Drop size

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

Complex Coacervation. This process occurs ia aqueous media and is used primarily to encapsulate water-iminiscible Hquids or water-iasoluble soHds (7). In the complex coacervation of gelatin with gum arabic (Eig. 2), a water-iasoluble core material is dispersed to a desired drop size ia a warm gelatin solution. After gum arabic and water are added to this emulsion, pH of the aqueous phase is typically adjusted to pH 4.0—4.5. This causes a Hquid complex coacervate of gelatin, gum arabic, and water to form. When the coacervate adsorbs on the surface of the core material, a Hquid complex coacervate film surrounds the dispersed core material thereby forming embryo microcapsules. The system is cooled, often below 10°C, ia order to gel the Hquid coacervate sheU. Glutaraldehyde is added and allowed to chemically cross-link the capsule sheU. After treatment with glutaraldehyde, the capsules are either coated onto a substrate or dried to a free-flow powder. 

The second step is to disperse the core material being encapsulated in the solution of shell material. The core material usually is a hydrophobic or water-knmiscible oil, although soHd powders have been encapsulated. A suitable emulsifier is used to aid formation of the dispersion or emulsion. In the case of oil core materials, the oil phase is typically reduced to a drop size of 1—3 p.m. Once a suitable dispersion or emulsion has been prepared, it is sprayed into a heated chamber. The small droplets produced have a high surface area and are rapidly converted by desolvation in the chamber to a fine powder. Residence time in the spray-drying chamber is 30 s or less. Inlet and outlet air temperatures are important process parameters as is relative humidity of the inlet air stream. 

When an impeller is rotated in an agitated tank containing two immiscible Hquids, two processes take place. One consists of breakup of dispersed drops due to shearing near the impeller, and the other is coalescence of drops as they move to low shear zones. The drop size distribution (DSD) is decided when the two competing processes are in balance. During the transition, the DSD curve shifts to the left with time, as shown in Figure 18. Time required to reach the equiHbrium DSD depends on system properties and can sometimes be longer than the process time. 

Fig. 18. Variation in drop size distribution with time.

Drop breakage occurs when surrounding fluid stresses exceed the surface resistance of drops. Drops are first elongated as a result of pressure fluctuations and then spHt into small drops with a possibiUty of additional smaller fragments (Fig. 19). Two types of fluid stresses cause dispersions, viscous shear and turbulence. In considering viscous shear effects, it is assumed that the drop size is smaller than the Kohnogoroff microscale, Tj. 

Drops coalesce because of coUisions and drainage of Hquid trapped between colliding drops. Therefore, coalescence frequency can be defined as the product of coUision frequency and efficiency per coUision. The coUision frequency depends on number of drops and flow parameters such as shear rate and fluid forces. The coUision efficiency is a function of Hquid drainage rate, surface forces, and attractive forces such as van der Waal s. Because dispersed phase drop size depends on physical properties which are sometimes difficult to measure, it becomes necessary to carry out laboratory experiments to define the process mixing requirements. A suitable mixing system can then be designed based on satisfying these requirements. 

The value of is aiound —2/ > and depends on impeUei type and location. This coiielation does not impact on drop sizes and is apphcable when the... 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

Fig. 32. Dimensionless drop size vs Weber number A, empty pipe at pu j = 1 B through G, Kenics mixer at = 25, 10, 2, 1, 0.75, and 0.5,...

Hquid is fed into center of spinning disk, cup, or wheel, and spreads out toward rim produces a 360° spray pattern and relatively uniform drop size used in spray drying and cooling appHcations... 

Liquid viscosity generally produces adverse effects on drop size. It increases the initial film thickness and hinders the growth of unstable waves. 

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. 

Use k values for drops (Table 5-25). Enhancement due to packing is at most 20%. Packing decreases drop size and increases interfacial area. 

The largest droplet in a spray poprJation is 3 times the diameter of the average drop size [see Eq. (12-66)]. 

Methods for calculating average and maximum drop sizes from various atomizers are given by Marshall (op. cit.). For pneumatic nozzles, an expression developed by Nuldyama and Tanasawa is recommended ... 

These mechanisms coexist, and the one that gives the smallest drop size will control. The four mechanisms follow distinctly different velocity dependencies ... 

Breakup of a. meet of liquid (Ih/elocity) . This governs drop size in most hydraulic spray nozzles. 

Note that comes out with units of length. Since E typically varies with (gas velocity), this results in drop size dependence with (Ih/eloc-... 

For these three applications, Eq. (14-190) gives good prediction of drop size when the design variables are used to c culate E, as illustrated by Eqs. (14-198) and (14-201). 

For a typical nozzle, the drop size varies with L/(pressure drop). When (velocity)" is substituted for pressure drop, droplet size is seen to vary with (velocity)". ... 

Sauter mean D39. This has the same ratio of surface to volume as the total drop population. It is typically 70 to 90 percent of D. n- II is frequently used in transport processes and is used here to characterize drop size. 

However, any average drop size is fictitious, and none is completely satisfactory. For example, there is no way in which the high surface and transfer coefficients in small drops can be made avail le to the larger drops. Hence, a process calculation based on a given droplet size describes only what happens to that size and gives at best an approximation to the total mass. 

There are a variety of ways to describe the droplet population. Figures 14-88 and 14-90 illustrate one of the most common methods, the plot of cumulative volume against droplet size on log-normal graph paper. This satisfies the restraint of not extrapolating to a negative drop size. Its other advantages are that it is easy to plot, the results are easy to visualize, and it yields a nearly straight line at lower drop sizes. 

Effect of Physical Properties on Drop Size Because of the extreme variety of available geometries, no attempt to encompass this variable is made here. The suggested predictive route starts with air-water droplet size data from the manulac turer at the chosen flow rate. This drop size is then corrected by Eq. (14-195) for different viscosity and surface tension ... 

The exponential dependencies in Eq. (14-195) represent averages of values reported by a number of studies with particular weight given to Lefebvre [Atomization and Sprays, Hemisphere, New York, (1989)]. Since viscosity can vary over a much broader range than surface tension, it has much more leverage on drop size. For example, it is common to find an oil with 1000 times the viscosity of water, while most liquids fall within a factor of 3 of its surface tension. Liquid density is generally even closer to that of water, and since the data are not clear mat a liquid density correction is needed, none is shown in Eq. 

Effect of Pressure Drop and Nozzle Size For a nozzle with a developed pattern, the average drop size can be estimated to fall with rising AP (pressure drop) by Eq. (14-196) ... 

For similar nozzles and constant AP, the drop size will increase with nozzle size as indicated by Eq. (14-197) ... 

TABLE 14-12 Exponential Dependence of Drop Size on Different Parameters in Two-Fluid Atomization... 

Further differences from hydraulic nozzles (controlled by sheet and ligament breakup) are the stronger increase in drop size with increasing surface tension and decreasing gas density. 

As shown by Fig. 14-90, entrainment droplet sizes span a broad range. The reason for the much larger drop sizes of the upper curve is the short disengaging space. For this cui ve, over 99 percent of the entrainment has a terminal velocity greater than the vapor velocity. For contrast, in the lower cui ve the terminal velocity of the largest particle reported is the same as the vapor velocity. For the settling velocity to limit the maximum drop size entrained, at least 0.8 m (30 in) disengaging space is usually required. Note that even for the lower cui ve, less than 10 percent of the entrainment is in drops of less than... 

Information on the coefficients is relatively undeveloped. They are evidently strongly influenced by rate of drop coalescence and breakup, presence of surface-active agents, interfacial turbulence (Marangoni effect), drop-size distribution, and the like, none of which can be effectively evaluated at this time. 

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