Mass mean diameter

In the present case, which is concerned with power consumption per unit mass, the mass mean diameter is probably of the greatest relevance. For the purposes of calculation a mean value of 4.0 mm will be used, which agrees with the value obtained by Bond s method. 

The mass mean diameter of the crushed dolomite may be calculated thus ... 

Mass market soap manufacture, 22 723 Mass Mean Diameter (MMD), 23.T87 Mass of catalyst, in photocatalysis, 19 77-78 Mass particle diameter, 78 134 Mass polymerization, 70 206 ABS, 7 422... 

The mean abscissa in Figure 1.5 is defined as the volume mean diameter dv, or as the mass mean diameter, where ... 

In practice, when one measures the size distributions of aerosols using techniques discussed in Chapter 11, one normally measures one parameter, for example, number or mass, as a function of size. For example, impactor data usually give the mass of particles by size interval. From such data, one can obtain the geometric mass mean diameter (which applies only to the mass distribution), and crg, which, as discussed, is the same for all types of log-normal distributions for this one sample. Given the geometric mass mean diameter (/) ,) in this case and crg, an important question is whether the other types of mean diameters (i.e., number, surface, and volume) can be determined from these data or if separate experimental measurements are required. The answer is that these other types of mean diameters can indeed be calculated for smooth spheres whose density is independent of diameter. The conversions are carried out using equations developed for fine-particle technology in 1929 by Hatch and Choate. 

Tests of the WWEP were conducted with 4 in, 8 in and 16 in diameter units at flow rates ranging from 100 to 4000 ft /min. Particle collection efficiency of these units was measured with atmospheric dust, AC fine test dust (mass mean diameter (MMD) 12 pm), artificial cotton dust (MMD = 4.0 pm) and cotton dust drawn from the processing area of a card (MMD = 3.0 pm). 

Samples of dust from each of the two dust sources were collected for testing. They were dispersed in an electrolyte and analyzed for size on a volume basis. Model card dust had a mass mean diameter of 3.6 with a geometric standard deviation of 1.6. The cotton dust released by tapping the loaded filter varied from 4.5 to 6.7 urn mass mean diameter with a geometric standard deviation of about 2. All test concentrations were in the range of 0.5 to 1.5 mg/m, which are typical of cotton mill fine dust concentration. 

Number concentrations are dominated by submicron particles, whereas the mass concentrations are strongly influenced by particle concentrations in 0.1-10 pm diameter range [13]. Similarly, the variability of the number-based measurements is strongly dominated by variability in smaller diameter ranges, whereas the variability of mass-based properties, such as PM10, are dominated by variability in the accumulation mode (usually around 500 nm of mass mean diameter) and in the coarse mode. This means the variabilities of these properties are not necessarily similar in shorter timescales, due to sensitivity of variance from very different air masses and thus aerosol types. This is demonstrated in Fig. lb, where the variance of the each size class of particle number concentrations between 3 and 1,000 nm is shown for SMEAR II station in Hyytiala, Finland. The variance has similarities to the particle number size distribution (Fig. la), but there are also significant differences, especially on smaller particles sizes. Even though in the median particle number size distribution the nucleation mode is visible only weakly, it is a major contributor to submicron particle number concentration variability. 

Particle size distributions were measured 20 nozzle diameters downstream of the nozzle exit, on the Jet centerline (Fig. 10.10). At low DBP vapor concentrations, the size distributions were unimodal with count mean diameters of 0.4 to 0.5 fjLtn and mass mean diameters of about 3 /zm. As the vapor mole fraction increased, the count mean diameter... 

The same approach could be taken for mass and the characteristic diameters of each group weighted by mt/M, the fraction of the total mass in the size group. Let the average diameter calculated in this way be the mass mean diameter [Pg.31]

The mass mean diameter will not equal the diameter of average mass. Hinds definition (Hinds, 1982) is useful ... 

The mass mean diameter is found from the equation... 

Particle size distribution. Bourne found that for a mixture of particle sizes Njs was less than that required for the largest when only particles of that size were present. Baldi et al. found that for binary mixtures, a mass mean diameter, idp), enabled Njs to be correlated with that from closely-sieved sizes and this has recently been confirmed for up to five sizes. ... 

Some materials that are otherwise quite stable can become potentially explosive as their particle size is reduced to the colloidal size range. For example, aluminium particles that are not explosive in air at particle sizes of about 1 mm can become weakly explosive at about 100 pm in size and very explosive at about 10 pm in size. The critical mass mean diameter for explosibility of pyrrhotite (Fe 2) and pyrite (FeS) has been reported to be 49-63 and 85-145 pm, respectively [48]. Similarly, particle size affects the ease of ignition of a metal particle when subjected to heat or an explosion. For example, the critical size for prompt ignition of spherical magnesium particles has been reported to be between 85 and 240 pm [49]. 

Hewitt [34] derived formulas for Mass Mean Diameter (MMD) and Number Mean Diameter (NMD) for air-assist nozzles. He claims that SMD is primarily a function of liquid density and air velocity. The effects of nozzle geometry are neglected from his study, as his study was aimed more at rotary nozzles (as explained later in Rotary Nozzles section). 

During injection, the effectiveness of the spray against elemental iodine vapor is chiefly determined by the rate at which fresh solution surface area is introduced into the containment building atmosphere. The rate of solution surface created per unit gas volume in the containment atmosphere may be estimated as (6F/VD), where F is the volume flow rate of the spray pump, V is the containment building net free volume, and D is the mass-mean diameter of the spray drops. The first-order removal coefficient by spray, A., may be taken to he = 6 T FfV D, where A g is the gas-phase mass-transfer coefficient, and T is the time of fall of the drops, which may be estimated by the ratio of the average fall height to the terminal velocity of the mass-mean drop (Reference...). 

Ohtsubo et al. have described a method to identify those parameters which determine the physical strength of PU microcapsules containing liquid insecticide (viz., fenitrothion) [45]. These microcapsules have been found to be effective in con-troUing household pests such as cockroaches. As expected, the strength of the microcapsule depends mainly on the microcapsule mass mean diameter (D), the thickness of the membrane wall (T), and particle size distribution expressed as polydispersity (e.g., D /DJ. The coefficient of variation of the particle size distribution (CV) is first determined using any suitable instrument (particle size analyzer) and method. Wall thickness T is calculated from the following equation ... 

Table 5.5 Relationship between mass mean diameter/wall thickness ratio (D/T) and PjQ. (From [45].)...

Powder X-ray di action of the gold partides dispersed on alumina support produced a very broad peak at 20 = 40.0° after subtradion of the background pattern from the alumina (see Fig. 3). Recent Debye Function Analysis (DFA) shows this pattern to be consistent with decahedra (decahedral multiply twinned particles, MTPs) of about 2.2 nm mass-mean diameter [7]. X-ray diffraction from a... 

Effect of Solids Particle Size and Distribution. Solids particles encountered in industrial applications usually have a distribution of sizes. Larger particles settle faster than smaller ones. Studies by Baldi et al. (1978) suggest that for a distribution of particle sizes, the appropriate particle diameter to use in the expressions above is the mass-mean diameter, (dp)43- This is calculated from size distribution data by... 

Impeller diameter (ft, m) diffusivity (ft /h, mVs) mass-mean diameter (ft, m) mean particle diameter of the ith size (ft, m) particle size or diameter (ft, or m) gravitational constant (32.17 ft/sec or 9.81 m/sec ) diffusional mass transfer coefficient rate of diffusional mass transfer impeller speed (rps) number of particles in the ith size class impeller speed for just suspended state of particles (rps) impeller power (hp, W) vessel diameter (ft, m) particle-free settling velocity (ft/s, or m/s) particle-hindered settling velocity (ft/s, or m/s) mass ratio of suspended solids to liquid time 100 (kg solid/kg liquid) X100 liquid depth in vessel (ft, m)... 

Another commonly used mean drop diameter is the mass mean diameter where d43 is the ratio of the fourth to third moments of the DSD. Since drop mass is proportional to the cube of diameter, eq. (12-3) represents a mass-weighted average. 

A pilot scale spray dryer was equipped with three different atomisers to generate droplets of different size and to see the effect of droplet size on the particle morphology. The dimensions of the spray tower were diameter 1.5 m and total height 4.7 m (Fig. 14.3). A heatable main air stream was entering the tower axially at the top. The product was collected with a product container at the bottom of the spray tower. A cyclone was applied to separate fines. Inlet temperature (Tax) and outiet temperature (Tout) were recorded appropriately. The atomisers and atomiser operation were chosen in order to obtain droplets with approximately 130, 50 and 20 pm mass mean diameter. Experiments were conducted with a feed concentration of 15 % (wt-%) mannitol in purified water of 20 and 70 °C with a feed rate of 10 L/h [31]. 

The most confusing aspect of moment distributions (also called weighted distributions) is the mean value, the mass mean diameter (for the mass distribution), and the distinction between the mass mean diameter and the diameter of average mass, described in the previous section. The arithmetic mean of the number distribution, or the count mean diameter, (Eq. 4.11), can be written for grouped data with I intervals as... 

For the distribution of mass, which describes the fraction of the total mass in the various size ranges, the mass mean diameter can be written in a completely analogous fashion. Let m, be the mass of all the particles in group i (midpoint diameter dj) and let A/be the total mass for all groups. 

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