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

The spreading of liquid filaments on solid surfaces is of paramount importance to a wide range of applications including ink-jet printing, coating, and direct ink writing (DIW). However, there is a considerable lack of experimental, numerical, and theoretical studies on the spreading of filaments on solid substrates. In this work, we studied the dynamics of spreading of Newtonian filaments via experiment, numerical simulations, and theoretical analysis. More specifically, we used a novel experimental setup to validate a 2D moving mesh computational fluid dynamics (CFD) model. The CFD model is used to determine the effect of processing and fluid parameters on the dynamics of filament spreading. We experimentally showed that for a Newtonian filament, the same spreading dynamics and 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 the initial filament radius. Using a numerical model, we showed that the initial filament radius manifests itself in two important dimensionless parameters, Bond number, Bo, and viscous timescale, τ_μ. Furthermore, the results clearly show that the dynamics of spreading are governed by the static advancing contact angle, θ_s. These three parameters determine a master spreading curve that can be used to predict the spreading of cylindrical filaments on flat substrates. Finally, we developed a theoretical model that was parameterized using experimental data to correlate the steady-state shape of filaments with Bo and θ_s. These results are particularly applicable for predicting and controlling the dynamics of filaments in DIW and other extrusion-based processes.