Rayleigh instabilities

When a fiber is covered with a liquid film of constant thickness, h, the area of the liquid-air interface is larger than if the same amount of liquid is distributed in a film of sinusoidal profile with a wave length larger than the radius of the fiber.So, a constant thickness film is unstable and spontaneously evolves towards a minimum energy configuration. In Fig. 21, an example is shown a spider covers the threads 

Analyzing the Laplace pressure difference in a film sinusoidally perturbed (given by the two principal radii of curvature) it results that the pressure in a valley is larger than in a crest if the wavelength of the perturbation (A.) is larger than Ina, where a is the fiber radius. In this case, the liquid flows from the valley to the crest and the perturbation is increased. A first order instability analysis shows that the fastest growing perturbation has a wavelength 

When the film is covering the interior wall of a capillary tube and its thickness is large enough, the crests collapse producing droplets. If the liquid partially wets the solid, the thin film finking the droplets breaks and dewets (see Fig. 22). 

On the other hand, when at least one of the extremes of the annular film is free, it can retract before Rayleigh instabifity appears. Which of the processes occur first depend on its characteristic times, for Rayleigh instability it is  

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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. 

This has come to be known as the Rayleigh instability. The lowest admissible value of n is 2, for which... 

Since for liquids ry is of the order of 2 x 109 dyn/cm3, Sps must be of the order of 7,000 V/micron by this mechanism. Schultz and Wiech suggest that filaments of liquid may first be formed by Rayleigh instability from which are torn finer drops by local electrostatic stresses exceeding the tensile strength. 

Such columns can be used for the CEC separation of small neutral compounds. The problem with this type of open-tubular column, however, is the low efficiency obtained due to the small diffusion coefficients of the analytes in the polymeric stationary phase, and the heterogeneous film structure caused by Rayleigh instability. 

Figure 1.13. Mechanism of rupturing. Under shear, drops elongate into long cylinders (a) that undergo a Rayleigh instability leading to identical aligned droplets (b). (Adapted from [149].)...

The previous experiments were all performed on dilute emulsions for which the dispersed phase represents 2.5 wt% of the emulsion. The results obtained for a concentrated emulsion with oil mass fraction equal to 75% sheared at 500 s and 3000 s are reported in Fig. 1.16 [156]. The primary emulsion was polydisperse with d = 57 am. The two previously described regimes still exist. The first regime is particularly efficient in reducing the diameter because one drop breaks into 160 droplets through the Rayleigh instability for an applied shear rate of 500 s (di( = 10.5 am) and into 6200 droplets for an applied shear rate of 3000 s ... 

In this section, the parameters influencing the mean diameter dR resulting from the Rayleigh instability are examined. Hereafter, the second fragmentation regime is not considered because a narrow size distribution is already obtained after the first one. The parameters that influence dR are the applied stress a, the viscosity ratio p, the rheological behavior, and the way the shear is applied. 

Figure 1.18. (a) Diameter resulting from the Rayleigh instability as a function of the shear stress, (b) Shear stress as a function of the Laplace pressure of the resulting drops. The linear fit gives a slope of 0.087. (Adapted from [149].)... 

The applied shear and stress are high enough to rapidly induce the Rayleigh instability. 

Therefore, the energy decreases continuously with time if the Rayleigh instability condition is satisfied,... 

The Rayleigh instability (Section 14.1.2) of the pore channel is neglected. Pores attached to grain boundaries have increased critical Rayleigh instability wavelengths [7],... 

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