An analytical and numerical study of droplet formation and break-off for jetting of dense suspensions

Sammanfattning: The jet printing of solder paste from a uid dynamics perspective involves viscosity change due to varying shear rate and eventual break o of the ejected solder paste droplet from the uid in the printer head. The ability to model the jetting process in a simulation package is important as it can be used as a tool for future development of the jetting device. The jetting process is modelled as a two phase (air - solder paste) ow with interface tracking performed using phase eld method and temporal stepping based on a second-order Backward Di erence Formula with relaxed tolerences. This thesis investigates the droplet morphology, volume and speed predictions for three di erent piston actuation modes and solder paste viscosity denitions given by the Carreau- Yasuda model. A Darcy condition with the porosity parameter is calibrated equal to unity such that the droplet speed is within the realistic range of 20 m/s - 30 m/s. The simulations are compared against previous simulation results from IBOFlow, performed within a collaboration between Mycronic AB and Fraunhofer-Chalmers Centre. As the Carreau models cannot capture the dependence of the uid viscosity of ow history, an indirect structure based viscosity model is used to compare the thixotopic behaviour. The expressions for the parameters of the structure based viscosity model are derived based on an analytical model which assumes that shear rate is constant. Experimental data for constant shear rate is curve tted on a Carreau model and an initial estimate of the parameters are obtained. The parameters are then adjusted to match experimental thixotopic behaviour. This method can be used to obtain parameter values for structure based viscosity models for uids with no previous data. Once the solder paste is ejected through the nozzle and the piston retracts, the uid undergoes stretching. Studying lament stretching during jetting is dicult as it can be driven by both droplet and piston motion. The data from an extensional rheometer is analyzed to study the lament stretching phenomenon for solder pastes. An analytical model for the critical aspect ratio is derived for a Newtonian uid lament undergoing a pure extension and modelled as a cylinder whose radius is decreases with time. The exponential decrease of the lament radius predicted by the analytical model is found to reproduce the experimental observations very well. The lament radius calculated based on the lament height from the experiments and analytical model shows that the model captures the stretching process, but the formation of beads usually seen in suspensions is not accounted for.