Surface/volume average diameter

For a bed containing spheres of different sizes, the definition for Dg, eqn (3.6), leads to the same form as the monosize sphere expression, eqn (3.7), if the surface volume average diameter dp is used in place of dp. 

This map subdivides fluidization quality into four broad categories, Groups A, B, C and D, according to the basic powder properties particle diameter dp (or the surface volume average diameter, eqn (3.8), in eases of significant size distribution) and particle density pp. 

Other possible geometrical diameters can be used to determine the mean particle diameter of a polydisperse system. Examples are the surface average, ds, and volume average diameters, dv where ds is defined as the diameter of a sphere having the same surface area as the particle and dw is the diameter of a sphere having the same volume as the particle. These are given by ... 

The support has an internal pore structure (i.e., pore volume and pore size distribution) that facilitates transport of reactants (products) into (out of) the particle. Low pore volume and small pores limit the accessibility of the internal surface because of increased diffusion resistance. Diffusion of products outward also is decreased, and this may cause product degradation or catalyst fouling within the catalyst particle. As discussed in Sec. 7, the effectiveness factor Tj is the ratio of the actual reaction rate to the rate in the absence of any diffusion limitations. When the rate of reaction greatly exceeds the rate of diffusion, the effectiveness factor is low and the internal volume of the catalyst pellet is not utilized for catalysis. In such cases, expensive catalytic metals are best placed as a shell around the pellet. The rate of diffusion may be increased by optimizing the pore structure to provide larger pores (or macropores) that transport the reactants (products) into (out of) the pellet and smaller pores (micropores) that provide the internal surface area needed for effective catalyst dispersion. Micropores typically have volume-averaged diameters of 50 to... 

The values of these averages can be very different. Typically, the higher the values of n and m are, the larger is the value of the average size. Which one you should use simply depends on the application. When it relates to the surface area (think of emulsion stability, amormt of surfactant needed, energy required to make the emulsion, etc.) then the Sauter diameter is probably the best one. If the application is related to the volume (e.g., amount of oil in the product, material dissolved in the particles), the volume average diameter may be more suitable. 

Zn(II) was employed as a print molecule because of its strong interaction with the bifunctional monomer, DDDPA. Divinylbenzene, L-glutamic acid dioleylester ribitol and toluene were used as matrix-forming monomer, emulsion stabiliser and diluent, respectively. After polymerisation, the print molecules were removed from the resin, upon which selective recognition sites were formed. The schematic illustration of surface template polymerisation with DDDPA is shown in Scheme 9.8. The Zn(II)-imprinted resins were ground into particles, whose volume-averaged diameters were ca. 40 pm. The yield was ca. 80%. 

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. 

For spherical particles the average diameter of the pores, defined as four times the pore volume divided by the surface area, can be shown to be... 

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. 

Equation (li ) can be used to calculate uncorrected diameter averages. For the number, surface, volume, specific surface, weight and turbidity diameter averages (their definitions have been stated elsewhere (11,12), the following relations can be derived ... 

ERYTHROCYTES. Erythrocytes are biconcave diskshaped, blood cells (with pits or depressions in the center on both sides), the primary function of which is to transport hemoglobin, the oxygen-carrying protein. The biconcave shape of the erythrocyte provides a large surface volume ratio and thereby facilitates exchange of oxygen. The average diameter of erythrocytes is 7.5 pm, and thickness at the rim is 2.6 pm and in the center about 0.8 pm. The normal concentration of erythrocytes in blood is approximately 3.9-5.5 million cells per pL in women and 4.1-6 million cells per pL in men. The total life span of erythrocytes in blood is 120 days. 

Samples, assuming they do not need to be ground, are at a minimum sieved through a number 10 sieve that has openings of 2 mm. This is done because the upper limit of sand, for consideration as part of soil, is 2 mm in average diameter. Components larger than this have a relatively low surface-to-volume ratio and very little sorptive capacity. Sieved samples can be further mixed and then divided into subsamples. 

The physical properties of silica are determined by its specific surface area, pore volume, average pore diameter, porosity, and the particle diameter and shape [8]. The latter two are responsible for the efficiency, the physical stability and the pressure drop of the packed columns and do not contribute to retention and selectivity. 

To explore this further, we present some additional data about the 400 spheres in Table 1.5, namely, that the sample possesses a total surface area of 5.85 102 m2 or 5.85 102/ 400 = 1.46 fj.m2 per particle. Likewise, the total volume of the 400 spheres is 76 m or 0.19 m3 per particle. We see in Chapter 9 how the surface areas of actual powdered samples are measured and the volume is readily available from mass when the density of the bulk material is known. Now let us calculate the average diameter of an equivalent sphere from these data. 

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