Weber number large

The emulsification process in principle consists of the break-up of large droplets into smaller ones due to shear forces (10). The simplest form of shear is experienced in lamellar flow, and the droplet break-up may be visualized according to Figure 4. The phenomenon is governed by two forces, ie, the Laplace pressure, which preserves the droplet, and the stress from the velocity gradient, which causes the deformation. The ratio between the two is called the Weber number. We, where Tj is the viscosity of the continuous phase, G the velocity gradient, r the droplet radius, and y the interfacial tension. 

Boiling in the liquid film can throw large chunks of liquid into the vapor core, characterized by the Weber number based on the local relative velocity between the vapor core and the liquid film. 

In Madejski s full model,l401 solidification of melt droplets is formulated using the solution of analogous Stefan problem. Assuming a disk shape for both liquid and solid layers, the flattening ratio is derived from the numerical results of the solidification model for large Reynolds and Weber numbers ... 

The maj or limitation of the TAB model i s that it can only keep track of one oscillation mode, while in reality there are many oscillation modes. Thus, more accurately, the Taylor analogy should be between an oscillating droplet and a sequence of spring-mass systems, one for each mode of oscillations. The TAB model keeps track only of the fundamental mode corresponding to the lowest order spherical zonal harmonic 5541 whose axi s i s aligned with the relative velocity vector between the droplet and gas. Thi s is the longest-lived and therefore the most important mode of oscillations. Nevertheless, for large Weber numbers, other modes are certainly excited and contribute to droplet breakup. Despite this... 

As described in the previous section, solid particles can be broken up if the applied shear stresses are sufficiently large. In contrast, however, liquid droplets cannot be dispersed under certain conditions, even in shear fields with very large shear stresses. The Weber number We is often used to characterize the dispersion of droplets (another notation often used instead... 

When the turbulence is not too large, the main force on the droplets is caused by the shear imposed by the surrounding eddies. With the help of the Kolmogorov theory for turbulent flow, the external, disrupting force is can estimated as Text = V(e /c)- We then end up with a definition of the critical Weber number ... 

For low viscosity liquids when the dimensionless viscosity group [7], NJ, = /LtiAcrp,) is less than 1, a droplet wiU be stable below a maximum size, defined by the critical Weber number and the gas liquid contact time. For long gas—liquid contact times, two large droplets are produced. For short contact times, many smaU droplets are produced. This tjq) of droplet breakup yields a very broad droplet size distribution. 

For Rushton turbines, Chen and Middleman found C2 = 0.053 (Fig. 8) for a broad range of liquid-liquid pairs. Eqs. (1) and (3) show that, at equilibrium, dispersed phase systems created by turbulent flow scale-up by maintaining constant Smax or for practical industrial purposes, by constant Savg. which is equivalent to constant P/Vl- Large Weber numbers result in small drops and vice versa. These expressions are valid for dilute, noncoalescing systems of low pd. at equilibrium. Many stabilized or noncoalescing industrial systems with 0 > 0.05 can also be scaled by the constant P/Vl criterion. 

Also if t]c breakup is difficult. At t]D/t]c = 10 4, which is about the magnitude in most foams, Wecr would be as large as 30. At such a small viscosity ratio, the bubble or drop is deformed into a long thread before breaking. However, for some protein surfactants, the surface layer of the drop can be stagnant (Section 10.8.3) and then the drop can presumably break at a smaller Weber number. 

At lower gas speed and higher drops surface tension, formation of bag structures and breakup into smaller droplets have been observed following the initial drop deformation into a disk [5], In the current experiment, these smaller drops are not observed, primarily due to the large Weber number. A mist with scales smaller than the camera resolution, which Wcis 1.2 /mi/pixel, was visible both... 

Tlie Reynolds, Froude, and Weber numbers are proportional to ND, N D, and N D, respectively. It is obvious that if one of these groups is used for scale-up, the scale-up rules represented by the other groups aie automatically violated, provided that the physical properties of the fluid remain the same. The groups could, of course, be made compatible by using fluids having different physical properties on the large and small scales. 

They found that Rayleigh s results are relevant only in the case of large Weber numbers. They also showed that in the limit of We oo, the spatial growth rate k( can be inferred from the temporal growth rate, (Or by the relation ki = a>r - - 0 /We), while the disturbance travels at the jet velocity relative to the laboratory frame. For Weber numbers less than the order of one, they found a new mode of faster-growing disturbances whose wavelengths are so long that they may not be actually observable on finite jets. 

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