Sphere area/volume

Sphericity. Sphericity, /, is a shape factor defined as the ratio of the surface area of a sphere the volume of which is equal to that of the particle, divided by the actual surface area of the particle. 

E] Gas absorption aud desorption from water aud organics plus vaporization of pure liquids for Raschig riugs, saddles, spheres, aud rods, dp = nominal pacldug size, Cp = dry pacldug surface area/volume, = wetted pacldug surface area/volume. Equations are dimensionally consistent, so any set of consistent units can be used. <3 = surface tension, dynes/cm. 

To be specific, we will consider a spherical cell of radius r into which an electrogenic influx of chloride ions occurs by active transport, /a"c. The amount of charge transported in time t across the surface of the sphere (area of 4jrr2) is /a"a 4jrr2/. This active uptake of CF increases the internal concentration of negative charge by the amount moved in divided by the cellular volume, or 4nr2t/ 4nr> / 3), which is 3/atF/r. Let us suppose that has a typical value of 10 nmol m-2 s-1 and that the cell has a radius of 30 pm. In 1 second the concentration of CF actively transported in is... 

State 2. //mixing = ffpoiymer/Boivent (2 Sphere area L - interaction volume) + poiymer/poiymer (interaction Volume)... 

Molecular globularity is defined as with surface area of a sphere of volume V, where S and Vare the molecular surface and volume described above, respectively. Globularity is 1.0 for perfect spherical molecules. It assumes values greater than 1.0 for real spheroidal molecules. Globularity is also related to molecular flexibility. 

Table I. Silica spheres. Pore volume and average pore size according to manufactures, surface area BET, and bulk density...

CN - coordination number Nf- average number of faces of the VDPs N t, - average number of non-bonding contacts per one U-O bond PVdp -volume of the VD polyhedron Svdp - total area of faces of the VDP Rsd- radius of the sphere with volume equal to that of the VDP Da -vector that originates in the U atom and ends in the centroid of the VD polyhedron G3-the second moment of inertia, which describes deviation of the VD polyhedron from ideal sphere A - difference between the shortest and the longest bonds in the coordination polyhedron p - total number of faces. Standard deviations are given in parentheses. 

Volume of solution or mixture, also particles, column, and porous medium London attractive energy between two molecules or particles Coarse particle volume Fine particle volume Carrier liquid volume London attractive energy per unit area between two infinite flat plates London attractive energy between two identical spheres Elution volume, Eq. (4.7.3)... 

Particle suspensions must be fairly dilute to avoid problems of coincident passage of several particles through the aperture. The volume sampled is set by electronic probes in the mercury column, which start and stop switches as the mercury passes. The instrument used for this work had settings for sample volumes of 50 /xL, 500 /xL, and 2,000 /xL, and was operated with four apertures, 30 /xm, 70 /xm, 140 /xm, and 280 /xm. The Coulter Counter was calibrated with polystyrene latex (PSL) spheres. A computer program was used to convert channel counts and calibration information to particle diameters, surface areas, and volumes after editing spurious data from the paper tapes. Particles were assumed to be solid spheres, since output from the Coulter Counter for sludge is that for spheres of volume equivalent to the randomly shaped particles in the suspension. 

What are the virtues of these emerging photoelectrode materials The first is related to their enormous surface area. Consider that the 3D structure is built up of close-packed spheres of radius, r. Then ignoring the void space, the specific area. As (area/volume) is given by 3/r [205]. For r = 10 nm, Ag is on the order of 10 cm , and for a 1 cm film of 1 pm thickness, this value corresponds to an internal sxtrface area of 100 cm (i.e. a surface roughness factor of 100). Clearly, this becomes important if we want the electrolyte redox species to be adsorbed on the electrode surface (see following). Alternatively, a large amount of sensitization dye can be adsorbed onto the support semiconductor although this dye sensitization approach is not considered... 

The shape of particles can have important effects e.g. on the specific surface. The concept of the equivalent here may be extended by shape ctors to take account of the real sur ce or volume riien compared with that of the equivalent sphere. Sur ce area is proportional to yp, i.e. sur ce area =fiP (for a sphere ) and volume is proportional to x, i.e., volume = kP, (for a sphere tix /6). Hence/ is a sur ce ctor or coefficient and is a volume fector or coefficient. Tlie coefficients / and k are fimctions of the geometrical shape and the relative proportions of the particle their values depend on the equivalent sphere diameter used. Sphericity is defined as ... 

Figure 5.5 The area (volume) of adjacent permeable circles (spheres) of radius b and the corresponding attached excluded circles of radius 2b (a). The area of circles of a hard core radius b and soft shell d, their corresponding...

Sphere - Weights, Volumes, Areas, Pressures Loads... 

Volume of circumscribed parallelepiped, ellipsoid, and sphere Area of circumscribed ellipsoid Symmetry index... 

The effect of shape of non-spherical particles on their drag coefficient has proved difficult to define. This is probably due to the difficulty in describing particle shape for irregular particles. Engineers and scientist often require a single number to describe the shape of a particle. One simple approach is to describe the shape of a particle in terms of its sphericity, the ratio of the surface area of a sphere of volume equal to that of the particle to the surface area of the particle. For example, a cube of side one unit has a volume of 1 (cubic units) and a surface area of 6 (square units). A sphere of the same volume has a diameter, Xp of 1.24 units. The surface area of a sphere of diameter 1.24 units is 4.836 units. The sphericity of a cube is therefore 0.806 (= 4.836/6). 

The interactions of an ice particle of linear dimension a with radiation of wavelength A are determined by the complex index of refraction of ice, m(A), and the size parameter x(a,A) = 27ra/A. For atmospheric ice particles a is usually defined as the radius of the equivalent area (volume) sphere for computations... 

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