Taylor instabilities

Taylor instabilities involve effects of buoyancy or acceleration in fluids with variable density a light fluid beneath a heavy fluid is unstable by the Taylor mechanism. The upward propagation of premixed flames in tubes is subject to Taylor instability (11). 

Because the bubble population increases with heat flux, a point of peak flux may be reached in nucleate boiling where the outgoing bubbles jam the path of the incoming liquid. This phenomenon can be analyzed by the criterion of a Hemholtz instability (Zuber, 1958) and thus serves to predict the incipience of the boiling crisis (to be discussed in Sec. 2.4.4). Another hydrodynamic aspect of the boiling crisis, the incipience of stable film boiling, may be analyzed from the criterion for a Taylor instability (Zuber, 1961). 

Bellman, R., and R. H. Pennington, 1954, Effects of Surface Tension and Viscosity on Taylor Instability, Quarter. Appl. Math., 12 151. (6)... 

Particles Penetrate Into Bubble Roof Due to Taylor Instability When Penetration Completely Pierces Bubble - Bubble Splits... 

Taylor instability, 77 763 Taylor number, 77 747, 23 190 Taylor System, 27 171 Tazarotene, 25 789 Tazettine, 2 87 TBASE database, 72 467 TBCCO films, 23 872 TBTS, 2 550t TCCA, 73 115... 

Dm =(4 3c7/pi 02)1/3 Dm = 0.42 3 for largg pL(Oqc 2o Derived on the basis of capillary wave theory in terms of Taylor instability, for thick films Peskin Raco [483]... 

Further extensions of Madej ski s mod ell4011 may include (a) turbulence effect, (b) Rayleigh instability or Taylor instability and droplet breakup, (c) vibrational energy, and (d) influence of solidification on flow)514 Some issues related to the deformation and solidification of droplets on a flat substrate in splat quenching have been addressed in Refs. 380 and 514. To date, analytical models addressing droplet impingement on a semi-solid surface have not been found in available literature. 

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. 

A horizontal interface between two fluids such that the lower fluid is the less dense tends to deform by the process known as Rayleigh-Taylor instability (see Section UFA). Spikes of the denser fluid penetrate downwards, until the interface is broken up and one fluid is dispersed into the other. This is observed, for example, in formation of drops from a wet ceiling, and of bubbles in film boiling. For low-viscosity fluids, the equivalent diameter of the particle formed is of order Ja/gAp. 

When one fluid overlays a less dense fluid, perturbations at the interface tend to grow by Rayleigh-Taylor instability (LI, T4). Surface tension tends to stabilize the interface while viscous forces slow the rate of growth of unstable surface waves (B2). The leading surface of a drop or bubble may therefore become unstable if the wavelength of a disturbance at the surface exceeds a critical value... 

There is some evidence that isolated drops may shake themselves apart if shape oscillations become sufficiently violent (L7). It has been suggested (El, Gil, H22) that breakup occurs when the exciting frequency of eddy shedding matches the natural frequency of the drop. However, other workers (S7) have found that oscillations give way to random wobbling before breakup occurs. While it is possible that resonance may produce breakup in isolated cases, this mechanism appears to be less important than the Taylor instability mechanism described above. 

Remark. Instability and bistability are defined as properties of the macroscopic equation. The effect of the fluctuations is merely to make the system decide to go to one or the other macroscopically stable point. Similarly the Taylor instability and the Benard cells are consequences of the macroscopic hydrodynamic equations. ) Fluctuations merely make the choice between different, equally possible macrostates, and, in these examples, determine the location of the vortices or of the cells in space. (In practice they are often overruled by extraneous influences, such as the presence of a boundary.) Statements that fluctuations shift or destroy the bistability are obscure, because on the mesoscopic level there is no sharp separation between stable and unstable systems. Some authors call a mesostate (i.e., a probability distribution P) bistable when P has two maxima, however flat. This does not correspond to any observable fact, however, unless the maxima are well-separated peaks, which can each be related to separate macrostates, as in (1.1). 

Physical Model We propose a symplified model for the non-linear-like phenomena in X-ray sources, considering the properties of Rayleigh-Taylor instability on the magnetopause which is formed by the accreting matter to the neutron star, and then obtain the motion of this magnetopause. ... 

An interesting class of exact self-similar solutions (H2) can be deduced for the case where the newly formed phase density is a function of temperature only. The method involves a transformation to Lagrangian coordinates, based upon the principle of conservation of mass within the new phase. A similarity variable akin to that employed by Zener (Z2) is then introduced which immobilizes the moving boundary in the transformed space. A particular case which has been studied in detail is that of a column of liquid, initially at the saturation temperature T , in contact with a flat, horizontal plate whose temperature is suddenly increased to a large value, Tw T . Suppose that the density of nucleation sites is so great that individual bubbles coalesce immediately upon formation into a continuous vapor film of uniform thickness, which increases with time. Eventually the liquid-vapor interface becomes severely distorted, in part due to Taylor instability but the vapor film growth, before such effects become important, can be treated as a one-dimensional problem. This problem is closely related to reactor safety problems associated with fast power transients. The assumptions made are ... 

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. 

Thus, the streaming velocities Ui and U2 do not affect the response of the system. If in addition, p > 1, i.e. a heavier liquid is over a lighter liquid, then the buoyancy force causes temporal instability (if / is considered real) - as is the case for Rayleigh-Taylor instability (see Chandrasekhar (I960)). 

---