Volume-surface mean

This is the mean abscissa of a graph of cumulative area fraction versus size. Otherwise known as the Surface Volume Mean (or Sauter Mean)... 

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 ... 

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... 

The definition of the surface-volume mean diamefer given by equation 1.11 must be modified for use wifh dafa from a sieve analysis. By assuming that the shape and density of fhe particles are constant for all size fractions, a number distribution can be transformed fo a mass distribution (Smith, 2003) and therefore the surface-volume diameter becomes... 

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... 

Note that re-arranging the above relationship to give d/, = 6ea/a shows how a mean bubble size might be calculated from measurements of and a. A mean bubble diameter defined in this way (Volume 2, Chapter 1) is called a Sauter mean (i.e. a surface volume mean see also Section 4.3.4). 

The Sauter-mean diameter, a surface-volume mean, can be calculated by measuring drop sizes directly from photographs of a dispersion according to Eq. (9.21). 

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 ... 

Another important mean diameter in the pharmaceutical industry that weighs the effects of both the total surface area and volume is the surface-volume mean diameter. This mean diameter can be very useful when the specific surface area is desired as it is inversely related to the specific surface area. 

Example 6. Calculate the volume, surface factor and specific surface for a perfect sphere with density of l.Og/cm and surface-volume mean diameter of 100pm. 

McClements and Dungan reported, based on light scattering measurements, that the Sauter or surface-volume mean diameter of drops in a dilute emulsion of n-hexadecane in water remained constant while the number of drops decreased with time during solubilization of the hydrocarbon into a 2 wt% solution of Tween 20 (sorbitan monolaurate). Weiss et al. found similar results for the same surfactant with n-tetradecane and n-octadecane. This result, which seems surprising in... 

Use the moment equations for constant growth rate in a MSMPR crystallizer to calculate (a) the surface-volume mean size and (6) the mass average size, (c) Compare these values with the sizes where a maximum occurs in the corresponding distribution curves. 

Using 6-blade disc turbines in baffled tanks with pure liquids, i.e. coalescing systems, Calderbank measured interfacial area and hold-up and obtained an equation for the surface/volume mean bubble diameter (in SI units) ... 

Clb liquid reactant concentration (moles/m ) ds bubble diameter (surface-volume mean) (m)... 

Specific surface may be e q>ressed on a mass basis using the material density to modify the volume. The diameter of the here having the same equivalent ecific sur ce as the particle is sometimes termed the surface volume mean or the Sauter mean diameter. 

The mercury porosimetry results presented in Figure 5.6 illustrate the influence of particle size and size distribution on the size and size distribution of the porosity in green ceramic filled glass (CFG) composites consisting of 65 vol % of 0.4—1.5-)lm median particle size alumina and 35% borosilicate glass. The porosimetry results reveal that a relatively broad size distribution of pores exist within the green powder compacts and that pore size distribution and mean pore radius decreases with the substitution of fine alumina for the coarse in the CFG composites. The mean equivalent cylindrical pore radius, r, and surface-volume mean equivalent spherical particle radius, of a powder compact consisting of >l- J,m particles are proportional to one another and related by the fractional porosity, e, of the powder compact by... 

There are a great number of different mean sizes and a question arises which of those is to be chosen to represent the population. The selection is of course based on the application, namely what property is of importance and should be represented. In liquid filtration for example, it is the surface volume mean Xsv (surface arithmetic mean Xa surface) because the resistance to flow through packed beds depends on the specific surface of the particles that make up the bed (see equation 9.36). It can be shown that Xsv is equal to the mass harmonic mean Xh (see Appendix 2.2). For distributions that follow closely the log-normal equation (see section 2.5) the geometric mean Xg is equal to the median. 

Each mean can be shown to conserve two properties of the original population of particles. Eor example, the arithmetic mean of the surface distribution conserves the surface and volume of the original population. This is demonstrated in Worked Example 1.3. This mean is commonly referred to as the surface-volume mean or the Sauter mean. The arithmetic mean of the number... 

For Equation (1.8), which defines the surface-volume mean, please see Worked Example 1.3. 

Summarizing, then, the surface-volume mean may be calculated as the arithmetic mean of the surface distribution or the harmonic mean of the volume distribution. The practical significance of the equivalence of means is that it permits useful means to be calculated easily from a single size analysis. 

This is the definition of the mean which conserves surface and volume, known as the surface-volume mean, rsv-... 

We recall that the harmonic mean of the volume distribution is equivalent to the surface-volume mean of the population. 

Determine the surface-volume mean diameter and the specific surface of the powder sample. 

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