Weber number values

Figure 3.6 Droplet breakup as a function of viscosity ratio. The solid line represents the critical Weber number value above which droplet breakup will occur. Data from Isaacs and Chow [130].

Besides, a decrease in the critical particle size for the polymer/polymer systems could also be obtained due to the decrease in the Weber number values, caused by an increase in the interfacial area available. A saturation level at the interaction plane across the interphase and in the concentration of the interfacial modifiers also emerges from the finite dimensions of the interphase. Above a critical concentration, the interfacial modifier could form its own phase, and then a nth phase ought to be considered in the studies rather than a model based on modified interfaces. Following sections show some examples of the role of the interfacial modifiers from the matrix side for both rigid and nondeformable dispersed phase polypropylene/mineral reinforcement system and polymer/polymer binary system based on polypropylene and polyamide 6. 

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. 

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). 

In their analysis, however, they neglected the surface tension and the diffusivity. As has already been pointed out, the volumetric mass-transfer coefficient is a function of the interfacial area, which will be strongly affected by the surface tension. The mass-transfer coefficient per unit area will be a function of the diffusivity. The omission of these two important factors, surface tension and diffusivity, even though they were held constant in Pavlu-shenko s work, can result in changes in the values of the exponents in Eq. (48). For example, the omission of the surface tension would eliminate the Weber number, and the omission of the diffusivity eliminates the Schmidt number. Since these numbers include variables that already appear in Eq. (48), the groups in this equation that also contain these same variables could end up with different values for the exponents. 

At a given Weber number, condition (8.71) may be satisfied at some values of the Euler number, which play the role of eigenvalues. 

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

The values of the Weber number pertinent to this correlation were suggested to be sufficiently small so that viscous and solidification effects can be neglected. Another analytical expression, derived from Madej ski s full model after simplification under the conditions... 

The rate parameters of importance in the multicomponent rate model are the mass transfer coefficients and surface diffusion coefficients for each solute species. For accurate description of the multicomponent rate kinetics, it is necessary that accurate values are used for these parameters. It was shown by Mathews and Weber (14), that a deviation of 20% in mass transfer coefficients can have significant effects on the predicted adsorption rate profiles. Several mass transfer correlation studies were examined for estimating the mass transfer coefficients (15, jL6,17,18,19). The correlation of Calderbank and Moo-Young (16) based on Kolmogaroff s theory of local isotropic turbulence has a standard deviation of 66%. The slip velocity method of Harriott (17) provides correlation with an average deviation of 39%. Brian and Hales (15) could not obtain super-imposable curves from heat and mass transfer studies, and the mass transfer data was not in agreement with that of Harriott for high Schmidt number values. 

If an extensional force is also applied in addition to the pure shear force (for types of flow, see Fig. 9.2), the critical value of the Weber number is considerably lower. It is possible to break up droplets in an extensional flow even when the viscosity ratios are very high. Thus, extensional flow is significantly more effective than pure shear flow when attempting to disperse droplets and break up high-viscosity gels or polymer particles. 

It is more difficult here to find a value of the critical Weber number, since the exact local flow conditions are not known. Usually, one takes the power density as a measure for the intensity of the eddies. The power density (symbol, with unit W/m ) is the amount of energy per that is used to establish the flow pattern. The larger the power input, the more intense and the smaller the eddies will be. 

The maximum observable particle size (x ax) is a function (eq.l) of the surface tension between continuous and disperse phase (y), the Weber number (We) and inversely proportional to the shear energy (t) introduced by the colloid mill. Small particles can be expected with high shear and small surface tension values [10-12]. 

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