Capillary breakup process

Illustration Satellite formation in capillary breakup. The distribution of drops produced upon disintegration of a thread at rest is a unique function of the viscosity ratio. Tjahjadi et al. (1992) showed through inspection of experiments and numerical simulations that up to 19 satellite drops between the two larger mother drops could be formed. The number of satellite drops decreased as the viscosity ratio was increased. In low-viscosity systems p < 0(0.1)] the breakup mechanism is self-repeating Every pinch-off results in the formation of a rounded surface and a conical one the conical surface then becomes bulbous and a neck forms near the end, which again pinches off and the process repeats (Fig. 21). There is excellent agreement between numerical simulations and the experimental results (Fig. 21). 

Linear stability theories have also been applied to analyses of liquid sheet breakup processes. The capillary instability of thin liquid sheets was first studied by Squire[258] who showed that instability and breakup of a liquid sheet are caused by the growth of sinuous waves, i.e., sideways deflections of the sheet centerline. For a low viscosity liquid sheet, Fraser et al.[73] derived an expression for the wavelength of the dominant unstable wave. A similar formulation was derived by Li[539] who considered both sinuous and varicose instabilities. Clark and DombrowskF540 and Reitz and Diwakar13161 formulated equations for liquid sheet breakup length. 

For a 5-mm-diameter water jet the characteristic capillary time (pa Ia) is 4.14 X 10 s, so we may expect such a slow-moving jet to break up very quickly, in distances on the order of a centimeter for speeds approximately 0.1 ms The jet breakup length is predicted remarkably well by Rayleigh s linear result over a wide range of disturbance amplitudes even though the breakup process may be strongly nonlinear. 

Some authors report the next guide principles that may be applied for blend morphology after processing, (i) Drops with viscosity ratios higher than 3.5 cannot be dispersed in shear but can be in extension flow instead, (ii) The larger the interfacial tension coefficient, the less the droplets will deform, (iii) The time necessary to break up a droplet (Tj,) and the critical capillary number (Ca ) are two important parameters describing the breakup process, (iv) The effect of coalescence must be considered even for relatively low concentrations of the dispersed phase. 

Sheets produced in zone A (Re < 800) have relatively stable rim. The Reynolds numbers are low, therefore, viscous effects are dominate. Open rim sheets are typically broken at their open edges. As the Reynolds number is increased, the rims become unstable rapidly. Therefore, in zone B (800 < Re < 3,000), the sheet breakup process includes both a laminar capillary instability at the rims and Taylor instability on open edges of the sheet. Similar breakup process is observed in zone C, except that the whole flow is turbulent. Therefore, the breakup process in this zone is identified as turbulent rim instability combined with turbulent sheet instability. The data points in this zone are within 7,000 < Re < 18,000. For Re > 18,000 the rim cannot be distinguished, and the breakup process is mainly turbulent sheet breakup [26]. 

Fig. 4.10 Schematic representation of the interfacial tension measurements by the capillary breakup method do is the initial diameter of the fiber, h and a are the maximum and minimum diameters observed during the breakup process, respectively... 

Fig. 22.12 Span value for different dimensionless viscosities and flow rates depending on the gas-Weber number. The threads emerge from vertically orientated completely filled capillaries. The curves show similar tendency for all process conditions, as the span value increases considerably for low gas-Weber numbers. Afterward, it rises steadily. The increasing disturbance due to cross-wind flow leads to perturbation of the surface-driven breakup process [33]...

Another important parameter of the droplet breakup process is the time necessary for the interfacial-driven instabilities to cause breakup, tb, when the actual capillary number exceeds the critical capillary number. Grace (1982) provided this information in Figure 6.21 for Newtonian fluids. Note that the dimensionless burst time is denoted as which is equal to tb/r, where r is the time scale of the bursting process and it is equal to Rp-Jy- For example, for a polymer blend with p = 0.1,)/ = 10 mN/m, / = 10 qm, Pc = 1.000 Pa s, and Ca/Cac — 10, the dimensionless burst time is 11, and the time scale is equal to 1 s. Thus, the burst time, tb, is equal to 11 s. 

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. 

Mitulovic etal., 2003). An additional benefit of online HPLC/ESI-MS is that sample cleanup, analyte concentration and separation are accomplished in an automated process. However, polypeptides of high hydrophobicity are often retained on reversed-phase columns using a standard gradient and will therefore not be transferred into the MS device for mass analysis. Additionally, very hydrophobic peptides and proteins (e.g., membrane proteins) tend to precipitate in the small glass capillaries during the electrospray process, which leads to the breakup of the spray. 

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. 

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