Jet stability

As described previously, in the atomization sub-model, 232 droplet parcels are injected with a size equal to the nozzle exit diameter. The subsequent breakups of the parcels and the resultant droplets are calculated with a breakup model that assumes that droplet breakup times and sizes are proportional to wave growth rates and wavelengths obtained from the liquid jet stability analysis. Other breakup mechanisms considered in the sub-model include the Kelvin-Helmholtz instability, Rayleigh-Taylor instability, 206 and boundary layer stripping mechanisms. The TAB model 310 is also included for modeling liquid breakup. 

Establishing a criterion for blowoff during opposed-jet stabilization is difficult owing to the sensitivity of the recirculation region formed to its stoichiometry. This stoichiometry is well defined only if the main stream and opposed jet compositions are the same. Since the combustor pressure drop is of the same order as that found with bluff bodies [76], the utility of this means of stabilization is questionable. 

The jet stability and break-off behavior with respect to the fluid properties are stated in well-known theories such as Navier-Stokes equations and the Rayleigh theory. During recent years many computer simulations have aimed at predicting the jetting process in specific print heads and, more importantly, for establishing a methodology for selection of ink additives. ... 

The physical entrainment rate of gas varies over orders of magnitude as a function of jet stability, which acts as the surface shape generator. The controllable parameters of the system are nozzle geometry, nozzle velocity, nozzle height, jet length, and jet velocity. McCarthy et al. (Ml) have analyzed gas entrainment in such contactors in terms of the surface roughness of the jet and have proposed an entrainment ratio ... 

Weber C. On the breakdown of a fluid jet. Z Angew Math Mech 1931 11 136-154. Fenn RW, Middleman S. Newtonian jet stability— the role of air resistance. AIChE J 1969 15 379. 

Even if the jet velocity is low enough that just capillary forces need be accounted for, the hydrodynamic stability problem is relatively simple when only the jet stability to small disturbances is considered, that is, disturbances whose amplitudes are small compared with the jet radius. When this is not the case, nonlinear mechanisms enter, which are manifest in various phenomena, including the formation of satellite droplets, which are small spherules that form between the drops (Fig. 10.4.2B). For literature on these and other nonlinear effects of jet instability, see Bogy (1979). 

Much of the procedure for the analysis of jet stability has already been set down in connection with the discussion of undamped surface waves on deep water. A fundamental difference in the jet problem from plane deep water waves is that it is axisymmetric with an imposed characteristic length scale equal to the jet radius a. Since the undisturbed jet is considered to be inviscid and in uniform flow, it can be reduced to a state of rest simply by a Galilean transformation. With gravity neglected and only surface tension forces acting, the pressure at any point within the jet is -I- ala. This then describes the basic flow needed for the first step of the stability analysis. 

Pearson s theoretical treatment was based on a linear stability analysis of the type described in Section 10.4 in connection with jet stability to small disturbances and paralleled Rayleigh s analysis for buoyancy driven instability. He assumed an infinite homogeneous liquid film of uniform thickness h whose lower surface is in contact with a rigid heat conductor at a fixed temperature and whose upper surface is free. Gravity is neglected (Ra = 0) and a linear temperature distribution across the film is assumed, with the high temperature at the lower surface. The surface tension is a function of temperature alone, and the rate of heat loss from the free surface is also a function of temperature only. 

Jets leaving the orifices may be unstable they may move laterally or even break into spray. This can be visualized by experimenting with a household tap. Kaiser (183a) proposed a correlation in terms of the Reynolds and Weber numbers to predict jet stability. However, jet stability is also dependent on surface irregularities at the orifices, and these are difficult to predict. 

Both aqueous and solvent based solutions of Nafion has been printed using ink-jet methods. The solvent based solution of Nafion has a tendency to dry around the nozzle of the jetting device. Further dilution with a solvent with higher boiling point helped to mitigate drjdng around the nozzle. Overall, aqueous solutions of Nafion showed better jet stability and are more conducive to printing membranes. 

Fig. 27.2 Jet stability curve dripping flow (A-B-C), Rayleigh breakup (C-D), wind-induced regime (D-F), atomization regime (F-G oiH)...

Commercial wire drawing processes produce metal wires with round cross sections but they are highly energy and labor intensive. Wire drawing falls outside the scope of this book. Commercial rapid solidification processes yield amorphous metallic ribbons. Inviscid melt spinning yields metal fibers by a chemically assisted jet stabilization process. 

Continuous aluminate glass fibers are formed in the presence of propane, but not in its absence. A viable mechanism of jet stabilization must therefore explain (1) the function of carbon which enters into the surface or skin of the molten jet, (2) the function of carbides and carbonates which are instantly formed in the molten jet surface, and (3) the increase in tetrahedral from octahedral coordination of aluminum atoms in the surface [51] before the fiber solidifies and secondary overgrowth with carbon can occur. 

F. T. Wallenberger, N. E. Weston, K. Motzfeldt, and D, G. Swartzfager, Inviscid melt spinning of alumina fibers chemical jet stabilization, Journal of the American Ceramic Society. 75 [3], 629-639 (1992). 

Surfactants, such as glycerine can be used in these cases. Viscosity has jet-stabilizing effect, but on the other hand, higher repulsion forces are required to stretch a more viscous hquid. Below the proposed viscosity, bead formation on fibers can be seen, and further decrease of the viscosity leads to electrospraying. To avoid bead-forming instability, the viscosity and surface tension should be increased [25], or increasing the conductivity may help [82],... 

Dukhin, S. S., Zhu, C., Dave, R., Pfeffer, R., Luo, J. J., Chavez, F., et al. (2003). Dynamic interfacial tension near critical point of a solvent-antisolvent mixture and laminar Jet stabilization. Colloids and Surfaces A Physicochemical and Engineering Aspects, 229, 181-199. 

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