Droplet impact velocity

Splashing can be seen to begin in droplets with Weber (We) numbers of 100-1000, and fingers have been observed in droplets that have a Reynolds (Re) number of 15000 and a We of 1000. (Re = p.u.d)/iJL and We = p.u. d)fa, where p,u,d,pt and a are the liquid density, droplet impact velocity, droplet diameter, liquid viscosity, and hquid surface tension respectively.) As the drops used in inkjet printing typically have diameters below 100 microns, values of Re = 2.5—2000, and We = 2.7-1000 can be expected. 

A limited number of polyanion-polycation systems were tested using a droplet/falling annulus method (Fig. 4). This technique, which has been described elsewhere [64] reduces the net impact velocity between the droplet with the oppositely charged counterion fluid. A stream of droplets was directed into a collapsing annular liquid sheet. By matching the velocities of the droplet and sheets, the impact conditions can be moderated. It has been shown to produce monodisperse spherical capsules, though it requires several days of calibration for each new system and is obviously not practical for a massive screening such as was carried out herein. 

To validate the model developed in the present study, the simulations are first conducted and compared with the experimental results of Wachters and Westerling (1966). In their experiments, water droplets impact in the normal direction onto a hot polished gold surface with an initial temperature of 400 °C. Different impact velocities were applied in the experiment to test the effect of the We number on the hydrodynamics of the impact. The simulation of this study is conducted for cases with different Weber numbers, which represent distinct dynamic regimes. 

The simulation shown in Fig. 10 is an impact of a saturated water droplet of 2.3 mm in diameter onto a surface of 400°C with an impact velocity of 65 cm/s, corresponding to a Weber number of 15. This simulation and all others presented in this study are conducted on uniform meshes (Ax — Ay — Az = A). The mesh resolution of the simulation shown in Fig. 10 was 0.08 mm in grid size, although different resolutions are also tested and the results are compared in Figs. 11 and 12. The average time-step in this case is around 5 ps. It takes 4000 iterations to simulate a real time of 20 ms of the impact process. The simulation... 

The simulations were also performed under same conditions as the case of Fig. 10 but for higher impact velocities. The simulated-droplet dynamics and heat-transfer rate at the solid surface at different impact velocities are given in Ge and Fan (2005). 

Three different subcooled impact conditions under which experiments were conducted and reported in the literature are simulated in this study. They are (1) K-heptane droplets (1.5 mm diameter) impacting on the stainless steel surface with We — 43 (Chandra and Avedisian, 1991), (2) 3.8 mm water droplets impacting on the inconel surface at a velocity of 1 m/s (Chen and Hsu, 1995), and (3) 4.0 mm water droplets impacting on the copper surface with We — 25 (Inada et al., 1985). The simulations are conducted on uniform Cartesian meshes (Ax = Ay — Az — A). The mesh size (resolution) is determined by considering the mesh refinement criterion in Section V.A. The mesh sizes in this study are chosen to provide a resolution of CPR =15. 

Fig. 14 shows the comparison of the photographs from Chandra and Avedisian (1991) with simulated images of this study for a subcooled 1.5 mm n-heptane droplet impact onto a stainless-steel surface of 200 °C. The impact velocity is 93 cm/s, which gives a Weber number of 43 and a Reynolds number of 2300. The initial temperature of the droplet is room temperature (20 °C). In Fig. 14, it can be seen that the evolution of droplet shapes are well simulated by the computation. In the first 2.5 ms of the impact (frames 1-2), the droplet spreads out right after the impact, and a disk-like shape liquid film is formed on the surface. After the droplet reaches the maximum diameter at about 2.1ms, the liquid film starts to retreat back to its center (frame 2 and 3) due to the surface-tension force induced from the periphery of the droplet. Beyond 6.0 ms, the droplet continues to recoil and forms an upward flow in the center of the... 

The impact process of a 3.8 mm water droplet under the conditions experimentally studied by Chen and Hsu (1995) is simulated and the simulation results are shown in Figs. 16 and 17. Their experiments involve water-droplet impact on a heated Inconel plate with Ni coating. The surface temperature in this simulation is set as 400 °C with the initial temperature of the droplet given as 20 °C. The impact velocity is lOOcm/s, which gives a Weber number of 54. Fig. 16 shows the calculated temperature distributions within the droplet and within the solid surface. The isotherm corresponding to 21 °C is plotted inside the droplet to represent the extent of the thermal boundary layer of the droplet that is affected by the heating of the solid surface. It can be seen that, in the droplet spreading process (0-7.0 ms), the bulk of the liquid droplet remains at its initial temperature and the thermal boundary layer is very thin. As the liquid film spreads on the solid surface, the heat-transfer rate on the liquid side of the droplet-vapor interface can be evaluated by... 

Fig. 17. Droplet impacts on the flat surface with a small tangential velocity. Other conditions are the same as those in Fig. 16.

Fig. 23. Experimental photos (left) and simulated images (right) of the 2.1mm acetone droplet impact on 5.5-mm particle at 250 °C. Impact velocity V = 45cm/s.

The spreading behavior of droplets on a non-flat surface is not only dependent on inertia and viscous effects, but also significantly influenced by an additional normal stress introduced by the curved surface. This stress leads to the acceleration-deceleration effect, or the hindering effect depending on the dimensionless roughness spacing, and causes the breakup and ejection of liquid. Increasing impact velocity, droplet diameter, liquid density, and/or... 

This number is conceptually an energy ratio, but independent of the interface heat extraction rate and thus the contact area. Since the interface heat transfer is assumed to control the solidification process of an impacting droplet, the choice of a dimensionless number should involve an evaluation of the influence exerted by this key factor. Therefore, the use of this newly defined dimensionless number is limited to an initial decision on which of the Impact number and the Freezing number is most appropriate for the application to a given material system at a know impact velocity. 

Generally, the occurrence of a specific mode is determined by droplet impact properties (size, velocity, temperature), surface properties (temperature, roughness, wetting), and their thermophysical properties (thermal conductivity, thermal capacity, density, surface tension, droplet viscosity). It appeared that the surface temperature and the impact Weber number are the most critical factors governing both the droplet breakup behavior and ensuing heat transfer. I335 412 415]... 

Figure 3.30. Schematic showing the impact phenomena of multiple droplets on a substrate surface spreading pattern at low impact velocities (fop) and splashing mechanism at high impact velocities (bottom).

Yarin and Weiss[357] also determined the number and size of secondary droplets, as well as the total ejected mass during splashing. Their experimental observations by means of a computer-aided charge-coupled-device camera and video printer showed that the dependence of the critical impact velocity, at which splashing initiates, on the physical properties (density, viscosity, and surface tension) and the frequency of the droplet train is universal, and the threshold velocity may be estimated by ... 

Comparing Eq. (51) to Eq. (43) or Eq. (52) to Eq. (44a), it is clear that for the same liquid properties and droplet diameter at impact, splashing takes place at lower impact velocities on a liquid film than on a dry surface. 

For the deformation of droplets of normal liquids at low impact velocities on a horizontal plane surface without phase change, Tan et al)513 developed a physical-mathematical model with a droplet falling from a certain height under the influence of gravity. They derived quantitative relations for the dimensions of the deformed droplet, including the effects of initial droplet diameter, height of fall, and thermophysical properties of liquid. In this model, the behavior of droplet deformation was assumed to be governed by... 

The compressible models resolve a very early stage of droplet deformation when the compressible wave generated by impact has not yet traveled throughout the droplet. In this stage, the shock wave separates the compressed liquid from the undisturbed liquid that is above the compressed liquid and at the initial impact velocity. The intersection of the compressed and undisturbed liquids constitutes a contact ring. As long as the velocity of the contact ring is... 

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