Direct writing of liquids by micro dispensing: Stability and shape of laminar jets with high Froude numbers

Abstract

Nowadays, a wide range of industrial manufacturing processes require high precision for product manufacturing. Micro dispensing is concerned with jetting of liquids through nozzles with a typical diameter on the order of magnitude of 100 microns. In this work, various aspects of micro dispensing of a Newtonian liquid are studied, including jet break-up and the (equilibrium) profile of a printed line on a substrate. Contrary to the investigations of others, this work is concerned with jets of high Froude (Weber) numbers in the range of 40≲Fr≲1500(1≲We≲100). Phenomenological correlations between the liquid properties, dispensing conditions and the jet break-up ratio are inferred based on dimensional reasoning and a comprehensive set of experiments. These correlations are used to create maps that indicate stable dispensing regimes. Furthermore, when the liquid is dispensed from the nozzle, the jet diameter usually contracts over the jet length. An analytical solution of the Navier-Stokes equation, valid to describe the shape of gravity-driven jets, is modified to obtain a correlation for inertia-driven jets. Finally, a correlation is derived to (numerically) obtain the three-dimensional profile of a liquid that is dispensed on a flat substrate.