Mean droplet diameter volume

Hollow Sprays. Most atomizers that impart swid to the Hquid tend to produce a cone-shaped hoUow spray. Although swid atomizers can produce varying degrees of hoUowness in the spray pattern, they aU seem to exhibit similar spray dynamic features. For example, detailed measurements made with simplex, duplex, dual-orifice, and pure airblast atomizers show similar dynamic stmctures in radial distributions of mean droplet diameter, velocity, and Hquid volume flux. Extensive studies have been made (30,31) on the spray dynamics associated with pressure swid atomizers. Based on these studies, some common features were observed. Test results obtained from a pressure swid atomizer spray could be used to iUustrate typical dynamic stmctures in hoUow sprays. The measurements were made using a phase Doppler spray analyzer. 

In many applications, a mean droplet size is a factor of foremost concern. Mean droplet size can be taken as a measure of the quality of an atomization process. It is also convenient to use only mean droplet size in calculations involving discrete droplets such as multiphase flow and mass transfer processes. Various definitions of mean droplet size have been employed in different applications, as summarized in Table 4.1. The concept and notation of mean droplet diameter have been generalized and standardized by Mugele and Evans.[423] The arithmetic, surface, and volume mean droplet diameter (D10, D2o, and D30) are some most common mean droplet diameters ... 

Whereas few actual values of n for sprays from various fuel injectors are reported, it is usually possible to obtain a fairly reliable estimate of x. This is so because x is uniquely related to various mean droplet diameters solely in terms of n, and data for Sauter mean diameter are rather frequently reported. Sauter mean diameter (SMD) is that diameter representative of the surface area per unit volume which is characteristic of the actual spray. 

Figure D3.4.7 Change in cumulative particle size distribution of a 20% (w/v) oil-in-water emulsion stabilized by 2% (w/v) Tween 20 at the lower port (A) and upper port (B). (C) Change in mean droplet diameter and volume fraction of the emulsions as a function of time.

In (5) D00 is the median diameter and a is the standard deviation of the distribution. By fitting the experimental R-values, the parameters D0 0 and a can be determined and hence the size distribution of the droplets in the emulsion can be obtained. For microbiological safety aspects Dj 3 is more important. D3>3 is the volume weighted mean droplet diameter and a is the standard deviation of the logarithm of the droplet diameter. The parameter D3 3 is related to the parameter D00 according to ... 

Figure 6.21 The influence of emulsifier concentration on the relative viscosity of sorbitan mono-oleate stabilised W/O emulsions in paraffin. The emulsions had dispersed phase volume fractions in the range 0.37 to 0.68 and mean droplet diameters, am, as plotted along the x-axis. From data in Sherman [215].

Two studies have been concerned with measurement of the interfacial area obtained by agitation of liquid-liquid systems. Each of these investigations relied on the use of a photoelectric probe which measured the light transmission of the two-phase dispersion. Vermeulen and co-workers (V2) made measurements in two geometrically similar, baffled vessels of 10- and 20-in. diameter. They used a very simple four-blade paddle-like stirrer, with a tank-to-impeller diameter ratio of about 1.5, and a 0.25 blade-width/impeller-diameter ratio. The impeller was located midway between the top and bottom of the vessel, which had a cover and was run full. Impeller speeds varied from about 100 to 400 r.p.m. A wide variety of liquids was employed. Volume fractions of dispersed phase varied from 10% to 40%. The mean droplet diameters observed ranged from 0.003 to 0.1 cm. The results were correlated with a mean deviation of about 20% by an empirical equation relating the specific interfacial area near the impeller to several system and operating variables as follows ... 

We have compared these theoretical predictions of the low-frequency modulus to experimental measurements on compressed emulsions and concentrated dispersions of microgels [121]. The emulsions were dispersions of silicone oil (viscosity 0.5 Pas) in water stabilized by the nonionic surfactant Triton X-100 [102, 121]. The excess surfactant was carefully eliminated by successive washing operations to avoid attractive depletion interactions. The size distribution of the droplets was moderately polydisperse with a mean droplet diameter of 2pin. The interfacial energy F between oil and water was 4mJ/m. The contact modulus for these emulsions was thus F 35 kPa. The volume fraction of the dispersed phase was easily obtained from weight measurements before and after water evaporation. Concentrated emulsions have a plateau modulus that extends to the lowest accessible frequencies, from which the low-frequency modulus Gq was obtained. Figure 11 shows the variations of Gq/E"" with 0 measured for the emulsions against the values calculated in the... 

The third factor that affects emulsion rheology is the droplet size distribution. This is particularly the case at high-volume fractions. When ( ) > 0.6, T) is inversely proportional to the reciprocal of the mean droplet diameter (18). The above equations do not show any dependence on droplet size and an account should be made for this effect by considering the average distance between the droplets in an emulsion. At high shear rate, the droplets... 

A gas having a density of 13 kg/m and a d5Tiamic viscosity of 0.006 cp flows through a pipe of 30 cm internal diameter at 6.7 m/s. Entrained in this gas is a liquid hydrocarbon having a density of 930 kg/m . A two-phase flow map indicates mist-annular flow. The interfacial tension (or IFT ) = 20 dynes/cm. Compute the Sauter-mean and volume-mean droplet diameters. 

An important measure of the droplet size distribution in spray appHca-tions is the Sauter mean diameter 32 = (d )/(d ). This measure is so important because during evaporative drying the mass transfer happens at the interface of the droplets and the surrounding air. To enhance the evaporation of a population of droplets, one has to maximize the active surface areas and minimize the internal volumes. The DSMC simulations showed that the Sauter mean diameter is a very nontrivial function of the axial and radial position in the spray. Figure 16 shows that at a given axial position, with increasing distance from the central axis the mean droplet diameter first increases, then decreases, and finally increases again. Exactly, the same trends... 

Thep and q denote the integral exponents of D in the respective summations, and thereby expHcitiy define the diameter that is being used. and are the number and representative diameter of sampled drops in each size class i For example, the arithmetic mean diameter, is a simple average based on the diameters of all the individual droplets in the spray sample. The volume mean diameter, D q, is the diameter of a droplet whose volume, if multiphed by the total number of droplets, equals the total volume of the sample. The Sauter mean diameter, is the diameter of a droplet whose ratio of volume-to-surface area is equal to that of the entire sample. This diameter is frequendy used because it permits quick estimation of the total Hquid surface area available for a particular industrial process or combustion system. Typical values of pressure swid atomizers range from 50 to 100 p.m. 

In all these tasks, the achievable (as narrow as possible) droplet size distribution represents the most important target quantity. It is often described merely by the mean droplet size, the so-called Sauter mean diameter J32 (Ref. 19), which is defined as the sum of all droplet volumes divided by their surfaces. Mechanisms of droplet formation are ... 

Volume Mean Diameter The diameter of a droplet whose volume, if multiplied by the total number of droplets, will equal the total volume of the sample. 

In continuous mechanical emulsification systems based on turbulent flow, the power density Py viz. power dissipated per unit volume of the emulsion) and residence time, L, in the dispersing zone have been found to influence the result of emulsification as measured by the mean droplet size 0(3 2 which is called the Sauter diameter . This dependency is in most cases described by the following expression ... 

The above mean is also referred to as the mean length diameter, dy, because it represents the sum of the length of the droplets divided by the total number of droplets. It is also possible to express the mean droplet size in a number of other ways (Table 2). Each of these mean sizes has dimensions of length (meters), but stresses a different physical aspect of the distribution, e.g., the average length, surface area, or volume. For example, the volume-surface mean diameter is related to the surface area of droplets exposed to the continuous phase per unit volume of emulsion, As ... 

The results of Figure 13 suggest that as the droplet size increases, the emulsion retention increases. The large droplets have a higher capture probability and fill up more of the pores faster, a result that explains why they elute later than the smaller droplets. Emulsions with small droplet size diameters elute with essentially the inlet size distributions. Two factors control permeability reduction the total volume of droplets retained and the effectiveness of these droplets in restricting fiow. For a given porous medium, a critical mean droplet size of the emulsion controls permeability reduction. Below this value, retention of oil in porous media is dominant, and above the critical mean droplet size, their obstruction ability is pronounced. This situation explains the trends shown in Figure 13 for the effect of droplet size on permeability reduction. These conclusions are valid for stable, very dilute OAV emulsions and are based on a few experiments. 

Another important parameter is the mean surface-to-volume droplet diameter d, which affects the velocity and the absorption behavior of the liquid phase. Among the available correlations the most widely used is that of Nukiyama and Tanasawa (N13),... 

Industrial liquid-liquid extraction most often involves processing two immiscible or partially miscible liquids in the form of a dispersion of droplets of one liquid (the dispersed phase) suspended in the other liquid (the continuous phase). The dispersion will exhibit a distribution of drop diameters d, often characterized by the volume to surface area average diameter or Sauter mean drop diameter. The term emulsion generally refers to a liquid-liquid dispersion with a dispersed-phase mean drop diameter on the order of 1 pm or less. 

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]... 

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