Breakup of liquid threads

The previous discussion focused on the breakup of liquid thread suspended in a quiescent Newtonian fluid. In real mixing operations quiescent conditions will usually not occur, except perhaps for short periods of time. The more important issue, therefore, is how the breakup occurs when the system is subjected to flow. Good reviews on the breakup of liquid threads are available from Acrivos [304], Rallison [305], and Stone [306]. Probably the most extensive experimental study on drop breakup was performed by Grace [286] data was obtained over an enormous range of viscosity ratios 10- to 10 Grace determined the critical Weber (Capillary) number for breakup both in simple shear and in 2-D elongation the results are represented in Fig. 7.152. 

Gramlich, S., Mescher, A., Piesche, M., Walzel, P. (2011). Modeling and numerical simulation of the gas-induced breakup of liquid threads stretched by gravity. Chemical Engineering and Technology, 34(6), 921-926. 

Khakhar DV, Ottino JM. Breakup of liquid threads in linear flows. Int J Multiphase Flow 1987 13(l) 71-86. 

Figure 10(a) can be used to calculate parameters related to the drop formation. These parameters include speed of these representative points at various positions, speed of the primary drop and of satellites, pinch-off length and time of the liquid thread from the nozzle exit, time of breakup of liquid thread into satellites and the primary drop, sizes of the primary drop and of satellites, drop oscillation frequency, and the life expectancy of satellites. 

Fig. 22.5 Dimensionless breakup lengths of liquid threads plotted against the gas-Weber number for two dimensionless flow rates and viscosities. With increasing gas relative velocity, the breakup length decreases. Higher viscous threads show minor decay of breakup length compared to threads with lower viscosity. Increasing flow rate expressed by F leads to longer threads. Test liquids are glycerol water mixtures [33]...

The breakup of a cylindrical thread at rest has been studied [142,145,151]. A varicosity of wavelength A, (Fig. 1.14) at the surface of a liquid cylinder immersed in another liquid will be amplified if its development causes a decrease of the interfacial area. Such a condition is satisfied if A is larger than 2jtrc, tc being the radius... 

Droplet formation occurs primarily through the surface tension and viscosity dominated breakup of these liquid threads due to symmetric (or dilational) waves as described by Rayleigh (6) for inviscid liquids and by Weber (J) for viscous fluids. Figure 3 shows the double pulsed image of the droplet formation process for No. 2 and SRC-II fuel sprays under identical atomizer conditions. These two photographs illustrate typical differences seen between these two fuels. 

The inset in Fig. 1.23 shows a characteristic deceleration of the later stage of the capillary breakup of a dilatant jet, when significant rates of elongation in the liquid threads connecting the drops are reached, and the corresponding reinforcement of the liquid in the threads occurs. At this late stage, the evolution of the jet surface is so slow that the calculations can be made in the inertialess approximation. 

Papageorgiou, D. T. On the breakup of viscous liquid threads. Phys. Fluids 7, 1529-1544 (1995). 

Goren, S. L. Gottlieb, M. Surface-tension-driven breakup of viscoelastic liquid threads. 

Three different types of microsystem have been reported for the emulsification of a polymerizable liquid (Figure 18.1), namely the terrace-like microchannel device, the T-junction microchannel device and the flow focusing device (FFD). The emulsification mechanism, which is similar for these three devices, proceeds from the breakup of a liquid thread into droplets when the phase to be dispersed is sheared by the continuous and immiscible phase. 

The interfacial tension will want to reduce the interface between the two phases, minimizing the surface-to-volume ratio. The smallest surface-to-volume ratio is achieved in a sphere, S/V = 3/R. Thus, an extended liquid thread will tend to break up due to the interfacial tension. The breakup is initiated by small disturbances at the interface, so-called Rayleigh disturbances. These disturbances grow due to the interfacial tension and eventually breakup can occur. The progress of the breakup process is illustrated in Fig. 7.149. 

The first theoretical analysis of the breakup of a Newtonian thread in a quiescent Newtonian matrix was performed over a century ago by Rayleigh [284]. The disturbances that initiate the breakup process are often referred to as Rayleigh disturbances. Rayleigh analyzed only the effect of surface tension, neglecting the viscosities of the two phases. This work was extended by Tomotika [285] by including the effect of viscosity. The analysis considers a sinusoidal liquid cylinder the radius as a function of axial distance z is ... 

Mescher, A., Walzel, P. (2010). Breakup of stretched liquid threads at low gas relative velocities—Comparison of the laminar rotary atomization to the gravity condition. In 23th Annual Conference on Liquid Atomization and Spray Systems ILASS, Brno, Czech Republic, 6-8 September 2010. 

Breakup of Stretched Liquid Threads Influenced by Cross-Wind Flow Similarity Trials... 

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