## 1 Introduction  
Conductive pastes are widely used in general electronic components, including the front electrodes of photovoltaic modules [1], the circuits of flexible electrodes [2], transparent electrodes [3], printed circuit boards (PCBs) [4], multilayer chip ceramic capacitors [5], the inorganic non-metallic substrates of new energy storage devices [6], etc. Traditional forming methods for conductive paste with a high viscosity are mainly screen-printing-based contact forming; this method has high requirement on the flatness of the substrate and wastes a lot of conductive paste [7; 8; 9; 10; 11]. Non-contact forming methods can effectively avoid these problems [12]. Non-contact forming methods include Electrohydrodynamic Jet Printing (E-Jet Printing) [13], Light-Induced Plating [14], Ink-Jet Printing [15], and Buried Contact Solar Cells (BCSC) [16]. Different processing methods are suitable for different materials. E-Jet Printing and Ink-Jet Printing can print structures on the micron or even nanometer scale, but they are only suitable for specific fluids. Light-Induced Plating and BCSC are highly accurate, but the processing steps are complicated and inefficient. Different from general non-Newtonian fluids that do not contain solid particles, conductive paste has the characteristics of high viscosity, a high solid content, and poor fluidity [17], and so it is difficult for it to be extruded from a small nozzle. To solve this problem, [PERSON] [18] used a metal aerosol jet printing method to deposit metal aerosol onto the substrate by using the gas flow focusing principle, avoiding contact between the aerosol and the nozzle tip. [PERSON] used an approximately 200 um nozzle outlet to obtain the first layer of 50-140 um, and then used Light-Induced Silver Plating to obtain the second layer. The width of the contact fingers increased by approximately 20-30 \(\upmu\)m. However, the contact between the first and second layers was sometimes not strong enough to meet the requirements, and the processing steps were tedious, resulting in low efficiency and difficulty with commercializing. Direct-ink writing (DIW) is an extrusion 3D printing technology that has the advantages of simple installation, convenient operation, and a wide selection of printing materials [19]. DIW technology can achieve relatively smooth extrusion for conductive pastes. [PERSON] et al. [20] created a Starlet for solar cell metallization processes, and their print head was used to eject jets of molten metal with diameters as small as 50 \(\upmu\)m to print fingers of a 70 \(\upmu\)m minimal width, but this method is not yet as fine as screen printing. [PERSON] et al. [21; 22] designed a printing nozzle that co-extruded metal paste between two layers of sacrificial layer materials, and the sacrificial layer could be completely removed in subsequent processing. The size of the nozzle was approximately 220 \(\upmu\)m and the line width was approximately 50 \(\upmu\)m. However, the design of the nozzle was too complex and the flow balance between the metal paste in the middle and the sacrificial layer on both sides was difficult to control, which may have been the reason why this method was not widely adopted. Recently, [PERSON] [23; 24; 25] designed and processed a print head with 50 integrated ceramic nozzles to achieve the fast and efficient printing of conductive pastes, and this print head is currently at the world-leading level. They used a group-dispenser with D = 20 \(\upmu\)m sized nozzle openings, with corresponding finger widths of 17 \(\upmu\)m. However, the influence of printing parameters on the quality of paste formation and the prediction of printing results requires more study. Generally, conductive paste has a high viscosity and a high internal solid particle content. It often faces the problem of clogging during the printing process, and so the related experiments have higher requirements than usual for the nozzle.