Computational simulation of the printing of Newtonian liquid from a trapezoidal cavity

A Lagrangian finite element algorithm is described for solving two‐dimensional, time‐dependent free surface fluid flows such as those that occur in industrial printing processes. The algorithm is applied using a problem specific structured meshing strategy, implemented with periodic remeshing to control element distortion. The method is benchmarked on the problem of a stretching filament of viscous liquid, which clearly demonstrates the applicability of the approach to flows involving substantial free surface deformation. The model printing problem of the transfer of Newtonian liquid from an upturned trapezoidal trench (3‐D cavity with a large transverse aspect ratio) to a horizontal substrate, which is pulled perpendicularly downwards from the cavity, is solved computationally using the Lagrangian scheme. The idealized 2‐D liquid motion is tracked from start‐up to the point where a thin sheet forms – connecting the liquid remaining in the cavity to a “sessile” drop on the moving substrate. The effect of varying substrate separation speed is briefly discussed and predictions are made for approximate drop volumes and “limiting” domain lengths.