Heterogeneous droplets in contact

Additive manufacturing has developed from the production of prototypes towards the direct printing of functional parts. Recent developments include the use of multiple materials during a single additive manufacturing step, especially using inkjet printing. To increase the capabilities even further, understanding of interactions of these materials is required. The main goal of this thesis is to study the influence of heterogeneous interactions in droplets. Of fundamental importance to additive manufacturing, is the solidification and final footprint of printed droplets. In Chapter 2 the interplay between the phase transition effects and the contact-line motion of spreading droplets is investigated. The early solidification patterns and dynamics of spreading hexadecane droplets arerevealed employing total internal reflection (TIR) imaging. With this method the conditions leading to the contact-line arrest is determined. The overall nucleation behavior was quantified depending on the applied undercooling of the substrate. By combining the Johnson-Mehl-Avrami-Kolmogorov nucleation theory and scaling relations for the spreading of droplets, the temporal evolution of the solid
area fraction was calculated. In Chapter 3 the freezing kinetics during the solidification of a droplet while it impacts on an undercooled surface is investigated by TIR-imaging. At sufficiently high undercooling, a peculiar freezing morphology exists that involves sequential advection of frozen fronts from the center of the droplet to its boundaries. This phenomenon is examined by combining elements of classical nucleation theory to the large-scale hydrodynamics on the droplet scale. It was shown that the interaction
of crystal growth with the hydrodynamical boundary layer leads to the periodical
advection of solidified crystals. Furthermore, a self-peeling phenomenon of the frozen splat is revealed. This peeling is driven by the thermo-mechanical stresses in the solidified footprint and the existence of a transient crystalline state during solidification. Of further importance is the modelling of the solidification of droplets. Chapter 4 described the extension of the geometrical Volume-of-Fluid interface method, with an enthalpy-porosity formulation to study solidification. The numerical method is validated against experiments available in the literature and favorably compared to earlier numerical methods. A study of 1 mm sized tin droplets is performed, showing various impact regimes: deposition, capillary ejection, and (partial) break-up. The dependence of the spreading behavior on the Weber (We) and the Stefan (Ste) number is quantified. At early times, the spreading is found to be similar to that of isothermal droplets, but later the solidification arrests the moving interface. An analytical model is developed to determine the maximum spreading diameter as a function of dimensionless parameters. This model is based on a combination of the hydrodynamics
and the solidification rate, and gives good estimates for the maximum droplet
diameter of solidifying droplets. Next to droplet solidification, the effect of variable surface tension on the behavior of droplet interactions was investigated. Chapter 5 describes an experimental method using stroboscopic illumination by nanosecond laser pulses. With this, the Marangoni-driven spreading of droplets over droplets is studied. The distance L(t) over which a low-surface-tension drop spreads over a high-surface-tension drop was measured for a large array of liquid properties. This reveals that a power-law L(t) ~ t^a with a spreading exponent a ~ 0:75, reasonably captures the experiments in this chapter, as well as previous experiments for different geometries, miscibilities, and surface tension modifier for ten orders of magnitude in dimensionless time. Finally, in Chapter 6 a novel methodology for the inclusion of variable surface tension acceleration in a geometrical Volume-of-Fluid method is developed. This method provides an accurate method for computing surface tension gradients based on the local reconstruction of the interface. It is applicable to both temperature and concentration gradients. This model has been validated for two situations, one with two stacked fluids with a flat interface and one with a droplet with a curved interface, showing that the method accurately calculates liquid flow driven by variations in surface tension.