Number Weber

Weatherp r o o fing Weather stripping Weber number... 

Weber numbers Weber s law Web formation Web knitting Web offset inks Webster hardness gauge Weed killers... 

This correlation is valid when turbulent conditions exist in an agitated vessel, drop diameter is significantly bigger than the Kohnogoroff eddy length, and at low dispersed phase holdup. The most commonly reported correlation is based on the Weber number ... 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

Fig. 32. Dimensionless drop size vs Weber number A, empty pipe at pu j = 1 B through G, Kenics mixer at = 25, 10, 2, 1, 0.75, and 0.5,...

Based on such analyses, the Reynolds and Weber numbers are considered the most important dimensionless groups describing the spray characteristics. The Reynolds number. Re, represents the ratio of inertial forces to viscous drag forces. 

The Weber number. We, is defined as foUows and represents the ratio of the dismptive aerodynamic forces to the restoring surface tension forces. 

The Weber number becomes important at conditions of high relative velocity between the injected Hquid and surrounding gas. Other dimensionless parameters, such as the Ohnesorge ((We /Re), Euler (AP/Pj y i)y and Taylor (Re/ We) numbers, have also been used to correlate spray characteristics. These parameters, however, are not used as often as the Reynolds and Weber numbers. 

The first term is essentially the reciprocal of the Weber number and the second term is a function of the Ohnesorge number. Equation 13 may be invaHd for airblast atomizers operating at high pressures, >1 MPa (>10 atm), or with high viscosity Hquids. 

Because of the wide range of appHcations and complexity of the physical phenomena, the values of the exponents reported in the Hterature vary significantly. Depending on the range of Reynolds and Weber numbers, constant a ranges between 0.25 and 0.6, constant b between 0.16 and 0.25, constant (/between 0.2 and 0.35, and constant dfiom 0.35 to 1.36. 

Both effects can produce coarser atomization. However, the influence of Hquid viscosity on atomization appears to diminish for high Reynolds or Weber numbers. Liquid surface tension appears to be the only parameter independent of the mode of atomization. Mean droplet size increases with increasing surface tension in twin-fluid atomizers (34). is proportional to CJ, where the exponent n varies between 0.25 and 0.5. At high values of Weber number, however, drop size is nearly proportional to surface tension. 

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. 

As an approximate rule, break-up of droplets occurs for a Weber number in excess of one, a rule of thumb that is actually valid for the range of viscosity ratios of the dispersed phase to the continuous phase of less than approximately five. Higher viscosities of the disperse phase lead to serious difficulties with emulsification because the shear energy is then dispersed in rotation of the droplets. 

Impeller Weber number, Dimensionless Dimensionless decanter m ... 

Concerning a liquid droplet deformation and drop breakup in a two-phase model flow, in particular the Newtonian drop development in Newtonian median, results of most investigations [16,21,22] may be generalized in a plot of the Weber number W,. against the vi.scos-ity ratio 8 (Fig. 9). For a simple shear flow (rotational shear flow), a U-shaped curve with a minimum corresponding to 6 = 1 is found, and for an uniaxial exten-tional flow (irrotational shear flow), a slightly decreased curve below the U-shaped curve appears. In the following text, the U-shaped curve will be called the Taylor-limit [16]. 

Both dimensionless Weber number and viscosity ratio are defined by ... 

The purpose of our calculation was to quantitatively evaluate the deformational behavior of the TLCP droplets and their fibrillation under the processing conditions, and finally, to establish a relationship among the calculated Weber number, the viscosity ratio, and the measured aspect ratio of the fibers. Figure 13 illustrates this procedure. All calculated results were plotted as... 

With a computer program, which solved Eqs. (5) and (7) for We by numerical method, Weber numbers were obtained from layer to layer for each injection molding operation. The calculated points were then connected to curves, depending on the normalized thickness. Figure 17 shows these theoretically deduced Weix)... 

Clark and Vermeulen (C8) measured gas holdup in three different liquids —isopropyl alcohol, ethylene glycol, and water. They measured the increase in holdup with agitation as compared to no agitation, and correlated their results as a function of the volumetric gas velocity, Weber number, P/P0, and a geometric factor. Typical volumetric gas holdup values reported in the literature vary from about 2% to 40% of the total dispersion volume (Cl, C2, C8, F2, G10). 

Clark and Vermeulen (C8) later reported an extensive experimental study of power requirements in agitated gas-liquid systems. They correlated their data in dimensionless form as a function of fractional gas holdup, Weber number, and a geometrical factor. Their correlation is shown in Fig. 5. 

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