Breakup initial

A jet emerging from a nonciicular orifice is mechanically unstable, not only with respect to the eventual breakup into droplets discussed in Section II-3, but, more immediately, also with respect to the initial cross section not being circular. Oscillations develop in the Jet since the momentum of the liquid carries it past the desired circular cross section. This is illustrated in Fig. 11-20. 

The first is a pyrolytic approach in which the heat dehvered by the laser breaks chemical bonds in vapor-phase reactants above the surface, allowing deposition of the reaction products only in the small heated area. The second is a direct photolytic breakup of a vapor-phase reactant. This approach requires a laser with proper wavelength to initiate the photochemical reaction. Often ultraviolet excimer lasers have been used. One example is the breakup of trimethyl aluminum [75-24-1] gas using an ultraviolet laser to produce free aluminum [7429-90-5], which deposits on the surface. Again, the deposition is only on the localized area which the beam strikes. 

Internal Flow. Depending on the atomizer type and operating conditions, the internal fluid flow can involve compHcated phenomena such as flow separation, boundary layer growth, cavitation, turbulence, vortex formation, and two-phase flow. The internal flow regime is often considered one of the most important stages of Hquid a tomiza tion because it determines the initial Hquid disturbances and conditions that affect the subsequent Hquid breakup and droplet dispersion. 

J ct Spra.y, The mechanism that controls the breakup of a Hquid jet has been analy2ed by many researchers (22,23). These studies indicate that Hquid jet atomisation can be attributed to various effects such as Hquid—gas aerodynamic interaction, gas- and Hquid-phase turbulence, capillary pinching, gas pressure fluctuation, and disturbances initiated inside the atomiser. In spite of different theories and experimental observations, there is agreement that capillary pinching is the dominant mechanism for low velocity jets. As jet velocity increases, there is some uncertainty as to which effect is most important in causing breakup. 

It has been postulated that jet breakup is the result of aerodynamic interaction between the Hquid and the ambient gas. Such theory considers a column of Hquid emerging from a circular orifice into a surrounding gas. The instabiHty on the Hquid surface is examined by using first-order linear theory. A small perturbation is imposed on the initially steady Hquid motion to simulate the growth of waves. The displacement of the surface waves can be obtained by the real component of a Fourier expression ... 

Pipe Lines The principal interest here will be for flow in which one hquid is dispersed in another as they flow cocurrently through a pipe (stratified flow produces too little interfacial area for use in hquid extraction or chemical reaction between liquids). Drop size of dispersed phase, if initially very fine at high concentrations, increases as the distance downstream increases, owing to coalescence [see Holland, loc. cit. Ward and Knudsen, Am. In.st. Chem. Eng. J., 13, 356 (1967)] or if initially large, decreases by breakup in regions of high shear [Sleicher, ibid., 8, 471 (1962) Chem. Eng. ScL, 20, 57 (1965)]. The maximum drop size is given by (Sleicher, loc. cit.)... 

Bubble stability and breakup were reviewed by Hinze (H16). Early stages in the motion and breakup of two-dimensional air bubbles in water have been followed by Rowe and Partridge (R8), using high-speed cinephotography. The initial diameter of their circular bubble was about 4 in. 

Mechanical compatibilization is accomplished by reducing the size of the dispersed phase. The latter is determined by the balance between drop breakup and coalescence process, which in turn is governed by the type and severity of the stress, interfacial tension between the two phases, and the rheological characteristics of the components [9]. The need to reduce potential energy initiates the agglomeration process, which is less severe if the interfacial tension is small. Addition... 

Bubble and drop breakup is mainly due to shearing in turbulent eddies or in velocity gradients close to the walls. Figure 15.11 shows the breakup of a bubble, and Figure 15.12 shows the breakup of a drop in turbulent flow. The mechanism for breakup in these small surface-tension-dominated fluid particles is initially very similar. They are deformed until the aspect ratio is about 3. The turbulent fluctuations in the flow affect the particles, and at some point one end becomes... 

Fig. 16. Drop breakup in the journal bearing flow. The drop initially in the chaotic region of the flow deforms into a thin filament that breaks to produce a fine dispersion of droplets. The drop initially in the regular region of the flow (island) remains undeformed (Tjahjadi and Ottino, 1991).

In the context of the preceding model, a drop is said to break when it undergoes infinite extension and surface tension forces are unable to balance the viscous stresses. Consider breakup in flows with D mm constant in time (for example, an axisymmetric extensional flow with the drop axis initially coincident with the maximum direction of stretching). Rearranging Eq. (26) and defining a characteristic length Rip113, we obtain the condition, for a drop in equilibrium,... 

Fig. 22. Radius of drops produced by capillary breakup (solid lines) and binary breakup (dotted lines) in a hyperbolic extensional flow for different viscosity ratios (p) and scaled shear rate (p,cylo) (Janssen and Meijer, 1993). The initial amplitude of the surface disturbances is ao = 10 9 m. Note that significantly smaller drops are produced by capillary breakup for high viscosity ratios.

Breakup due to capillary instabilities dominates when the length of the filament is more than 15 times the initial radius of the drop. 

The basic procedure of the VILM model is to send an initial distribution of drops through a specified number of strong and weak zones. With each pass through the strong and weak zones, the evolution of the drop distribution is determined based on the fundamentals of breakup and coalescence. 

A solution to this problem (Hansen and Ottino, 1996a) reveals that the cluster size distribution is bimodal, as expected, with c(x,t) for large x dependent upon the initial conditions (Fig. 35a). The distribution thus does not approach a self-similar form and the scaling results just given are not valid for this problem. This is a result of the non-homogeneous relative rate of breakup. 

Fig. 43. Capillary breakup of closely spaced molten nylon-6 threads in molten polystyrene. Photograhs at different times are shown (frames a through f correspond to 0, 210, 270, 360, 390, and 510 s). The initial thread diameter is 70 fim (Elemans el at., 1997).

Stone, H. A., and Leal, L. G., Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399-427 (1989). 

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