Weber number for

The Weber number for mixing WeM represents the ratio of the applied to the opposing surface tension forces. 

The Weber number for mixing WeM is only of importance when separate physical phases are present in the liquid mixing system as in liquid-liquid extraction. 

For scale-up from system 1 to system 2 for the same liquid properties and system geometry, equation 5.14 which defines the Reynolds number for mixing ReM, equation 5.15 which defines the Froude number for mixing FrM, and equation 5.16 which defines the Weber number for mixing WeM, can be written respectively in the following forms ... 

Table 3.3 Values of Weber Number for Transitions from No Deformation Regime up to Shear Breakup Regime at 0hd <0.1...

Figure 3.5 The critical Weber number for disruption of droplets in simple shear flow (solid curve), and forthe resulting average droplet size in a colloid mill (hatched area) as a function ofthe viscosity ratio for disperse to continuous phases. Redrawn from data in Walstra [131].

Figure 9.13 Critical Weber number for breaking up droplets as a function of the viscosity ratio, in pure shear flow and in extensional flow...

How do the techniques described above work First, a coarse premix emulsion is made. Then, when the premix is subjected to an intense flow field, the droplets are broken apart by the forces exerted by the flow around the droplets. If one applies a force that is bigger than the forces that keep a droplet together, the droplet will be disrupted. The ratio of the externally applied stress and the internal, coherent tension is called the Weber number. For many situations this is defined as ... 

TABLE 8.1 Critical Weber Numbers for Droplet Breakup [7]... 

Purity of solute i in feed wt % wt % We Weber number for an Dimensionless Dimensionless... 

For satisfactory gas distribution from a ring spar-ger/ " Weber number for the orifice. 

FIGURE 9.44 Sauter mean drop diameter versus Weber number for Kenics KM mixers. 

FIGURE 11.8 The effect of the viscosity ratio, drop over continuous phase inn/tlc), on the critical Weber number for drop breakup in various types of laminar flow. The parameter a is a measure of the amount of elongation occurring in the flow for a — 0, the flow is simple shear for a — 1, it is purely (plane) hyperbolic. 

Figure 35 The critical Weber number for simple and multiple emulsions disruption as a function of the viscosity ratio dispersed to continuous phase. (From Ref 103.)...

Weber number for these waves to appear when the two jets were turbulent, which lied between 66 < We < 165, where the Weber number is defined as We = pDU sin 0/(T. Heidman [8] did a similar work, and found a range of 84 < We < 126. 

In addition to the critical Weber number for a drop-on-demand breakup, the criterion of We > 8 for a Rayleigh breakup has also been reported [16]. This limit can also be motivated by the lower limit of jet formation in the case of dripping out of a vertical capillary with diameter Dnozzis under the action of gravity. The static pressure pstat inside a hanging droplet is... 

The first approaches to modeling the drop breakage process in liquid-liquid dispersions were based on the Weber number for the calculation of the mean drop diameter (see Table 5.2), as well as a maximum stable drop diameter for breakage to occur and a minimum drop diameter above which coalescence will take place (2, 27, 37). Both diameters depend on the intensity of agitation and on physical properties of the constituents. However, these calculations were limited to very low dispersed phase viscosities and holdup fractions. Doulah [25] proposed a correction to the derived correlations to account for high holdup dispersed fi actions, whereas Arai et al. [48 ] derived an expression for the maximum droplet diameter by incorporating the viscosity of the dispersed phase. Similar expressions were also proposed by Calabrese etal. [41]. 

Figure 6. The critical Weber number for a given viscosity ratio, reducing the interfacial tension increases the Weber number, lowering the energy needed to cause droplet breakup. (From [11]. Copyright 1992 American Chemical Society, Washington, DC, USA.)...

Figure 2. Critical Weber number for drop burst as a function of viscosity ratio for different values of the flow parameter a = 0.2 (upper curve), 0.4, 0.6, 0.8 and 1, respectively.

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