Mean diameter volume

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. 

Volume dux is the volume contained by the droplets passing through a unit cross-sectional area per unit interval of time. It can be calculated as follows, where is the volume mean diameter and n is the total number of droplets. 

Volume mean diameter e Entrainment, mass liquid/mass gas... 

Note the mean diameter used by Geldart (1973) is actually a surface volume mean diameter dsvm, based on Eq. (3). However, comparing the fluidization curves of several materials with the Geldart (1973) diagram (e.g., fly ash, pulverized coal, coarse ash, PVC powder and screened coke), Wypych (1989b) found the following ... 

Volume changes, by vitreous silica, 22 438 Volume flux, of droplets, 23 187 Volume fraction, in filtration, 11 328 Volume fraction calculation, in equivalent box model, 20 345—346 Volume mean diameter, 23 186 Volume of activation, 13 407-408... 

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

Substituting all the possible combinations of characteristics, i.e. values of p and q, info equation 1.10 gives rise to a number of differenf definitions of the mean size of a distribution. At minimum fluidization the drag force acting on a particle due to the flow of fluidizing gas over the particle is balanced by the net weight of fhe particle. The former is a function of surface area and the latter is proportional to particle volume. Consequently the surface-volume mean diameter, with p = 2 and = 3, is the most appropriate particle size to use in expressions for minimum fluidizing velocity. It is defined by equafion 1.11... 

For non-spherical particles, values of sphericity lie in the range 0 < < 1. Thus, the effective particle diameter for fluidization purposes is the product of the surface-volume mean diameter and the sphericity (Kunii and Levenspiel, 1991). The sphericity of regular-shaped particles can be deduced by geometry whilst the sphericity of irregular-shaped... 

Xi lower limit of size distribution Xu upper limit of size distribution X3 2 surface-volume mean diameter... 

Because mass and volume are directly related, with p as the constant of proportionality, th expression for the geometric volume mean diameter, Dg /, is the same as that for DgM given in Eq. (H). ... 

Abbreviations SF, solid fraction D(4,3) = volume mean diameter. 

Table I. Comparison of Total Oil, Surface Oil, Moisture and Oil Droplet Volume Mean Diameter...

Emulsion Stability. The samples were examined for emulsion stability using centrifugation and light scattering techniques (oil droplet volume mean diameter). In general, these tests were used to determine stability of the emulsions to creaming effects. The results of the analyses are presented in Table I and Figure 1. 

With the exception of beta-cyclodextrin, the data showed good correlation. The emulsion stability was highest for samples having oil droplet volume mean diameters closest to 1 micron. In contrast, the beta-cyclodextrin showed rapid emulsion de-stabilization with time, although the oil droplet volume mean diameter was 1.52 microns. 

SMD = Sauter mean diameter, surface-to-volume mean diameter of a spray T = gas or vapor temperature t = elapsed time for vaporization to proceed dt = differential change of vaporization time... 

Dvm Volume mean diameter m ft Hg Height of a gas phase transfer unit m ft... 

The volume mean diameter dy is the diameter of a hypothetical particle having the same averaged volume as that of the given sample dy is determined by... 

The sizes of a powder sample are found to follow a log-normal distribution with arithmetic mean diameter, (b) the surface mean diameter, (c) the volume mean diameter, (d) the Sautermean diameter, and (e) the DeBroucker mean diameter. 

In the case of low-dose drug products, content uniformity of the dosage form can be negatively affected if the particle size of the API is either too large or the size distribution is too broad. This could result in the need to deliver API below a certain size to ensure content uniformity. Recently, Rohr et al.4 expanded upon previous work to develop a statistical model predicting the volume mean diameter of API necessary to meet USP stage 1 criteria on content uniformity for tablets with a 99% confidence level [Eq. (8.1)] ... 

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. 

The fineness of the powder is characterized by a number (e.g., a diameter d). Particles, of course, will have different shapes so that there are different ways of defining a diameter. The technique for obtaining d, given above has been used microscopically. More conventional is the so-called surface mean diameter, which, is the diameter of a sphere that has the same surface area as the particle. The so-called single-particle volume mean diameter is possible if there are instruments that can measure the volume of an odd-shaped particle. If the shape factor is indepen-... 

Since most particles handled in engineering are multisized, a characteristic mean diameter has to be defined. The most commonly used mean diameter is the so-called surface-to-volume mean diameter defined as... 

Aerodynamic diameter of a real median size particle Diffusion coefficient Sauter mean diameter Volume mean diameter Entrainment, mass liquid/mass gas Plate or stage efficiency, fractional Power dissipation per mass Murphree plate efficiency, with entrainment, gas concentrations, fractional... 

Examples. To determine the surface-volume mean diameter from a number distribution, put t = 0,r = 2,k= 1. 

Light attenuation is a simple, widely used method for determining interfacial area, i.e. surface-volume mean diameter if droplet concentration is known but cannot be used for size distribution determination [206-208]. 

The surface volume mean diameter for a suspension of spherical particles is given by ... 

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