Mixing and internal dynamics of droplets impacting and coalescing on a solid surface

The coalescence and mixing of a sessile and an impacting liquid droplet on a solid surface are studied experimentally and numerically in terms of lateral separation and droplet speed. Two droplet generators are used to produce differently colored droplets. Two high-speed imaging systems are used to investigate the impact and coalescence of the droplets in color from a side view with a simultaneous gray-scale view from below. Millimeter-sized droplets were used with dynamical conditions, based on the Reynolds and Weber numbers, relevant to microfluidics and commercial inkjet printing. Experimental measurements of advancing and receding static contact angles are used to calibrate a contact angle hysteresis model within a lattice Boltzmann framework, which is shown to capture the observed dynamics qualitatively and the final droplet configuration quantitatively. Our results show that no detectable mixing occurs during impact and coalescence of similar-sized droplets, but when the sessile droplet is sufficiently larger than the impacting droplet vortex ring generation can be observed. Finally we show how a gradient of wettability on the substrate can potentially enhance mixing.

Figure 1

Schematic diagram of the two-droplet generator system. The generator on the left contains an uncolored mixture of glycerol and water and the one on the right contains a blue-colored mixture.

Figure 2

Contact angle hysteresis analysis showing advancing and receding contact angles of a drop on an inclined PMMA surface just starting to slip. The image shows a comparison of experimental measurement and numerical modelling of an uncolored mixture of glycerol and water with a viscosity of 85.8 mPa s. The droplet starts to slip when the surface is inclined at approximately 25${}^{\circ }$.

Figure 3

Color high-speed imaging of the impact and coalescence of an uncolored sessile and an impacting colored droplet. In these experiments, the impact speed is 1.12$\pm$0.04 m/s (Series 1 in Table ).

Figure 4

Color high-speed imaging of the impact and coalescence of an uncolored sessile droplet and an impacting colored droplet. These experiments corresponds to series 2, in which the sessile and the impacting droplet have a different volume.

Figure 5

Internal flow analysis of sessile and impacting droplet during spreading phase using lattice Boltzmann simulations. The configuration corresponds to experimental Series 2.

Figure 6

Numerical simulation showing vortex ring generation when a small droplet impacts on a sufficiently large sessile droplet.

Figure 7

Color high-speed imaging of the impact and coalescence of an uncolored sessile droplet and an impacting colored droplet. These experiments corresponds to Series 3 in which the impacting droplet has approximately twice the speed of the one in Series 1.

Figure 8

High-speed imaging of the impact and coalescence of an uncolored sessile droplet and an impacting colored droplet. Images are taken from underneath the substrate by oblique illumination. In these experiments, the impacting speed is of 1.12$\pm$0.04 m/s. Images have been color inverted to show the contact line and shapes more clearly.

Figure 9

Evolution of the dynamic contact line modelled by lattice Boltzmann method without (upper sequence) and with (lower sequence) contact angle hysteresis model. The configuration corresponds to Series 2.

Figure 10

Comparison of final footprints for different initial droplet separations. Red contours on the experimental images (left) correspond to contours modelled by the lattice Boltzmann method (right). The configuration corresponds to Series 2.

Figure 11

Mixing within a composite droplet moving on a substrate with a wettability gradient. Time is given in lattice Boltzmann time steps.