Forced capillary breakup

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

Equations 1.49-1.51 represent themselves a slightly modified version of the equations used in [30-32]. The modification introduced in [29] and references therein involves the exact (not the asymptotic) expressions for the capillary force at the jet surface and capillary pressure in the jet cross-section, which allows description of the capillary breakup until formation of drops. A detailed derivation of such equations based on the above-mentioned physical assumptions and the integral mass and momentum balances can be found in the monograph [29]... 

Water Uptake. There is evidence to suggest that water uptake caused by capillary forces is the crucial factor in the disintegration process of many formulations. In such systems the pore structure of the tablet is of prime importance and any inherent hydrophobicity of the tablet mass will adversely affect it. Therefore, disintegrants in this group must be able to maintain a porous structure in the compressed tablet and show a low interfacial tension towards aqueous fluids. Rapid penetration by water throughout the entire tablet matrix to facilitate its breakup is thus achieved. Concentrations of disintegrant that ensure a continuous matrix of disintegrant are desirable and levels of between 5 and 20% are common. 

If gravitational settling can be neglected and if the droplet Reynolds number Re = payout 9s is small, then the droplet deformation and possible breakup in the flow are controlled by two dimensionless groups, namely the ratio of viscous to capillary forces, or capillary number... 

The most efficient mechanism of drop breakup involves its deformation into a fiber followed by the thread disintegration under the influence of capillary forces. Fibrillation occurs in both steady state shear and uniaxial extension. In shear (= rotation + extension) the process is less efficient and limited to low-X region, e.g. X < 2. In irrotatlonal uniaxial extension (in absence of the interphase slip) the phases codeform into threadlike structures. 

There are a number of modes of jet breakup, but we consider only the breakup into spherical drops caused by capillary forces, which implies low jet velocities into an external medium whose density is low by comparison with the jet, say, air. At high velocities the dynamic effect of the surrounding medium on the jet surface will alter the surface pressure, and tangential stresses at the surface due to viscosity may also affect the breakup. It is a well-known observation that at sufficiently high velocities a jet will atomize into a large number of small droplets compared with a relatively smaller number of big drops at low velocities. 

There are many various kinds of jet breakup. Consider only those that result in a disintegration of the jet into spherical drops due to the action of capillary forces. 

Now, consider the droplet formation resulting from the breakup of relatively large drops in a gas flow. The drop is subjected to an external aerodynamic force (pressure pc). It should be counterbalanced by the internal pressure of the drop Pi and the capillary pressure p ... 

The application of chaotic flows leads to much smaller droplets than allowed by the equilibrium between the shear and interfacial forces [204-206] and than those obtained in some commercial mixers. The smaller size of droplets can be directly traced back to their precursor thinner flbrils as the droplets originate from the fibrils by capillary instability and breakup. The exponential stretching encountered in chaotic mixers subdues the growth of interfacial instabilities in both lamellas and fibrils and consequently smaller diameter fibrils are produced. In some cases, fibrils with an aspect ratio as high as 1000 are produced [204]. In addition, the chaotic mixing conditions have been shown to slow down the rate of coalescence of droplets [207]. Another study utilized the rapid intermaterial area generation in chaotic flows to promote chemical reactions in the synthesis of thermoplastic polyurethanes [140]. 

In practice, in a mixture much larger drops can be found than predicted by the critical capillary number because Grace s observations were based on single drops. In actual systems, where many drops exist, coalescence will occur. Because material elements also undergo varying levels of shear forces in time, the mixing process in polymer systems can be considered as a complex interaction between deformation, drop breakup, coalescence, and retraction. 

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