Weber number range

GL 27] [R 3] ]P 29] By means of sulfite oxidation, the specific interfacial area of the fluid system nitrogen/water was determined at Weber numbers ranging from lO " to 10 [10]. In this range, the interface increases from 4000 m m to 10 000 m m . The data are - with exceptions - in accordance with optically derived analysis of the interface and predictions from calculations. At stiU larger Weber number up to 10, the specific interfacial area increases up to 17 000 m m, which was determined optically. 

Droplets of heterogeneous composition appear to break faster than single compounds. Figure 6.4 shows a sequence of JP-10 with 5% ethyl-hexyl nitrate. The Mach number ranged from 2.15 to 2.31, and the Weber numbers ranged from 3900 to 5200 based on mixture measured surface tension. 

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. 

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. 

A range of correlations is available from the literature, usually relating the Sauter mean diameter to the Weber number, which is the ratio of shear forces to surface tension forces ... 

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. 

A typical example for a stirred two-phase system with a volume fraction of 30 vol.% organic phase dispersed in water, an interfacial tension of 25 mN m-1 and a specific power input of 0.5 W L 1 shows a droplet diameter in the range of 250 pun and a specific interface of about 10 m2 L 1. These dimensions maybe estimated from simple empirical correlations between the Sauter mean diameter of the dispersed phase (zf2.3) and the characteristic Weber number (We). In case of turbulent mixing the following correlation is proposed in the literature for calculation of the mean diameter of dispersed droplets [24]... 

Let us consider the motion of a gas bubble at high Reynolds numbers. For small We, the bubble shape is nearly spherical. The Weber numbers of the order of 1 constitute an intermediate range of We, very important in practice, when the bubble, though essentially deformed, conserves its symmetry with respect to the midsection. For such We, the bubble shape is well approximated by an ellipsoid with semiaxes a and b = xa oblate in the flow direction the semiaxis b is directed across the flow, and x 1 ... 

Under strong deformations, drops split into smaller ones, that is, are destroyed. The destruction process for drops is very complicated and is determined by surface tension, viscosity, inertia forces and some other factors. For various characteristic velocities of the relative phase motion, the character of destruction may be essentially different. A comparative analysis of many experimental and theoretical studies of drop destruction was given in [154, 312]. It was pointed out that there are six basic mechanisms of drop destruction, which correspond to different ranges of the Weber number. 

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