Droplet flattening

In case that the decay of impact kinetic energy due to viscous dissipation is the predominant mechanism in droplet flattening, Madejski s full model reduces to ... 

For droplets of high surface tension, the droplet flattening process may be governed by the transformation of impact kinetic energy to surface energy. In case that this mechanism dominates, the flattening ratio becomes only dependent on the Weber number, as derived by Madej ski by fitting the numerical results of the full analytical model ... 

Sobolev et al)5111 conducted a series of analytical studies on droplet flattening, and solidification on a surface in thermal spray processes, and recently extended the analytical formulas for the flattening of homogeneous (single-phase) droplets to composite powder particles. Under the condition Re 1, the flattening ratios on smooth and rough surfaces are formulated as ... 

Figure 15. The electrowetting effect. (According to Mugele et al. [260].) (a) If a voltage V is applied between a liquid and an electrode separated by an insulating layer, the contact angle of the liquid-solid interface is decreased and the droplet flattens , (b) Hydrophobic surfaces enhance the effect of electro wetting. For electrowetting on dielectrics (EWOD) several individual addressable control electrodes (here on the bottom) and a large counter-electrode are used. The droplet is pulled to the charged electrodes.

Dhiman and Chandra [41] photographed impact of water droplets on surfaces of different wettability at impact velocities up to 30 m/s. Figure 8.8 shows three different sequences of the impact of water droplets on a wax surface at three different impact velocities 10 m/s, 20 m/s and 30 m/s. Each vertical column shows successive stages of impact at one of the velocities, which yielded Reynolds numbers (Re) of 5,800, 11,600, and 17,400 respectively. Droplets flattened into a thin film after impact as they reached their maximum extension, followed by retraction until they eventually attained equilibrium. The diameter of the films at maximum extension increased with Re and hence their thickness decreased. Holes were formed in each film that grew larger, rendering the film unstable. 

Since the shape of an oil droplet is an indication of IFT as measured by sessile drop method, the oil droplet flattening time reflects the rate of change in IFT. The results clearly show that the presence of alcohol increases the rate of achieving the final value of interfacial tension. This implies that the surfactant molecules come to the interface much faster in the presence of alcohol. Zana (20) has shown that the kinetics of micellization is more rapid in the presence of alcohol. This is presumably due to loose packing of mixed micelles containing surfactant and alcohol. Thus, it appears that the kinetics of micellization could influence the rate at which molecules saturate the surface by the breakdown of micelles to provide monomers for adsorption. 

To explain the effect of equilibration on oil recovery, the liquid-liquid and liquid-rock interfaces (i.e., the IFT s and contact angles) were studied for these systems and the results are listed in Table 3. Except for the system of fresh oil/1% NaCl, the contact angle measurements followed the pattern shown in Figures 5 and 6. The oil drop formed nearly a sphere on the quartz surface initially. It then flattened out and finally, in some cases, disintegrated or emulsified into many small droplets. The time between the formation of the initial spherical droplet and the final emulsification is defined as the oil droplet flattening time. Except for system III, there is a good correlation between the flattening time, the IFT value and the oil displacement efficiency. 

These hydrophobic species are mainly responsible for the oil droplet flattening phenomenon. The flattening time of a single oil drop has a direct bearing on the oil displacement efficiency. Because there are large numbers of oil droplets within the porous media, the amount of oil recovered depends on how easily each of them can be mobilized. The faster they are flattened, the easier it would be to mobilize, interconnect and displace them. Cash et al. (12) demonstrated that oil displacement by the spontaneously emulsifying systems is better than the systems lacking spontaneous emulsification. 

To sum up, the following mechanism is proposed to account for the observed effects in IFT and oil droplet flattening phenomenon. As shown in Figure 4, mixed micelles in equilibrium with surfactant monomers are formed by the water-soluble and oil-soluble species in the bulk aqueous solutions. During equilibration, the surfactant monomers transfer to the water/oil interface and then to the interior of the oil drop resulting in a reduction of IFT. 

When drops impinge on a leaf surface one of several states may arise the droplet may bounce the droplet may undergo fragmentation the droplet flattens retracts - spreads - forms hemispherical cap. This is schematically illustrated in Fig. 3.54 where a droplet first flattens, retracts and finally forms a hemispherical cap with a certain contact angle 0. 

These factors make it necessary to reduce the amount of solvent vapor entering the flame to as low a level as possible and to make any droplets or particulates entering the flame as small and of as uniform a droplet size as possible. Desolvation chambers are designed to optimize these factors so as to maintain a near-constant efficiency of ionization and to flatten out fluctuations in droplet size from the nebulizer. Droplets of less than 10 pm in diameter are preferred. For flow rates of less than about 10 pl/min issuing from micro- or nanobore liquid chromatography columns, a desolvation chamber is unlikely to be needed. 

Comparing the 3-D images simulated and the experimental photographs in Fig. 10, it can be seen that the droplet shapes are well reproduced by the present model. During the first 3.5 ms of the impact (frames 1-3), a liquid film with flattened disc shape is formed immediately after the impact. The inertial force drives the liquid to continue spreading on the solid surface, while the surface tension and the viscous forces resist the spreading of the liquid film. As a result, the droplet spreading speed decreases and the fluid mass starts to accumulate at... 

Chloroplasts (29-36) are the sites of photosynthesis and their ribosomes can carry out protein synthesis. Chloroplasts that contain chlorophylls and carotenoids, are disc shaped and 4-6 pm in diameter. These plastids are comprised of a ground substance (stroma) and are traversed by thylakoids (flattened membranous sacs). The thylakoids are stacked as grana. In addition, the chloroplasts of green algae and plants contain starch grains, small lipid oil droplets, and DNA. 

A droplet is initially flattened to an oblate, lenticular ellipsoid and then may be converted into a torus, depending on the magnitude of the internal forces causing the deformation. The torus subsequently becomes stretched and splits into smaller droplets. 

Subjected to steady acceleration, a droplet is flattened gradually. When a critical relative velocity is reached, the flattened droplet is blown out into a hollow bag anchored to a nearly circular rim which contains at least 70% of the mass of the original droplet. Surface tension force is sufficient to allow the bag shape to develop. The bag, with a concave surface to the gas flow, is stretched and swept off in the downstream direction. The rupture of the bag produces a cloud of very fine droplets presumably via a perforation mode, and the rim breaks up into relatively larger droplets, although all droplets are at least an order of magnitude smaller than the initial droplet size. This is referred to as bag breakup (Fig. 3.10)T2861... 

The first stage, called dynamic stage, is the period during which a spherical droplet is flattened and deformed into a planetary ellipsoid with its major axis perpendicular to the flow direction as a result of the external pressure distribution. The eccentricity of the elliptical profile changes with time. 

Figure 3.13. Deformation process of a single droplet impinging on a flat surface (Re = 1600, We = 26.7) (a) simulation left), experiment right), and (b) comparison between calculated and measured dimensionless diameter and height ofa flattening droplet. (Photograph Courtesy of Prof. Dr. Jiro Senda at Doshisha University, Japan. Experimental data reprinted with permission from Ref. 334.)...

Fukanuma and Ohmori15101 also presented an analytical model for the flattening ratio of a molten metal droplet on a surface as a function of time and compared the model prediction to experimental data for molten tin and zinc droplets. An expression for the flattening ratio was derived based on some simplified assumptions and approximations ... 

Viscous Dissipation Domain The decay of kinetic energy of an impacting droplet is due to viscous dissipation during flattening. 

Solidification Domain Cooling and solidification of an impacting droplet occur simultaneously during flattening. 

---