Droplets shape

In many cases the potential P(z) is small compared with the surface energy of the liquid and the droplet shape is very close to a spherical cap. If the height e and the radius of curvature R at the top of the droplets can be measured, an effective contact angle can be defined through the expression ... 

When plotted as a function of drop size (Fig. 9), the contact angle was found to decrease with increasing drop height. A different analysis of these data was performed in the original paper. In that case the maximum slope near the drop edge was used, as well as a direct inversion of the droplet shape. The data could be fit to an empirical 1/z function. In the present analysis we use the method of the effective contact angles defined earlier, together with Eq. (18). For the Flamaker constant A, we calculated a value of approximately -2 X 10 ° J. However, the best fit to Eq. (18) is for a pure exponential decay of the form ... 

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... 

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... 

It should be noted that some problems may arise in the techniques or devices for producing monodisperse or near-monodis-perse sprays. One of the problems is droplet coalescence. Initially uniform droplets may coalesce rapidly to create doublets or triplets, particularly in a dense and turbulent spray, deteriorating the monodispersity of the droplets. This problem may be lessened by using appropriate dispersion air around the spray.[88] Another problem is non-spherical droplet shapes that make estimations of monodispersity difficult. 

Chandra and Avedisian 411] studied the collision dynamics of a liquid (n-heptane) droplet on a polished, solid, stainless steel surface, and on a liquid film created by deposition of a preceding droplet using a flash photographic method. They presented a comprehensive series of clear images of droplet shape, morphology, and structure during the deformation process. In their experiments, the... 

The final droplet/particle shape is determined by the time required for a deformed droplet to convert to spherical shape under surface tension force. If a droplet solidifies before the surface tension force contracts it into a sphere, the final droplet shape will be irregular. Nichiporenko and Naida[488l proposed the following dimensionally correct expression for the estimation of the spheroidization time, tsph ... 

A simple and direct method of contact angle measurement has also been proposed (Yamaki and Katayama, 1975 Carroll, 1976) by observing the shape of the liquid droplet attached to a single fiber, the so-called droplet aspect ratio method . The liquid is assumed to form a symmetrical droplet about the fiber axis as shown schematically in Fig. 2.21. Neglecting the effect of gravity, the droplet shape can be defined by the following expression ... 

It was previously shown that the formation of a stable emulsion of methylene chloride in water was vital for the successful formation of individual microspheres [4,9]. Two main factors played an important role in the emulsification of methylene chloride in water and influenced the microsphere size the interfacial tension of the methylene chloride droplets in the surrounding aqueous phase and the forces of shear within the fluid mass. The former tends to resist the distortion of droplet shape necessary for fragmentation into smaller droplets whereas the latter forces act to distort and ultimately to disrupt the droplets. The relationship between these forces largely determines the final size distribution of the methylene chloride in water emulsion which in turn controls the final size distribution of the solid microspheres formed. 

Since both components re generally non-Newtonian liquids and the droplet shape of the dispersed phase depends on shear stress, the rheological properties of these emulsions must be rather complicated. Consequently, the shear-stress dependence of the viscosity of the emulsions is caused not only by the characteristic properties of the macromolecular substances but also by the behavior of the dispersed phase in a shear field. 

Droplet Breakup—High Turbulence This is the dominant breakup mechanism for many process applications. Breakup results from local variations in turbulent pressure that distort the droplet shape. Hinze [Am. Inst. Chem. Eng.., 1, 289-295 (1953)] applied turbulence theory to obtain the form of Eq. (14-190) and took liquid-liquid data to define the coefficient ... 

Recently, surfactant adsorption and y have been measured at C02-water and C02-organic interfaces with a tandem variable-volume tensiometer (Harrison, 1996). A pendant drop of an aqueous or organic phase, saturated with C02, may be suspended in C02 or a C02-surfactant mixture and equilibrated. From the digitized droplet shape and density difference between the phases, y may be calculated from the Laplace equation. In Figure 8.1, y of the binary C02-water (da Rocha et al., 1999), -polyethylene... 

The forces acting on a single droplet include gravity, which acts vertically downward, and drag, which depends on the droplet shape and its relative velocity with respect to surrounding air. A force balance on a single droplet yields... 

Baker et al. [56] studied the viscosity of w/o ME systems containing water, xylene, sodium alkylbenzenesulfonate, and hexanol using Equation (1). They reported values of the viscosity constant a of 3.3-6.0, which is above the theoretical value of 2.5 for a sphere with an increase in the surfactant concentration. This finding was attributed to the increase in the ratio of surfactant layer thickness to droplet core radius as the surfactant concentration was increased. However, deviation in values of the viscosity constant a from the solid-sphere theoretical value of 2.5 could also be attributed to changes in the droplet shape or symmetry [57],... 

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