Sauter mean diameter calculated

Recently, Knoll and Sojka[263] developed a semi-empirical correlation for the calculation of the Sauter mean diameter of the droplets after primary breakup of flat-sheets in twin-fluid atomization of high-viscosity liquids ... 

Fig. 9.3 Sauter mean diameter < 32 calculated from drop size measurements at single nozzles of liquid systems (a) toluene (dispersed phase d) water (continuous phase c) and (b) butanol d) water (c), is dependent on the mean velocity Vjv of the dispersed phase in the nozzle. (From Ref. 5.)... 

The mass transfer coefficient kL of oxygen transfer in fermenters is a function of Sauter mean diameter D32, diffusivity DAB, and density p, viscosity pc of continuous phase (liquid phase). Sauter-mean diameter D32 can be calculated from measured drop-size distribution from the following relationship,... 

The interfacial area per unit volume can be calculated from the Sauter-mean diameter D32 and the volume fraction of gas-phase H, as follows ... 

The Sauter-mean diameter, a surface-volume mean, can be calculated by measuring drop sizes directly from photographs of a dispersion according to Eq. (9.21). 

Figure 5.4 Comparison between Sauter mean diameters measured and calculated by Eq. (5.6). A A before impingement after impingement dA water-air system A water-C02...

According to Assumption (4) above, the specific interface area calculated from the Sauter mean diameter of spray droplets, a, is kept constant. Thus, the integral amount of S02 absorbed within the residence time of the gas and droplets in the effective volume of the reactor, t, can be obtained as... 

This form is particularly appropriate when the gas is of low solubility in the liquid and "liquid film resistance" controls the rate of transfer. More complex forms which use an overall mass transfer coefficient which includes the effects of gas film resistance must be used otherwise. Also, if chemical reactions are involved, they are not rate limiting. The approach given here, however, illustrates the required calculation steps. The nature of the mixing or agitation primarily affects the interfacial area per unit volume, a. The liquid phase mass transfer coefficient, kL, is primarily a function of the physical properties of the fluid. The interfacial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dSM, which is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraction of the total fluid volume (gas plus liquid) which is occupied by gas bubbles. 

The average Sauter mean diameter of droplets is calculated from... 

A dished head tank of diameter DT = 1.22 m is filled with water to an operating level equal to the tank diameter. The tank is equipped with four equally spaced baffles whose width is one-tenth of the tank diameter. The tank is agitated with a 0.36-m-diameter, flat, six-blade disk turbine. The impeller rotational speed is 2.8 rev/s. The sparging air enters through an open-ended tube situated below the impeller, and its volumetric flow, Q, is 0.00416 m3/s at 25°C. Calculate the following the impeller power requirement, Pm gas holdup (the volume fraction of gas phase in the dispersion), H and Sauter mean diameter of the dispersed bubbles. The viscosity of the water, //, is 8.904 x 10 4 kg/(m-s), the density, p, is 997.08 kg/m3, and, therefore, the kinematic viscosity, v, is 8.93 x 10 7 m2/s. The interfacial tension for the air-water interface, a, is 0.07197 kg/s2. Assume that the air bubbles are in the range of 2-5 mm diameter. 

Calculate the Sauter mean diameter, Di2- The Sauter mean diameter is the diameter of a hypothetical droplet in which the ratio of droplet volume to droplet surface equals that of the entire dispersion. Use the formula... 

Example 2 The Sauter mean diameter and the volume weighted particle size and distribution given in Table 21-1 can be calculated by using FDIS-ISO 9276-2, Representation of Results of Particle Size Analysis—Part 2 Calculation of Average Particle Sizes/Diameters and Moments from Particle Size Distributions via Table 21-2. 

TABLE 21 -2 Table for Calculation of Sauter Mean Diameter and Volume Weighted Particle Size... 

The coupled equations had been solved by numerical computation using an implicit finite difference technique [34]. While solving the above equations, the emulsion globule size J32 (sauter mean diameter) was calculated by using the following correlation [35] ... 

A typical example for a stirred two-phase system with a volume fraction of 30 vol.% organic phase dispersed in water, an interfacial tension of 25 mN m-1 and a specific power input of 0.5 W L 1 shows a droplet diameter in the range of 250 pun and a specific interface of about 10 m2 L 1. These dimensions maybe estimated from simple empirical correlations between the Sauter mean diameter of the dispersed phase (zf2.3) and the characteristic Weber number (We). In case of turbulent mixing the following correlation is proposed in the literature for calculation of the mean diameter of dispersed droplets [24]... 

Equation 5.27 has the disadvantage that it ignores the viscous forces inside the polymerizing droplet. Calabrese et al. [41 ] proposed the following relation for the calculation of the Sauter mean diameter for a viscous dispersion system ... 

There are multiple spray measurements used to quantify an injectors spray quality. Some of these measurements include DIO (arithmetic mean), D32 (Sauter mean diameter), D31 (evaporative mean diameter), DvO.9, and droplet distribution curve. Figure 15.9 provides a description and equation used to calculate SMD, DIO, and D31. Figure 15.10 shows a typical droplet distribution curve with an overlay to show the DvO.9 calculation. The DvO.9 value represents the point where... 

To provide clarity when calculating Sauter mean diameter (D32), an example has been provided below. The SMD measurement represents a one number descriptor used to compare different sprays and is considered industry standard for comparing spray quality. Table 15.1 provides a truncated sampling of a hypothetical spray. For this example, whole numbers are used to signify the number of droplets counted for a given diameter measurement. This data can be used to calculate the SMD for the example outlined below. Equations 15.2-15.4 show an example of how to calculate SMD based on the data provided in Table 15.1. 

The experimental results confirmed the expectations based on the calculations. Figure 4 shows the dq>endence of the sucked-in dispersed phase on the flow rate of the continuous phase for the old and new geometries, respectively. It can be seen that the suction of the dispersed phase is much hi er with the new geometry, so no extra pump is needed to achieve the desired phase ratio of about 3 1 (continuous dispersed phase). The drop size distribution was about the same for both devices. Using the following conditions a mean diameter of around 1.5 pm and a Sauter mean diameter of around 2.5 pm could be obtained continuous phase dispersed phase ... 

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