Weber number dimensionless measure

Fig. 22.13 Comparison of the dimensionless mean drop size depending on the gas-Weber number between measurements at LamRot and the prediction on (22.11) [11]. The drop size is in good agreement for typical spray conditions [11]...

Typically, the Weber and Ohnesorge numbers are dimensionless measures of the relative strength of the inertia to the surface tension in a fluid, and the viscosity to the surface tension of a fluid, respectively. Here the Weber number is modified (with a hat. We) to consider the inertia of the surrounding atmosphere in comparison to the surface tension of the fluid extending from the nozzle. 

Considerable measurements data can be converted into a prediction of the breakup length of threads from completely filled capillaries. The prediction (. pred) depends on the gas-Weber number, the dimensionless viscosity, and flow rate and is given in (22.8), proposed in [33]. 

Fig. 22.7 Dimensionless breakup length depending on gas-Weber numbers for threads from open channel flow. The inclination of the capillary was a = 49° and Newtonian test liquid was used. To compare the breakup length to completely filled capillaries, the prediction in (22.7) and (22.8) is plotted. Noticeable smaller breakup lengths are measured for the threads from open channel flow...

The measurement of the drop size is compared for different process conditions and capillary configurations. For low gas-Weber number, the drop size increases slightly in all cases. The curves for the completely filled capillaries proceed nearly horizontally up to Weg = 2.3. Afterward, the drop size of fi = 0.9 and F = 1.5 increases and the drop size for fi = 0.33 and V = 3 stays constant. Higher dimensionless viscosities promote the increasing drop size. In case of the threads emerging from open channel flow, a similar trend is identified as the plots in Fig. 22.10 indicate. When comparing drop sizes from completely filled capillaries and open channel flow at similar process condition, it became obvious that the gas-Weber number of sudden drop size growth is considerably lower in case of open channel flow. 

Based on data series that show this transition within the measured range, a prediction for the critical gas-Weber number is developed. The critical gas-Weber number marks the cross-wind velocity above which the breakup is dominated by wind-induced breakup and it depends on the dimensionless flow rate and viscosity. Equation (22.12) gives the prediction for completely filled capillaries [11]. 

Weber number A dimensionless number, We, used in thin film gas-liquid flows where surface tension has a major effect on the strongly curved interface between two fluids such as in the formation of droplets and bubbles. It is a measure of the relation between surface... 

In addition to the dimensionless numbers, there are well-known others, such as the Sherwood (Sh), Reynolds (Re), Schmidt (Sc), Froude (Fr), Bodenstein (Bo), and Weber (We) numbers. On the basis of these types of dimensionless numbers, empirical correlations for a large number of bioreactors have been made (for example, Blanch, 1979 Schiigerl, 1980 Zlokarnik, 1979). The results of the experimental measurements of process engineering data are often presented in the form of a graph they have the form of the relationships given in Equs. 3.77a and 3.77b. For the volumetric mass transport coefficient (Ryu and Humphrey, 1972) (see Fig. 3.21)... 

---