometry parameters. The rectangular microchannel often was a universal form to describe the cross-section more properly. All the primitive parameters in experiments consisted of two parts, the independent and target variables. The independent variables included the geometry, process, and property parameters and governed the target variables. The implicit function between the independent and target variables was in Equation (2). \[F(geometry,\,\,process,\,property,\,\,target)\,=\,0 \tag{2}\]  
Where _geometry_ is geometry parameters, _process_ is process parameters, _property_ is property parameters, and _target_ is droplet characteristics. Besides the geometry parameters (\(W_{c}\), \(h_{c}\), \(W_{d}\), \(h_{d}\), \(W_{out}\), \(X\), \(\alpha\)), other independent variables had different parameters, which were the process parameters of \(u_{c}\) and \(u_{d}\), the property parameters of \(\rho_{c}\), \(\rho_{d}\), \(\mu_{c}\), \(\mu_{d}\) and \(\sigma\). As the target variables, it owned two parts of \(L_{d}\) and \(f\). Taking all the above parameters into Equation (2), the implicit equation was reformed by 17 primitive parameters with 3 basic dimensions: M (mass), L (length), and T (time) in Equation (3). \[F(W_{c},\,h_{c},\,W_{d},\,h_{d},\,W_{out},\,h_{out},\,X,\,\alpha,\,u_{c},\,u_{ d},\,\rho_{c},\,\rho_{d},\,\mu_{c},\,\mu_{d},\,\sigma,\,L_{d},\,f)\,=\,0 \tag{3}\]  
Due to the influence of dimensionality, the primitive parameters cannot be weighted directly, so that they should be converted to a dimensionless form. The Buckingham theorem, widely used in other fields [20; 21], was a mathematical method to transform the dimensional quantity to the dimensionless quantity. Solving the basic solutions of Equation (3) by the Buckingham theorem, 17 primitive parameters with dimensionality had been transformed into 14 dimensionless numbers (\(\pi\)) in Equation4. \[\varnothing(\pi_{1},\,\,\pi_{2},\,\cdots,\,\pi_{14})\,\,=\,0 \tag{4}\]  
The above equation stated that the transformation from the primitive parameters to dimensionless numbers could decrease the dimensionality of the implicit function. Table 2 lists the three solutions of dimensionless numbers, which are Set1, Set2, and Set3. The numbers in Set1 and Set2 were the common hydrodynamic dimensionless numbers (\(Oh\), \(We\), \(Re\), \(St\), \(Su\), \(Ca\)[35; 36; 37]) with a clear physical expression. On the contrary, in Set3, the target variable (\(\pi_{14}\)) was not clear on the physical expression. The input and output variables of ML algorithms should be chosen by these dimensionless numbers. As follows, this paper discussed the ML model accuracy in the three solution sets between the two-group experiments with different materials.