Critical droplet size

If the wetted perimeter of the droplet at the time of disengagement is only 5% of vO (a reasonable assumption experimental evidence is lacking), the critical droplet size. D, would be reduced to 0.0047 ft (1.400 Sim). In general, it is reasonable to assume that droplet disengagement sizes fall between 0.02 and 0.08 in. (500 - 2.000 sim). 

Figure 9.9 Dimensionless critical droplet size for breakup (capillary number Ca<- = Crj a/r) as a function of viscosity ratio M of the dispersed to the continuous phase for two-dimensional flows in the four-roll mill. The data sets correspond from bottom to top to ff — 1.0(0), 0.8 (A), 0.6 (0), 0.4 (V), and 0.2 ( ), with a defined in Eq. (9-17). The fluids are those described in Fig. 9-7. The solid lines are the predictions of a small-deformation theory, while the dashed lines are for a large-deformation theory. The closed squares are from Rallison s (1981) numerical solutions (see also Rallison and Acrivos 1978). (From Bentley and Leal 1986, with permission from Cambridge University Press.)...

The critical droplet size that can exist in the flow at a given thermodynamic mode is determined by the velocity of movement of the mixture of water and petroleum, interfacial tension between the phases and pulsation of flow. 

Fig. 32.6 Critical droplet size in the dripping mode. Electric field applied to a capillary containing distilled water. Experiment conditions Voltage applied at capillary tip was varied from 0 to 10,000 V flow rate set at 0.07 mL min , ground electrode is set at 10 mm below the emitter tip...

For water, the values for surface tension and density are yig = 72.99 N/m and p = 1,000 kg/m, respectively g is the gravitational constant (9.81 m/s ). Using (4.2), a critical droplet size of 2.7 mm can be obtained. A droplet smaller than jc generally remains stuck when placed on a solid surface because of the contact angle hysteresis. On the other hand, gravity would flatten a droplet of radius r > k. ... 

Ramshaw, C. and Thornton, J.D. (1967). Droplet breakdown in a packed column Part I the concept of critical droplet size. I. Chem. E. Symp. Sen, No. 26, p. 73. 

Most studies of the behavior of block copolymers as compatibilizing agents consider two opposing effects during deformation a reduction in critical droplet size due to a reduction in the interfhcial tension (droplet breakup) proposed by Taylor, and an increase in droplet size due to increased collision frequency between droplets (droplet coalescence) studied by Smoluchowski. The problem of droplet breakup in a... 

From Equation 1, it is apparent that by reducing the interfacial tension, or by increasing the shear rate, the critical droplet size decreases, Since the Taylor approach is only applicable to a single droplet suspended in a Newtonian fluid, multiple droplet interactions and non-Newtonian viscosities are not considered. Despite these drawbacks, the Taylor approach remains one of the most commonly used models for predicting the sizes of dispersed droplets during shear. 

The suppression of coarsening in the pure blend followed by an increase in coarsening has been addressed by Sundaiaraj and Macosko. They attributed the behavior to the balance between coalescence at high shear rates predicted by Smoluchowski and the critical droplet size of Taylor which can exist at low shear rates. The arguments presented for the critical droplet size were based on a viscoelastic fluid, while the sample we have examined splays Newtonian viscosity behavior, indicating the presence of viscoelasticity is not necessary to obs e the crossover from droplet breakup to coalescence. 

Based on the critical droplet sizes for breakup and coalescence in Equations 19.12 and 19.20, the droplet size in polymer blends as a function of flow intensity (shear rate) can be mapped out [28], as shown in Figure 19.4. The critical droplet sizes for droplet breakup and coalescence become equal at a certain critical shear rate. For shear rates larger than this critical value, the critical droplet size for breakup is smaller than the critical droplet size for coalescence and the final droplet size is determined by a dynamic equilibrium between breakup and coalescence. However, below the critical shear rate, the critical droplet size for breakup is larger than the critical droplet size for coalescence, which results in a range of droplet sizes for which neither breakup nor coalescence will occur. This phenomenon is called morphological hysteresis and changing the flow conditions within this region... 

Figure 2.11 Effect of surfactant concentration m on break-up of a single drop in simple shear flow, x is the critical droplet size for break-up relative to that in the absence of surfactant, as observed and as calculated for y is the ratio of...

A homogeneous metastable phase is always stable with respect to the fonnation of infinitesimal droplets, provided the surface tension a is positive. Between this extreme and the other thennodynamic equilibrium state, which is inhomogeneous and consists of two coexisting phases, a critical size droplet state exists, which is in unstable equilibrium. In the classical theory, one makes the capillarity approxunation the critical droplet is assumed homogeneous up to the boundary separating it from the metastable background and is assumed to be the same as the new phase in the bulk. Then the work of fonnation W R) of such a droplet of arbitrary radius R is the sum of the... 

Product diameter is small and bulk density is low in most cases, except prilling. Feed hquids must be pumpable and capable of atomization or dispersion. Attrition is usually high, requiring fines recycle or recoveiy. Given the importance of the droplet-size distribution, nozzle design and an understanding of the fluid mechanics of drop formation are critical. In addition, heat and mass-transfer rates during... 

The responses chosen all relate to important foam properties. We believed that yi, the emulsion droplet size, determines y2, the cell size in the resultant foam, and we wished to determine whether this is true over this range of formulations. The foam pore size ys should determine the wetting rate y7, so these responses could be correlated, and yg, the BET surface area, should be related to these as well. The density y and density uniformity ys are critical to target performance as described above, and ys, the compressive modulus, is an important measure of the mechanical properties of the foam. 

The critical radius at Tg is a multiple of Droplets of size N > N are thermodynamically unstable and will break up into smaller droplets, in contrast to that prescribed by F N), if used naively beyond size N. This is because N = 0 and N = N represent thermodynamically equivalent states of the liquid in which every packing typical of the temperature T is accessible to the liquid on the experimental time scale, as already mentioned. In view of this symmetry between points N = 0 and N, it may seem somewhat odd that the F N) profile is not symmetric about. Droplet size N, as a one-dimensional order parameter, is not a complete description. The profile F N) is a projection onto a single coordinate of a transition that must be described by order parameters—the... 

The phase inversion temperature (PIT) method is helpful when ethoxylated nonionic surfactants are used to obtain an oil-and-water emulsion. Heating the emulsion inverts it to a water-and-oil emulsion at a critical temperature. When the droplet size and interfacial tension reach a minimum, and upon cooling while stirring, it turns to a stable oil-and-water microemulsion form. " ... 

Subjected to steady acceleration, a droplet is flattened gradually. When a critical relative velocity is reached, the flattened droplet is blown out into a hollow bag anchored to a nearly circular rim which contains at least 70% of the mass of the original droplet. Surface tension force is sufficient to allow the bag shape to develop. The bag, with a concave surface to the gas flow, is stretched and swept off in the downstream direction. The rupture of the bag produces a cloud of very fine droplets presumably via a perforation mode, and the rim breaks up into relatively larger droplets, although all droplets are at least an order of magnitude smaller than the initial droplet size. This is referred to as bag breakup (Fig. 3.10)T2861... 

In some practical processes, a high relative velocity may not exist and effects of turbulence on droplet breakup may become dominant. In such situations Kolmogorov, 280 and Hinze[27°l hypothesized that the turbulent fluctuations are responsible for droplet breakup, and the dynamic pressure forces of the turbulent motion determine the maximum stable droplet size. Using Clay s data, 2811 and assuming isotropic turbulence, an expression was derived for the critical Weber number 270 ... 

Minimum packing size. For reproducible results the minimum packing size should be such that the mean void height is not less than the mean droplet diameter. As reported by Gayler el alS21 this critical packing size is given by ... 

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