Predicting the Dynamics and Steady-State Shape of Cylindrical Newtonian Filaments on Solid Substrates

The spreading of liquid filaments on solid surfaces isof paramountimportance to a wide range of applications including ink-jet printing,coating, and direct ink writing (DIW). However, there is a considerablelack of experimental, numerical, and theoretical studies on the spreadingof filaments on solid substrates. In this work, we studied the dynamicsof spreading of Newtonian filaments via experiment, numerical simulations,and theoretical analysis. More specifically, we used a novel experimentalsetup to validate a 2D moving mesh computational fluid dynamics (CFD)model. The CFD model is used to determine the effect of processingand fluid parameters on the dynamics of filament spreading. We experimentallyshowed that for a Newtonian filament, the same spreading dynamicsand final shape are obtained when the initial radius is constant,independent of the magnitude in printing parameters. In other words,the only important parameter on the spreading of filaments is theinitial filament radius. Using a numerical model, we showed that theinitial filament radius manifests itself in two important dimensionlessparameters, Bond number, Bo, and viscous timescale, & tau;(& mu;). Furthermore, the results clearly show that the dynamics of spreadingare governed by the static advancing contact angle, & theta;(s). These three parameters determine a master spreading curve thatcan be used to predict the spreading of cylindrical filaments on flatsubstrates. Finally, we developed a theoretical model that was parameterizedusing experimental data to correlate the steady-state shape of filamentswith Bo and & theta;(s). These results are particularly applicablefor predicting and controlling the dynamics of filaments in DIW andother extrusion-based processes.

Automated summary

In this study, the spreading dynamics of Newtonian filaments on solid surfaces were investigated through experiments, numerical simulations, and theoretical analysis. The experimental results showed that the only important parameter for Newtonian filaments is the initial filament radius. A numerical model was used to relate the initial filament radius to two dimensionless parameters, Bond number and viscous timescale. A theoretical model was developed to correlate the steady-state shape of filaments with these parameters. These findings have important applications in predicting and controlling fluid dynamics in direct ink writing and other extrusion-based processes.