Droplet size minimum/maximum

Droplet size, particularly at high velocities, is controlled primarily by the relative velocity between liquid and air and in part by fuel viscosity and density (7). Surface tension has a minor effect. Minimum droplet size is achieved when the nozzle is designed to provide maximum physical contact between air and fuel. Hence primary air is introduced within the nozzle to provide both swid and shearing forces. Vaporization time is characteristically related to the square of droplet diameter and is inversely proportional to pressure drop across the atomizer (7). 

The upper-limit distribution function assumes a finite minimum and maximum droplet size, corresponding to a y value of -oo and +oo, respectively. The function is therefore more realistic. However, similarly to other distribution functions, it is difficult to integrate and requires the use of log-probability paper. In addition, it usually requires many trials to determine a most suitable value for a maximum droplet size. 

Table 4.3. Correlations for Mean, Minimum and Maximum Droplet Sizes Generated in Pressure Jet Atomization by Plain-Orifice Atomizers... 

For prefilming type of atomizers, minimum droplet sizes are obtained with nozzle designs that spread liquid into thinnest sheet before subjecting its both sides to air-blast action 86] and provide maximum contact between liquid and air. 468 From experimental data obtained over a wide range of process conditions and material properties, it was found 469 that the effect of liquid viscosity on the mean droplet size is independent of that of surface tension and air velocity. Therefore, the mean droplet size can be expressed as a sum of two terms one dominated by surface tension, air velocity and air density, and the other by liquid viscosity, as suggested by Lefebvre 4691... 

The more finely the liquids are dispersed within one another, the more slowly will they settle, either in a separate decanter for a continuous operation or in the same vessel for a batch process. Most stable emulsions, those which settle and coalesce only very slowly if at all, are characterized by maximum particle diameters of the dispersed phase of the order of 1 to 1.5 microns. Presumably one could estimate through Eq. (6) what agitator speeds would produce such droplet sizes, but such calculations are not likely to yield completely useful results. For example, it has been observed on several occasions that the settling ability of some liquid dispersions passes through a minimum as agitator speed is increased. 

Rumscheidt and Mason [14] described particle deformation in a shear field as a function of viscosity ratio (p). There is a minimum and a maximum viscosity ratio where it becomes impossible to reduce the droplet size. The limits described by Karam and Bellinger [15] are 0.005 and 4. Breakup of droplets readily occurs when the viscosity ratio is of the order of 0.2 1. Intuitively, a ratio of 1 would be best because in this case there is a maximum transfer of energy between the... 

Emulsions are prepared using various ratios of the two surfactants. The total surfactant concentration is kept constant (e.g., 10%) based on the oil phase typically, for a 50 50 emulsion, 5% surfactant is used. The emulsions are placed in cylinders and their stability is assessed by visual inspection (looking for any oil separation), by droplet size analysis (e.g., using a Malvern Master Sizer), and by measuring the interfacial tension. For an 0/W emulsion the stability, droplet size and interfacial tension are plotted as a function of the % surfactant with a high HLB number. The stability reaches a maximum at an optimum % of the surfactant with the high H LB number, and at this optimum ratio the droplet size and interfacial tension reach a minimum. For W/O emulsions, the stability droplet size and interfacial tension are plotted versus % surfactant with a low FI LB number. The stability reaches a maximum at an optimum % of the surfactant with the low H LB number, and at this optimum ratio the droplet size and interfacial tension reach a minimum. 

Using the HLB system for the characterisation of surfactants, a minimum interfacial tension is observed when the HLBr is reached. Fig. 6.7 shows, as an example, the interfacial tension and the droplet size in emulsions of decane and sunflower oil, respectively, as a function of the HLB. For decane, the minimum y value and the minimum size of emulsion droplets are observed in the region of HLB 9 and for sunflower oil around 11, which corresponds to the required HLB values. Apparently, one of the reasons leading to an increase in emulsion stability when reaching HLBtp is the increase of emulsion dispersity under conditions of the maximum decrease in interfacial energy. 

A 3D liquid spraying is modeled by introducing 20 spatial droplet streams into the computational domain, as shown in Figure 10.5. In turn, each droplet stream is represented by 10 injections of different droplet diameters minimum and maximum diameters are 10.0 and 138.0 pm, whereas the intermediate droplet sizes are calculated by applying Rosin-Rammler distribution function with 70.5 pm of droplet average size as given by Equation 10.37. 

When measuring the droplet size manually, the diameter eomes out direetly. The automated proeedure will attempt to ealculate the diameter from the droplet outline resulting from the thresholding. If, for some reason, the droplet is distorted and has an ellipsoidal shape, the return value might be the maximum, the minimum, or an average value, aeeording to the set preferences. It may instead prove useful to measure the area within die outline and calculate the diameter on the basis of this, fri any event, it is crucial to be aware of the criteria on which the program founds its return values. 

Developmental goals considered to be necessary for acceptable performance include a turndown ratio of 3 1 or better, minimum burner-tip life of 2000 h, air preheating of less than 150°C (300°F), maximum droplet size of 300 rm, and carbon conversion efficiencies of greater than 99%. Small-scale tests suggest that these coals are achievable, but what is yet required is long-term demonstration in large electric-utility-size boilers in the 100-500 MW range. 

Experiments on atomization of various pasty materials showed that 100 m/s is the minimum amplitude velocity required for the narrow droplet size distribution. Based on assumption 3, the maximum (i.e., initial) velocity of liquid droplets is thus equal to 100 m/s. Furthermore, the spatial variation of droplet velocity will be the same as for the amplitude velocity of shock wave shown in Figure 10.3 and defined by the following equation ... 

Emulsifier Type and Concentration For a fixed concentration of oil, water, and emulsifier, there is a maximum interfacial area that can be completely covered by an emulsifier. As homogenization proceeds, the size of the droplets decreases and the interfacial area increases. Once the emulsion interfacial area increases above a certain level, there may be insufficient emulsifier present to completely cover the surface of any newly formed droplets. This will not only increase the energy required for subsequent droplet dismption but also increase the probability for droplet coalescence. The minimum size of stable droplets that can be produced during homogenization is governed by the type and concentration of emulsifier present ... 

Figure 25.14 shows the variation of droplet diameter with the diameter of the gas flow hole at the minimum and maximum pressures. This plot defines the attainable range of droplet diameters corresponding to a given gas flow hole size. It can be used as a guide in selecting dimensions for a particular application. 

The rubber droplets must be at least as large as the crack tip radius. This puts the minimum size at several hundred angstroms, and a maximum size at about 3000 to 5000 A. A size greater than 400 A is required for cavitation. 

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