Weber number decreasing

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]. 

The effect of various parameters on the difference between vapor and liquid pressure is illustrated in Figs. 8.3 and 8.4. The effect of the Fuler and Weber numbers as well as the thermal parameter is highly noticeable. An increase in Fu, We and d- leads to a decrease in AP, whereas the difference of both phase pressures is practically independent of Reynolds number. An increase in the Froude number is accompanied by an increase in AP for a small Fr. At Fr > 10 the effect of Fr on AP is negligible. 

The experimental results show that c/n decreases up to a certain flow rate at which it was found that Arwe = 0.8, after which a different behavior is exhibited, with an increase in c/V, as ArRe increases. At NRe = 280, a further break was observed this is due to the onset of turbulence in the film, which alters the manner in which u varies with ArRe. Hence, as in the case of the wavelengths, there appears to be an important change in the wave characteristics near the critical Weber number of unity. 

The dependence of drop deformation on the Weber number and the vorticity inside the drop was studied in [336]. It was shown that the drop is close in shape to an oblate ellipsoid of revolution with semiaxis ratio > 1 If there is no vortex inside the drop, then this dependence complies with the function We(x) given in (2.8.3). The ratio x decreases as the intensity of the internal vortex increases. Therefore, the deformation of drops moving in gas is significantly smaller than that of bubbles at the same Weber number We. The vorticity inside an ellipsoidal drop, just as that of the Hill vortex, is proportional to the distance TZ from the symmetry axis,... 

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. 

Qystallization of tatty acids using spray-evaporation of highly volatile solvents has been examined to obtain solids without inclusion of liquid. Hie powdery solids were collected in the spray column, and they were usually obtained on the glass tube near the nozzle and also on the bottom of the column. The mole fraction of first crystallizing component of the solids in the column decreases from the top to the bottom of the column. Hie percent of the solids collected on the bottom were correlated with the Weber Number. The more volatile solvents such as propane or isobutane reduced the percent of solids and the purity of solids on the bottom. Hie possibility of a separation process using spray-evaporation was suggested. 

The effect of the Weber number on the breakup time (and length) is shown in Fig. 3.12 for several values of initial disturbance amplitude and two values of the density ratio e. It can be seen that breakup time decreases as the Weber number is increased. This is because the bigger the Weber number, the larger the aerodynamic interactions between the liquid sheet and the surrounding gas, and the latter is what enables the growth of the surface waves and the eventual disintegration of the sheet. In addition, the breakup time is reduced by a larger value of the initial disturbance... 

Once the Weber number is increased from 1 to 10, the relative strength of the surface tension to the inertial forces decreases. Hence, less pressure difference across the interface can be tolerated (compared to the Wcg = 1 case) and the drop starts to deform, as shown in the left column (panel (a)) of Fig. 4.6. The deformed drop almost takes the shape of a flat ellipsoid and hence, the drop recirculating region in the downstream side of the drop grows larger. The enhanced vortex size... 

Grace [286] found that the breakup time decreases upon exceeding the critical Weber number. Similar experiments by Elemans [307] did not show a decrease in breakup time upon exceeding the critical Weber number. The breakup time for viscosity ratios between 0.1 and 1 was found to be around 50 to 100, i.e., tb = 50-100. Experimental work in an opposed-jet device [66] found that with flow occurring a droplet will stretch, while during the no-flow condition, breakup occurs via necking. This is illustrated in Fig. 7.155. 

To accelerate the diffusion rate and shorten the time for the formation of gas/polymer solutions, we must raise the temperature and shorten the diffusion distance. This is done by deforming the two-phase mixture of polymer and gas through shear distortion to decrease the diffusion path. This type of deformation occurs in an extruder under laminar-flow conditions. The bubbles are stretched by the shear field of the two-phase mixture and eventually break up to minimize the surface energy when a critical Weber number is reached (4). The disintegrated bubble size is calculated to be about 1 mm and the initial striation thickness after bubble disintegration is calculated to be about twice the bubble diameter (5). This striation thickness decreases with further shear, and the gas diffusion occurs faster as a result of the increase in the surface area and the decrease in striation thickness. The striation thickness in an extruder is estimated to decrease to about 100 /xm. At this thickness, the diffusion time is about 1 min in PET, from 10 to 20 s in polystyrene (PS), polyfvinyl chloride) (PVC), and high density polyethylene (HDPE), and in the range of a few seconds in low density polyethylene (LDPE). 

---