Volume Equivalent Diameter

Equation (1) points to a number of important particle properties. Clearly the particle diameter, by any definition, plays a role in the behavior of the particle. Two other particle properties, density and shape, are of significance. The shape becomes important if particles deviate significantly from sphericity. The majority of pharmaceutical aerosol particles exhibit a high level of rotational symmetry and consequently do not deviate substantially from spherical behavior. The notable exception is that of elongated particles, fibers, or needles, which exhibit shape factors, kp, substantially greater than 1. Density will frequently deviate from unity and must be considered in comparing aerodynamic and equivalent volume diameters. 

Figure 1.2. Schematic illustration of multidimensions of a particle and its equivalent volume diameter, surface diameter, and sieve diameter.

Equivalent volume diameter (pm) Mass percentage undersize ... 

Electrical sensing zone technique commonly used to determine equivalent volume diameter, required in Eq. (19), might be problematic. The error associated with this technique is contributed by the breakup of aggregates and inclusion of pores in volume measurement. With this technique, an aggregate will have to be suspended in a liquid. The challenge is to preserve the structure of aggregates. Hence the first method is preferred to obtain the mass fractal dimension of aggregates in situ. 

An advantage of equivalent diameters is that they provide a unique characterization of particle size for the given method of measurement. In addition, the diameter gives information about the particle properties. For example, the equivalent surface diameter would give information about the surface area of the particle and the equivalent volume diameter would give information about the volume. Thus, if the density of the particles is known, the mass and properties important to pharmaceutical applications can be calculated. The numerical value for equivalent diameters derived from different geometric properties will only be identical in the case of perfectly spherical particles, and if the particle irregularity increases so will the differences between the different equivalent diameters. 

Hence, Equation (10) yields the equivalent volume diameter of ... 

The newer la.ser diffraction instrument allows measurement for particle sizes ranging from 0.1 pm to 8 mm (7). Most of the laser diffraction instruments in the pharmaceutical industry use the optical model based on several theories, either Fraunhofer, (near-) forward light scattering, low-angle laser light scattering, Mie, Fraunhofer approximation, or anomalous diffraction. These laser diffraction instruments assume that the particles measured are spherical. Hence, the instrument will convert the scattering pattern into an equivalent volume diameter. A typical laser diffraction instrument consists of a laser, a sample presentation system, and a series of detectors. 

Figure 30 shows a simple model of a typical laser diffraction instrument where the diffraction pattern of light scattered at various angles from the sample particles that pass through the He-Ne laser beam is measured by different detectors and recorded as numerical values relating to the scattering pattern. These numerical values are then converted to the particle size distribution in terms of the equivalent volume diameter using a mathematical model from the instrument s software. 

Since the reported diameter is an equivalent volume diameter, proper consideration must be taken when comparing the results with other particle size analysis methods. For instance, the equivalent volume diameter reported for any non-spherical shaped particle will generally be higher than the particle size reported by sieve analysis, as the equivalent volume diameter is based on the volume of a perfect sphere. This theory becomes apparent if one compares the equivalent volume diameter with the sieve diameter of a square that has dimensions of 2(X)pm by 200 pm by 200 pm and that passes through a U.S. ASTM sieve 70 (212 pm) and is retained on a U.S, ASTM sieve 80 (180 pm). In this case, the sieve diameter reported will be 212 pm but the... 

SPHERICITY is the ratio of the surface area of a sphere having the same volume as the particle, to the actual particle surface area the reciprocal is known as the coefficient of rugosity or angularity. It can be shown that sphericity is also equal to the ratio of the surface-volume diameter to the equivalent volume diameter this makes sphericity a useful conversion factor between... 

In the above, <7C is the equivalent volume diameter, i.e. the diameter of a sphere having the same volume as an irregular particle. As Hinds (1982) points out The equivalent volume diameter can be thought of as the diameter of the sphere that would result if an irregular particle were melted to form a droplet <7C is calculated from microscopic measurement of the actual particles being considered, while x is the dynamic shape factor which is included to allow for the effects of shape on terminal velocity. For example, talc dust is characterized by a dynamic shape factor (/ ) of 1.88, sand particles by 1.57, etc. Spheres have a dynamic shape factor of 1.0 while cubes have a dynamic shape factor of 1.08. 

The particle shape factor (%) is a dimensionless constant used to relate drag force on an irregular particle moving in air to the particle s equivalent volume diameter (ICRP, 1994). The shape factor and the mass density are used to determine the particle s thermodynamic diameter in the model but in practice, the thermodynamic diameter can be measured for small particles. The shape factor is assumed to have a triangular distribution ranging from 1.1 to 1.9 with a mode of 1.5 (ICRP, 1994). The ICRP 66 default for the X is 1-5. 

Equivalent volume diameter The diameter of a sphere having the same volume as the species under consideration... 

Fundamentals productivity is limited by the gas flow. Ergun equation for pressure drop through a packed bed of particles of equivalent volume diameter D, and sphericity = rp. 

The aerodynamic behaviour of aerosol particles depends on their diameter, density and shape. To compare the behavioiu of particles that have different properties with each other, the aerodynamic diameter (Da) has been introduced, which standardises for particle shape and density. By definition the aerodynamic diameter of a particle is the diameter of a sphere with unit density having the same terminal settling velocity as the particle in consideratimi. Only for aqueous droplets with a spherical shape and unit density the aerodynamic diameter equals the geometric diameter. For non-spherical particles, the aerodynamic diameter can be expressed in terms of equivalent volume diameter (De), particle shape factor (x) and particle density (p) (see definitions) Da = De.(p/x)° ... 

The equivalent volume diameter (Dg) of an irregularly shaped particle is the diameter of a sphere having the same volume as the particle in consideration. The equivalent volume diameter is used to describe the dynamic particle behaviour of non-spherical particles in combination with the shape factor (see definition). 

Define the following equivalent sphere diameters equivalent volume diameter, equivalent surface diameter, equivalent surface-volume diameter. Determine the values of each one for a cuboid of dimensions 2 mm x 3 mm x 6 mm. 

Figure 2.3 Drag coefficient Cd versus Reynolds number Rep for particles of sphericity (p ranging from 0.125 to 1.0. (Note Rcp and Cd are based on the equivalent volume diameter)...

A particle of equivalent volume diameter 0.5 mm, density 2000 kg/m and sphericity 0.6 falls freely under gravity in a fluid of density 1.6kg/m3 and viscosity 2 x 10 3pas. Estimate the terminal velocity reached by the particle. 

Where dbvs is the equivalent volume diameter of a bubble at the surface. 

If the particle size distributions are characterized by the average diameters at the cumulative masses of 10, 50, and 90%, the data scattering measured by different techniques can be represented by the diameter ratios at the cumulative masses of 10, 50, and 90%, or DRio, DR50, and DR90. Since the particle diameter measured by the electrical sensing zone technique is to be the equivalent volume diameter and is independent of the particle shape, its particle diameter is defined to be one. The particle diameters measured by other techniques are then ratioed with this diameter. The experimental results of DRjo, DR50, and DR90 are summarized in Table 5. It can be seen that the results of particle analysis from different techniques can be quite different. 

Wall material is bright mild steel. See Table 2 for pipeline details. Equivalent volume diameter. Median particle diameter measured by sieving. ... 

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