Rayleigh-Taylor instability with

Figure 4. Rayleigh-Taylor instability with a descending front of butyl acrylate...

Figure 3. Rayleigh-Taylor instability with descending front of butyl acrylate polymerization. Although the polymer product is hot (> 200 °C) it still is about 20% more dense than the monomer below it.

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. 

However numerical simulations of early supernova-driven winds fail to find any evidence for substantial gas ejection from luminous ( L ) galaxies. One can ask what is wrong with the hydrodynamic simulations Certainly, the simulations lack adequate resolution. Rayleigh-Taylor instabilities enhance wind porosity and Kelvin-Helmholtz instabilities enhance wind loading of the cold interstellar medium. Both effects are certain to occur and will enhance the wind efficacity. Yet another omission is that one cannot yet resolve the motions of massive stars before they explode. This means that energy quenching is problematic and the current results are inconclusive for typical massive galaxies. 

Dzwinel W, Yuen DA (2001) Mixing driven by Rayleigh-Taylor instability in the mesoscale modeled with dissipative particle dynamics. Int l J Modem Phys C 12 91-118. 

Figure 11 Phenomena connected with drop breakup (a) deformation (splitting) of droplets, (b) deformation into lenticular shape, (c) development and separation of the boundary layer, (d) velocity distribution near the separation point of the boundary layer, (e) Kelvin Helmholtz instability, and (f) Rayleigh Taylor instability, pi < P2-...

Clearly, Gk > 0 for R > 0. Instability corresponding to R > 0 is the analog of Rayleigh Taylor instability. For a flat interface, we could have instability only for R > 0. Here, however, we may still have instability even if R <0, provided R/R is sufficiently large. To determine the condition for G > 0 in terms of controllable parameters, we can substitute for R/R in (4-315) by using the inviscid form of the Rayleigh Plesset equation, (4-204), with y = 0, that is,... 

The generalization of the analysis of the Rayleigh-Taylor instability to the acceleration of a spherical interface was independently reported by two authors M. S. Plesset, On the stability of fluid flows with spherical symmetry, J. Appl. Phys. 25, 96-8 (1954) G. Birkhoff, Note on Taylor instability, Q. Appl. Math. 12, 306-9 (1954) Stability of spherical bubbles, Q. Appl. Math. 13, 451-3 (1956). 

However, the inverse problem, with the film on the underside of the solid substrate, now features a competition between the stabilizing (leveling) effect of capillary forces against the destabilizing effect of gravity. This corresponds to a well-known stability problem, called Rayleigh-Taylor instability, applied to the thin film. In this case,... 

In a film of infinite lateral extent, k can range from 0 to oo, so a necessary condition for instability is that AH > 2npgh. Since all wave numbers are available in a film of infinite extent, we see that this analysis predicts that the thin film will always be unstable, even with the stabilizing influence of surface tension, to disturbances of sufficiently large wavelength when van der Waals forces are present. Similarly, the Rayleigh Taylor instability that occurs when the film is on the underside of the solid surface will always appear in a film of infinite extent. In reality, of course, the thin film will always be bounded, as by the walls of a container or by the finite extent of the solid substrate. Hence the maximum wavelength of the perturbation of shape is limited to the lateral width, say W, of the film. This corresponds to a minimum possible wave number... 

Problem 12-9. Rayleigh-Taylor Instability for a Pair of Superposed Fluids that are Bounded Above and Below by an Impermeable Wall. In this problem, we wish to determine the effect of a pair of horizontal bounding walls that exist at a finite distance above and below a horizontal fluid interface on Rayleigh Taylor instability. We suppose that the interface is located at z = 0 and that the two fluids are inviscid, with the density of the fluid below the interface p being less than the density of the fluid above the interface pi. The boundary above the interface is located at z = hi, whereas that below the interface is at z = —h. Show that... 

An alternative approach is to use direct numerical simulation (DNS). Numerical results can offer considerable detail and allow access to the complete fluid flow. For example, how big is the role of disturbances generated in the atomizer Does the Rayleigh-Taylor instability matter in primary atomization Do ijewly formed droplets immediately collide with ligaments and previously formed droplets How useful are small-perturbation analyses for primary atomization The disadvantage is that DNS is capable of simulating only a small part of the spray. 

Figure 9. Calculation of Rayleigh-Taylor instability using the Lagrangian technique with automatic zone restructuring. A heavy fluid falls through a light fluid, and there is a free surface on the top.

Garbey et al. also predicted that for a descending liquid/liquid front, an instability could arise even though the configuration would be stable for unreactive fluids (29-31). This prediction has yet to be experimentally verified because liquid/liquid frontal polymerization exhibits the Rayleigh-Taylor instability. A thermal frontal system with a product that is less dense than the reactant is required. 

Kelvin-Helmholtz instability arises because of shear along an interface between two different fluids. Being related to turbulence and transition phenomena, it also describes the onset of ocean wave formation, jetting instabilities, and cloud formation. In microfluidics, it is commonly seen in fluid-fluid interfaces. It is not to be confused with Rayleigh-Taylor or Rayleigh instability ( Rayleigh-Taylor instability). 

Taking a force balance between the surface tension along the surface of a fluid and the normal stresses across it, the Rayleigh instability will describe the tendency of a fluid stream to break up into droplets. It is not the same as the Rayleigh-Taylor instability, and not to be confused with Kevin-Helmholtz instabilities. 

Describes the formation of irregularities along an interface, typically fluid-fluid, as it is accelerated in a direction perpendicular to the interface. The phenomenon occurs in microfluidics in the atomization of sessile droplets. It is not the same as the Rayleigh instability ( Rayleigh-Taylor instability), and should not be confused with the Kevin-Helmholtz instability. 

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