Surface area mean diameter

Similarly, the diameter of average surface area (mean surface area diameter), assuming sphericity, can be expressed as in equation 3 and is used when the surface behavior of the particle system is of importance. 

The surface-area mean (sm) diameter, not to be confused with the number-based average surface area (eq. 3), also known as the Sauter diameter, can be calculated as follows ... 

Silica is unique among nonblack fillers. Its reinforcing ability is comparable to that of carbon black, especially when mixed with a suitable coupling agent, and its transparency affords many products. Additionally, it is chemically synthesized, which means that a wide range of silica (in terms of diameter, surface area, or surface activity) may be produced depending on the reaction routes and reaction conditions. 

D [3,2] is the surface area mean diameter also known as the Sauter mean, where d = diameter of each unit. 

Surface area mean diameter, Ds Diameter of the particle whose surface area equals the mean surface area of the population... 

Table 1. BET surface area, mean pore diameter, and pore volume for the supports and catalysts after calcination. For the nitrogen sorption data, the experimental error ( 2ff) is 5 m /g for the surface areas, 0.2 nm for the mean pore diameters, and 0.02 cm /g for the pore volumes.

Because many more latex particles are being formed than monomer droplets are being lost, the average diameter of the particles in the system falls, and, despite the smaller size of the latex particles, the total surface area of all the particles continues to increase. The greater total surface area means that more emulsifler molecules can be absorbed, however, and the concentration of free emulsifier therefore shows a steady decrease. Finally, practically no polymer-free micelles remain because the system is now at a lower concentration than the critical micelle concentration. At the same time, the surface tension increases sharply. 

Commercially available silicas differ in their physical (specific surface area, mean pore diameter, pore volume, etc.) and chemical (contamination of different metals such as Al, Mg, Fe) characteristics. These metal contaminations can cause secondary retention effects (e.g., strong tailing of basic solutes). Additionally, commercial silicas differ widely in their Na content. The higher the Na content of the silica, the more alkaline its behavior in contact with water. This often acts as a catalyst for the hydrolysis of the Si -C bonds of chemically modified silica phases (see Section 12.4.3). Good silicas have an Na content of < 30 ppm. Excessively high contents of metal contaminants could easily be removed by the manufacturer by means of a thorough acid-washing... 

When there is a range of particle sizes, the use of the surface area mean diameter is recommended [10] ... 

The surface area mean diameter d can be written in a form analogous to Eq. 4.26 with group surface area s, and total surface area S. 

Since the numerator of the right-hand side of (1.81) has the dimensions of volume and the denominator those of surface area, the quantity is termed the volume-surface mean diameter of the sample. 

Most tests of the validity of the BET area have been carried out with finely divided solids, where independent evaluation of the surface area can be made from optical microscopic or, more often, electron microscopic observations of particle size, provided the size distribution is fairly narrow. As already explained (Section 1.10) the specific surface obtained in this way is related to the mean projected diameter through the equation... 

The surface mean diameter is the diameter of a sphere of the same surface area-to-volume ratio as the actual particle, which is usually not a perfect sphere. The surface mean diameter, which is sometimes referred to as the Sauter mean diameter, is the most useful particle size correlation, because hydrodynamic forces in the fluid bed act on the outside surface of the particle. The surface mean diameter is directly obtained from automated laser light diffraction devices, which are commonly used to measure particle sizes from 0.5 to 600 p.m. X-ray diffraction is commonly used to measure smaller particles (see Size TffiASURETffiNT OF PARTICLES). 

The diametei of average mass and surface area are quantities that involve the size raised to a power, sometimes referred to as the moment, which is descriptive of the fact that the surface area is proportional to the square of the diameter, and the mass or volume of a particle is proportional to the cube of its diameter. These averages represent means as calculated from the different powers of the diameter and mathematically converted back to units of diameter by taking the root of the moment. It is not unusual for a polydispersed particle population to exhibit a diameter of average mass as being one or two orders of magnitude larger than the arithmetic mean of the diameters. In any size distribution, the relation ia equation 4 always holds. 

All definitions of the mean given (eqs. 1—4) are based on the number of particles being measured. As opposed to number-based means, length, surface-area, and mass-based means have also been defined. The linear, or length mean (Lm) diameter,dj, is defined by the foUowiag equation ... 

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. 

Figure 4 is a schematic of a typical hemodialyzer. Although other geometries are stiH employed, the preferred format is a hoUow fiber hemodialyzer about 25 cm in length and 5 cm in diameter. Devices typically contain 6,000 to 10,000 capillaries, each with an inner diameter of 200 p.m and a wall thickness of around 10 p.m. Mean total membrane surface area is 1.1 0.4. Well over 60 million hemodialyzers were produced in 1992. Because of... 

The test is carried out by washing down the test enclosures in every direction by means of a standard hose nozzle of 6.3 mm inside diameter, as illustrated in Figure 11.11, held at 3 m from the enclosure with a water pressure equal lo a head of nearly 3 m of water (— 30 kN/iiF), enough to give a delivery rate of 12.5 litres/min. The duration of Ihe lest will be determined at 1 min/m" of the surface area under test, subject lo a minimum of 3 minuies. 

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